ball four

Evaluating Outfielders’ Defense Using Fieldf/x

Thu, 27 Dec 2012 22:00:00 -0500

While I’m sure that teams have already begun analyzing Fieldf/x data, I wanted to draw up a concept for evaluating outfield defense using Fieldf/x data. The two main defensive responsibilities of an outfielder are preventing runners from advancing on fly balls and converting fly balls into outs. Fieldf/x data can help us determine how well outfielders are accomplishing these objectives by looking at outfielders’ arm strength and the routes that outfielders take to balls.

In order to evaluate routes to the ball, we must first plot the fielder’s path. We must then draw a straight line from the fielder’s original spot to the location where the ball landed or was caught. This is the quickest path to the ball. Below are a couple of images that depict the fielder’s path and the straight line to the ball.

The amount that the fielder’s path deviates from this straight line will determine the fielder’s route score. This deviation can be measured by the line integral of the arc approximating the fielder’s path. In order to account for the distance from the fielder’s original position and the ball’s ultimate landing location, we must divide the line integral by the magnitude of the straight-line vector between the fielder’s original position and the ball’s ultimate landing location.

Outfielder’s Route (ORt) = ∫∫ 1 dA / √[(a₂- a₁)+(b₂- b₁)]²

The route that outfielders’ throws take could serve as a proxy for measuring how good a player is at preventing runners from advancing. A similar approach can be taken here as the one taken in evaluating routes. We can measure the deviation of each throw from a perfect throw and normalize it with the distance of the perfect throw.

In other words, we would take the line integral of the arc approximating the fielder’s throw and divide it by the magnitude of the straight-line vector from the outfielder’s position to the intended target.

Outfielder’s Arm Accuracy (OAA) = ∫∫ 1 dA / √[(a₂- a₁)+(b₂- b₁)]²

Finally, we could index the speed of the outfielders’ throws against the league average speed to get the Outfielder’s Arm Strength (OAS).

Outfielder’s Arm Strength (OAS) = Outfielder’s Throw Speed / League Average Outfielder’s Throw Speed

These three metrics should give us a more comprehensive look at outfield defense as they evaluate how well outfielders run routes towards fly balls and how accurate and strong their throws are.

2012 Cubs Preview: Starting Rotation [Part III]

Sun, 15 Apr 2012 09:20:20 -0400

Chris Volstad | Can Volstad handle left-handed hitters?

In his career, Volstad has had trouble pitching to left-handed hitters. The trouble primarily comes from Volstad’s inability to keep left-handed hitters from hitting the ball out of the park and taking walks. In 2011, he gave up 2.16 HR/9 and posted a 3.86 BB/9 against lefties. Against righties, Volstad gave up 0.42 HR/9 and posted a 1.56 BB/9. The issue is pretty obvious: if Volstad wants to be a successful starter this year, he’s going to need to find a way to get left-handed hitters out.

While we should always be careful when we’re working with small sample sizes, I looked at Volstad’s spring performances to see if there were any signs of him figuring things out against lefties. Below is a chart comparing Volstad’s career lefty-righty splits against his spring lefty-righty splits.

As we can see, managers seemed to know of Volstad’s weakness and ended up stacking their lineups with left-handed hitters. Surprisingly, Volstad had no issues with the left-handed hitters. He didn’t allow a home run or a walk in the 10 innings that he pitched against lefties. While there are a number of other factors that could be in play here - the quality of the opposing left-handed hitters, small sample size, etc. - these numbers are encouraging. Let’s hope that this change is a result of a change in Volstad’s approach rather than just luck.

The Rest | How much better is our starting pitching depth this year as opposed to last year?

It’s pretty clear that we not only have more starting pitching depth to start off this year, but also a better quality of depth than we did last year. Going into Opening Day last year, we had Casey Coleman and James Russellas our extra starters. This year we have Randy Wells, Travis Wood, Casey Coleman, and Rodrigo Lopez.

While I should technically compare the two years based on the six pitchers that I have thus far named, I includedDoug Davis, Ramon Ortiz, and Rodrigo Lopez - they were all acquired within the first two months of the season - in order to make the analysis a little more worthwhile. Below is a chart with the production of the 2011 extra pitchers followed by a chart of the ZiPS projections for the 2012 extra pitchers.

There are a few points that I would like to discuss: the age of the pitchers, innings pitched per inning, and the actual effectiveness of the two staffs.

In 2011, we only had one true extra starter, (James Russell is clearly not a true starter), below the age of 30: Casey Coleman. The weighted average age of our extra pitchers was 30.3 years. This year, we have three extra starters below the age of 30: Casey Coleman, Travis Wood, and Randy Wells. The weighted average age of our extra pitchers is 28.2 years.

Last year, the extra starters averaged 5.05 innings pitched per game started. This year, the extra starters are projected to average 5.60 innings pitched per game started. While half an inning may not seem like a lot at first sight, let’s put it into perspective. Last year, our extra starters started 49 games; if the starters, on average, could have pitched an additional half inning per start they would have saved our bullpen about 25 innings pitched over the course of the season. Not only is that less wear and tear on the bullpen, but that could also provide the manager with a little more flexibility when it comes to how he uses his bullpen.

Lastly, we look at effectiveness. Last year, the extra starters put up a combined 5.91 ERA/4.90 FIP, which is pretty atrocious. This year, the extra pitchers are projected to put up a combined 4.60 ERA/4.50 FIP. While that isn’t remarkable, it’s certainly a significant improvement over last year’s numbers. Below is a chart summarizing of some of the key comparisons that we’ve looked at.

While we hope that none of these extra starters will have to log more than a few starts here and there, we can be confident that we’ll be much better prepared to deal with any injuries to our starting rotation this year as opposed to last. Not only do we have more quantity, but we also have better quality.

As always, let me know what you guys think. I’ll try and get a preview of the bullpen up by Thursday; if I can’t, look for it later this weekend. If you have any suggestions for questions you’d like me to answer about the bullpen, then please let me know in the comments.

I weighted the ages by innings pitched in order to arrive at a more representative average age of the extra pitchers.

As you probably noticed, ZiPS projections have each of this year’s extra pitchers logging over 130 innings. While that is highly unlikely, their rate statistics are not dependent upon the number of innings pitched, so measures such as strikeout, walk, and homerun rates, as well as ERA and FIP, should be, (in theory), the same if a pitcher pitches 50 innings or 150 innings.

2012 Cubs Preview: Starting Rotation [Part II]

Sat, 14 Apr 2012 09:58:39 -0400

Paul Maholm | Will the Cubs infield defense be good enough to convert Maholm’s ground balls into outs?

In my post about Maholm a few months ago I mentioned my concern with his declining swinging strike rate, and the subsequent increase in his contact rates. Higher contact rates will result in a greater number of balls in play, and will make Maholm’s results even more dependent on his defense.

In that same post, I posted a comment comparing Pittsburgh’s defense versus our defense looking forward. I’ve modified that comment to make it more salient.

Let’s look at the UZRs of the Pirates 2011 infield versus the projected UZRs of the Cubs 2012 infield. I focus on the infield because of Maholm’s high GB%.

1B: LaHair 1.5 UZR | Pirates -7.5 UZR
2B: Barney 6.1 UZR | Pirates -3.4 UZR
SS: Castro -7.7 UZR | Pirates -0.4 UZR
3B: Stewart 0.2 UZR | Pirates 7.7 UZR

Based on last year’s UZRs, (for Barney and Castro), and career average UZRs, (for LaHair at 1B and Stewart at 3B), the potential 2012 Cubs infield would post a 0.1 UZR, which would be significantly better than the 2011 Cubs, who posted a -15.9 UZR, and slightly better than the 2011 Pirates, who posted a -3.6 UZR.

However, the fact that Pena and the other Cubs 2011 first baseman only compiled a 0.9 UZR last year makes me question my projection for LaHair. Based on what many here on this site have mentioned about how LaHair has fielded first base this spring, I would feel much more comfortable projecting LaHair at a UZR much lower than his career average. Furthermore, LaHair’s fielding issues could negatively affect the rest of the defense. Based on these adjustments, I could see the best case scenario being a UZR closer to the -3.6 UZR of the 2011 Pirates.

If the 2012 Cubs infield defense is on par with the 2011 Pirates infield defense, Maholm’s ERA will be near 4.00, which I would gladly take from our fifth starter.

Ryan Dempster | Was 2011 the beginning of the end for Dempster?

In his four years as a starter for the Cubs, Dempster had his worst ERA in 2011. His 4.80 ERA was almost a full run above his previous high of 3.85. However, as we can see below, his FIP and xFIP were essentially in line with his 2008-2010 average.

When pitcher’s have ERAs that are higher than their FIPs and xFIPs that usually means that one of their “luck” statistics were out of whack. Sure enough, Dempster had a .324 BABIP, well above his the .292 BABIP that he posted between 2008 and 2010.

While I was tempted to chalk up Dempster’s struggles to him being unlucky, I wouldn’t have been doing my due diligence if I had ended here. This is because BABIP is driven by much more than just luck, in fact it’s driven by four factors: team defense, pitcher’s talent level, pitcher’s skill set, and luck. Let’s quickly examine a couple of these factors and how they relate to Dempster’s 2011.

Team Defense

If we look at the following chart, we can see that Dempster benefitted from the Cubs’ 2008 defense, and has been hurt in more recent years by the Cubs’ poor defense.

However, as bad as the Cubs 2011 defense was, it was only slightly worse than the 2010 defense by UZR standards, but Dempster’s BABIP was still 30 points above his previous year BABIP, and over 20 points above the Cubs team average BABIP. While defense has played a part in Dempster’s BABIPs between 2008 and 2011, it doesn’t explain Dempster’s .324 BABIP too well.

Pitcher’s Talent Level

When we’re evaluating major league pitcher’s, the most important variable for this factor is health. Aside from some minor hip and back issues that kept him from making an early July start, Dempster was healthy.

Pitcher’s Skill Set

It has been discovered that pitchers with high strikeout rates tend to generate weaker contact, and thus allow fewer hits on balls in play. Thus, we would expect pitcher’s with higher than average strikeout rates to have lower than average BABIPs. If we look at the past four years, we can see that Dempster’s strikeout rates have remained relatively high. At 8.5 K/9 last year, Dempster’s strikeout rate was well above the league average of 7.1 K/9, which would suggest that Dempster should have had a below average BABIP.

Luck

After evaluating the above factors, we’re left with luck, and in this situation luck likely played a large role in Dempster’s .324 BABIP. He didn’t experience any major changes in his team’s defense or his skill set that could have explained the BABIP change, and unless Dempster was suffering from an undisclosed injury, Dempster likely just suffered from bad luck.

Assuming that I looked over everything correctly, this is really the best answer that we could have hoped for; based on this, I would expect Dempster’s ERA to bounce back below 4.00 this year.

As always, let me know what you guys think. I’ll get to Part III within the next few days. If you have any suggestions for questions you’d like me to answer about the rest of our rotation or bullpen, then please let me know in the comments.

2012 Cubs Preview: Starting Rotation [Part I]

Fri, 13 Apr 2012 10:00:00 -0400

Matt Garza | Has Garza become a more efficient pitcher? Does he throw fewer pitches per inning?

During the Cubs vs. Rockies broadcast, Keith brought up the fact that Garza needs to cut down on his pitches per inning in order to provide more innings for the Cubs. I recalled Garza going deeper in games during the last month of the season, and wanted to see if he had become more efficient near the end of last year.

Here is a graph with Garza’s pitches per inning by start in 2011.

As we can see, there is a slight downward trend in the number of pitches he threw per inning. In his 15 post-All Star Break starts, Garza threw less than 16 pitches per inning in 9 of them. Why is 16 such an important number? Let’s look at Garza’s pitches per inning in his career.

As we can see, Garza has averaged over 16 pitches an inning in each of his four full seasons. The fact that he broke that mark in 60% of his post-All Star break starts is interesting, but not conclusive evidence that he has become a more efficient pitcher. Since 16 pitches is his career average, we would expect Garza to be above that 50% of the time and below that 50% of the time. Looking at his post-All Star break starts, we would expect Garza to be below 16 pitches per inning in 7.5 of his starts and above 16 pitches per inning in 7.5 of his starts. In actuality, Garza was below 16 pitches per inning in 6 of his starts and above it in 9 starts. This isn’t a large enough variation to indicate a change in Garza’s pitch efficiency, but it’s definitely something to keep tabs on as the season gets going.

Jeff Samardzija | Did Samardzija turn the corner in 2011?

Samardzija was very lucky in 2011. He sported a career-best .253 BABIP, (.300 BABIP is league average), career-best 75.0% LOB%, (70% LOB% is league average), and a 5.3% HR/FB rate, (9.5% is league average).

While Samardzija benefitted from good luck in 2011, there are some signs that point to skill-based improvement and not just luck-based improvement. First of all, Samardzija put up his highest strikeout rate of his career, 8.9 K/9, along with his highest swinging strike rate of his career, 9.9%, (8.5% is league average). Furthermore, though he ended the season with a pretty awful 5.11 BB/9, the majority of his control issues occurred early on in the season: in his first 18 appearances, (24.1 IP), Samardzija walked 23 batters. As we can see from the chart below, Samardzija ended up hovering between a 3.0 BB/9 and 4.9 BB/9 for the majority of the rest of the season. If we split the difference, we see that Samardzija’s true talent level is likely closer to 4.0 BB/9 than 5.0 BB/9, which would be good for a strikeout-to-walk ratio greater than 2.

Samardzija’s Pitch f/x data provides us with some interesting information regarding his pitch frequency and effectiveness.

Samardzija threw his changeup half as often in 2011 as he did in 2010. Furthermore, over the past three years, he has been phasing out his curveball, as he threw it only 1.3% of the time last year. He threw fewer changeups and curveballs last year in favor of more fastballs (65.6% in 2010 versus 71.6% in 2011), and sliders, (13.7% in 2010 versus 17.7% in 2011).

Samardzjia’s fastball and slider were his best pitches in 2011. For the fist time in his career, he had a fastball that was above average in effectiveness, (1.43 wFF/C - weighted average of all of his fastballs). Furthermore, his slider, (1.59 wSL/C), and changeup, (.61 wCH/C), both had above average effectiveness levels. While Samardzija had three above average pitches last year, he was primarily a fastball and slider pitcher as these two pitches accounted for over 90% of his pitches in 2011. Starters usually need more than two effective pitches - if Samardzija really wants to start this year, he might need to begin throwing that changeup with more regularity.

Lastly, I looked at some Pitch f/x velocity charts, which plot the velocity of his pitches by appearance.

2008

2009

2010

2011

If we look at Samardzija’s fastball velocity over his major league career, we see that it really picked up this year. In his first three years, Samardzija threw his fastball between 91 and 95 mph. He did the same for about the first 25 appearances of 2011, but then began consistently throwing between 95 and 98 mph for the rest of the season.

Samardzija’s uptick in velocity, change in pitch frequencies, and more effective fastball and slider helped him turn the corner in 2011. It will be interesting to see whether or not he can develop that changeup to the point where he’s comfortable throwing it more often. If he can, Samardzija could finally become a capable major league starter.

As always, let me know what you guys think. I’ll get to Part II within the next week. If you have any suggestions for questions you’d like me to answer about the rest of our rotation or bullpen, then please let me know in the comments.

* Here’s a short primer on pitch values.

Thanks to FanGraphs for Pitch f/x Pitch Values data.

Thanks to Joe Lefkowitz for his Pitch f/x data.

2012 Cubs Preview: Outfield

Thu, 12 Apr 2012 10:00:00 -0400

Right Field: David DeJesus | Is DeJesus our best lead-off option?

According to The Book, the optimal lead-off hitter (i) has a high OBP, (iii) should be one of the team’s three best hitters, and (iii) should have little power. Let’s see if DeJesus fits this mold.

High OBP

DeJesus sports a career .356 OBP - the highest of any current Cubs hitter. According to ZiPS, here are the three highest projected OBPs for the 2012 Cubs.

While DeJesus has a good career OBP, ZiPS projects him to get on base at a lower clip than his career level. Regardless, the difference between the top three OBPs is so small that it’s a toss-up.

Should be one of the team’s three best hitters

According to ZiPS here are the five highest projected wOBAs for the 2012 Cubs.

While DeJesus isn’t technically one of the three best hitters on the team, the projections have him right in the thick of things, as he’s only a handful of wOBA points away from the top three.

Little Power

I have ranked the five players whom we have considered in the previous two analyses by their projected ISOs.

DeJesus is projected to have more power than both Castro and Byrd, but significantly less power than Soto and LaHair.

DeJesus’s relative blend of power and patience does not make him our best lead-off option. However, this exercise has revealed who should actually be hitting first: Starlin Castro. He’s projected to have the highest OBP, be one of the three best hitters on the team, and have the lowest ISO in 2012. While many fans would like to see Castro move down in the order, he’ll have to develop a little more power and we’ll have to find a better lead-off hitter than him before he’s moved down. He’s the best lead-off hitter that we have this year.

What does this mean for DeJesus? He’s clearly one of the best OBP threats we have, one of our four best hitters, (with little separating him from the top three), and does not have enough power to bat in the heart of the order. That said, I see him slotting in very well in the #2 spot.

One last thought on our 2012 lineup: below is what I think is our optimal lineup.

3. Marlon Byrd

7. Ian Stewart

Center Field: Marlon Byrd | Did the ball to Byrd’s head affect his distance from the plate?

After taking a pitch to his head in Boston, we might expect Byrd to alter his plate approach by taking a step back in the batter’s box to avoid a reoccurrence of that hit by pitch. This would make Byrd more susceptible to off-speed pitches - particularly sliders - away from him. First, let’s take a look at some pictures.

On the left, we have Byrd batting against Houston in 2010. On the right, we have Byrd batting against Washington in 2011.

There doesn’t seem to be a visible difference between the two images. It looks like Byrd is as close to the plate post-injury as he was pre-injury.

However, if we look at Pitch f/x evidence, we get a slightly different story.

Byrd swings and misses at outside curveballs and sliders with much more frequency post-injury than he did in 2010. Keep in mind that the post-injury chart includes only three months of data, while the 2010 chart includes a full season’s worth of data; even if it looks like he’s swinging and missing at about the same number of pitches curveballs and sliders post-injury as in 2010, he’s done it in less than half a season’s worth of time. While this could just be the result of a small sample size, it could also be evidence of him standing further away from the plate. If Byrd was standing further away from the plate, he would be more concerned about letting pitches go by for strikes on the outside corner, thus expanding the outside portion of his strike zone in the process.

Left Field: Alfonso Soriano | Is Soriano the most overpaid player in baseball? Putting the money aside, is he even our best option in left field?

I cheated here and chose two questions, primarily because they were both easy to answer. I’ll address the overpaid question first.

Here is a list of the 20 highest paid players in 2011 ranked by the amount that they were overpaid or underpaid.

As we can clearly see, Soriano wasn’t the most overpaid player in 2011. In fact he wasn’t even the most overpaid player on the 2011 Cubs - that honor goes to Carlos Zambrano. While $13.15 million is nothing to sneeze at, at least it wasn’t the worst contract out there, (at least in 2011). Regardless, the end of the 2014 season can’t come soon enough.

Now let’s see if Soriano should even be one of our three outfielders. Below are 2012 ZiPS projections for our outfielders:

Until Brett Jackson is promoted, it looks like Soriano is far and away our best option in left. However once Jackson’s called up, things get a little murkier. Soriano and Byrd are essentially projected to provide the same offensive performance in 2012. Assuming that Byrd wouldn’t be opposed to moving to left field, Sveum could platoon the two in left. Ideally Sveum would play Byrd against righties, (105 wRC+ over the past four years), and Soriano against lefties, (124 wRC+ over the past four years), to maximize the offensive output of left field. It looks like Sveum will be allowed to pencil in the best lineup regardless of the amount of money that is sitting on the bench on any given day. If this in fact ends up being the case, Soriano could find himself on the bench for a large portion of the 2012 season.

As always, let me know what you guys think. Again, if you have any suggestions for questions you’d like me to answer about players I have yet to look at, please let me know in the comments.

Thanks to Dan Szymbroski for his ZiPS projections.

Thanks to Joe Lefkowitz for his Pitch F/X data.

2012 Cubs Preview: Corner Infield

Wed, 11 Apr 2012 10:00:00 -0400

First Base: Bryan LaHair | Is Bryan LaHair a Quad-A player?

Al recently put a good story together on this, but I figured we’d use some analytical tools to determine whether or not he has shown signs of being a Quad-A player.

The skill that differentiates Quad-A players from major league players is their ability - or inability in this case - to hit breaking pitches. Quad-A players face a lot of bad breaking pitches in the minors, and tend to lay off these in favor of fastballs. However, once they come up to the majors, they begin facing breaking pitches that are much better than the Triple-A pitches they have been accustomed to, and have trouble hitting them.

If we look at LaHair’s Pitch f/x Pitch Values, we see that he hits fastballs really well, (5.00 wFA/C), but that he struggles mightily against curveballs, (-2.64 wCU/C), and changeups, (-2.06 wCH/C).* To put this into context, I looked at two other players who recently reached the majors - Starlin Castro and Matt LaPorta. We know how good Starlin has been - he’s clearly not a Quad-A player. LaPorta on the other hand looks like a classic Quad-A player as he doesn’t hit curveballs or changeups well. Here are their 2011 Pitch f/x Pitch Values:

As we can see, both LaHair and LaPorta struggle against breaking and off-speed pitches, while on the whole, Castro has shown an ability to hit both breaking and off-speed pitches.

I then looked at Pitch f/x data to determine swing-and-miss rates on certain pitches. Here are their swing-and-miss rates:

As we can see, both LaHair and LaPorta swing-and-miss at a very high percentage of curveballs and changeups. While Castro swings-and-misses at a high percentage of curveballs, he makes up for this by making strong contact on the curveballs that he does hit, as evidenced by his 1.54 wCU/C. Unfortunately, we can’t say the same thing for LaHair or LaPorta. They not only have negative pitch values on breaking and off-speed pitches, but they also have very high swing-and-miss rates. In other words, even when they do end up making contact, they end up hitting them poorly, (or at least not well enough to make up for their high swing-and-miss rates).

Finally, I looked at LaHair’s Pitch f/x swinging strikes charts.

As we can see, there are a lot of squares, (curveballs), and diamonds, (changeups). 17 of LaHair’s 32 swings-and-misses came on the curveball and changeup. He was thrown one of these two breaking pitches 25.9% of the time. In other words, 53.1% of his swings-and-misses came on 25.9% of the pitches thrown; another indication that LaHair has trouble with major league breaking pitches.

Each of the three analytical tools that I’ve used shows us that LaHair struggles with major league breaking pitches, suggesting that he could be a Quad-A hitter. However, there are two things that give us some hope: (i) not only does he make contact on sliders, (something LaPorta doesn’t do well), but he hits sliders well, (0.78 wSL/C), and (ii) we’re looking at a very small sample size as LaHair only had 69 plate appearances last year. And if this isn’t enough hope for you, Bryan did say that he’s “probably in the best shape of [his] life.”

Third Base: Ian Stewart | What was wrong with Stewart in 2011?

Stewart’s 2011 was horrendous, plain and simple. There are some numbers that point to a potential bounce back - especially a career low .224 BABIP. Furthermore, Stewart has had an above average walk rate each year he’s been in the majors, and an above average ISO in three of the four years. However, I dived into some Pitch f/x numbers and found some glaring issues. Here are Stewart’s career Pitch f/x Pitch Values:

In the past, Stewart has clearly had some issues hitting curveballs and changeups, which made me wonder if he could be another potential Quad-A player. However, Quad-A players don’t typically have 25-home run seasons, even those who are lucky enough to call Coors Field their home, (although, in 2009, Stewart only hit 13 of his 25 home runs at home). I took a quick look at his HR%, and, as we can see from below, it’s been significantly higher than the league average, (3.42 HR%), in every year except 2011.

Getting back to his pitch values, we can see that while Stewart has struggled with breaking and off-speed pitches in his career, he was well above average against the changeup in 2008, only slightly below average against the changeup in 2009, and above average against the curveball in 2010. In other words, in each of his first three years, Stewart only really struggled with one of the three breaking and off-speed pitches. However, this trend didn’t continue in 2011 - he was well below average against the slider and changeup, and below average against the curveball. In fact, Stewart was even below average on the pitch that he made his living off of during his first three years in the league: the fastball. No longer could his production against fastballs make up for his lack of production against breaking and off-speed pitches. I then took a look at Stewart’s swing-and-miss rates:

Stewart has always had high swing-and-miss rates on sliders, curveballs, and changeups. In the past, despite his high swing-and-miss rates, he managed to be a productive hitter because of his ability to hit pitches well when he made contact. His high swing-and-miss rates finally caught up to him this past year; because of his negative pitch values, we can infer that even when he managed to make contact, his contact wasn’t strong enough to be productive, and he was consequently one of the worst hitters in the majors.

While we can hope that Stewart’s struggles were a result of his injuries and lack of consistent playing time, there are some warning signs that his issues may be too large to overcome with just good health and playing time. Here’s to hoping that I’m wrong.

As always, let me know what you guys think. Time permitting - I’ll be busy with exams over the next couple of weeks - my next post will focus on our pitchers. If you have any suggestions for questions you’d like me to answer about our rotation or bullpen, then please let me know in the comments.

* Here’s a short primer on pitch values.

Thanks to FanGraphs for Pitch f/x Pitch Values data.

Thanks to Joe Lefkowitz for his Pitch f/x data.

2012 Cubs Preview: Middle Infield

Tue, 10 Apr 2012 23:10:29 -0400

Catcher: Geovany Soto | Soto’s 2009 season was hampered by a low BABIP, was this what plagued him in 2011 too?

In 2009, Soto posted a .246 BABIP - the 13th lowest in the majors - well below the league average BABIP of .299. As we can see from the chart below, the slope of his BABIP decline from ‘08 to ‘09 is steeper than the slope of his wOBA decline during the same period of time. This indicates that while his BABIP fell, his wOBA didn’t fall as much as his BABIP might indicate.

On the other hand, in 2011, Soto posted a .280 BABIP - only slightly below the league average .295 BABIP. Flip back to the chart and we now see that the slope of the BABIP is less steep than the slope of the wOBA indicating that wOBA fell by more than what BABIP would suggest. What’s the most likely explanation? Enter BB% and K%.

In 2009, Soto’s walk and strikeout rates both improved, which is likely part of the reason that his wOBA didn’t fall by as much as his BABIP suggested it would. In 2011, however, both Soto’s walk and strikeout rates went in the wrong direction: he posted a career low walk rate and a career high strikeout rate. These two developments are likely why his wOBA fell by more than his BABIP suggested it would. While his 2009 season was likely a result of bad luck, his 2011 season was likely a result of his declining skills. Before you bring up his age, take a look at the following chart.*

The blue curve consists of all players. The red curve consists of 70 players since 1981 who spent at least four seasons with a minimum of 800 inning per season at the catcher position. The yellow curve consist of players who spent at least one season as a part time catcher since 1981.

Looking at the red curve, we see that catchers usually peak at the age of 26 and 27, and then begin declining at a rate similar to the all players sample. It’s definitely possible that, at the age of 29, Soto is in his decline phase.

In the event that his BABIP climbs closer to his career average of .303 in 2012, I wouldn’t be surprised to see Theo & Jed trade him at the deadline. Soto’s not getting any younger, and a team desperate for offense may be willing to overpay come July.

Second Base: Darwin Barney | Did Barney run out of steam near the end of the season?

Below is a chart of Barney’s 2011 cumulative wOBA on a daily basis.

While Barney’s wOBA was between .320 and .340 for most of the first quarter of the season, it fell below .300 mid-season. While he managed to pick it back up to about .310 soon after coming back from his time on the disabled list, he ended the season with a .293 wOBA. Which version is the true Barney: the .330 hitter who just ran out of steam, or the .293 hitter who played above his true talent level early on in the season?

Research says the .293 wOBA hitter.* Statistics such as OBP, SLG, and OPS have been shown to stabilize after 500 plate appearances. Since wOBA is an extension of these statistics, we can expect it to stabilize and be a reliable indicator of true talent level after 500 plate appearances. Looking at Starlin’s 2011 cumulative wOBA chart, we can see his wOBA stabilize almost as soon as hits 500 plate appearances.

Looking back at Barney’s wOBA chart, we see his wOBA hovering between .290 and .300 after 500 plate appearances, suggesting that his true talent level is likely closer to his sub-.300 wOBA than the .330 wOBA he displayed at the beginning of the season. Here’s to hoping I’m wrong.

Shortstop: Starlin Castro | How has his ability to hit for power developed since he broke into the majors?

The offensive numbers Castro put up in his age 21 season were phenomenal, and while there’s much to appreciate, I’m sure that many of us are interested in the development of his ability to hit for power. Below is a chart of Castro’s career cumulative ISO on the basis of plate appearances, (the first 506 plate appearances are from 2010, with the following 715 plate appearance occurring in 2011).

Once again, using research on the stabilization of statistics, ISO tends to stabilize at 550 plate appearances. If we look at Castro’s ISO at 550 career plate appearances, we see that it’s at around .110. By the end of the 2011 season, Castro’s career ISO was much closer to .120, constantly hovering between .118 and .120. While Castro’s ISO has clearly improved, his improvement might become even more apparent when we take a closer look.

If we compare Castro’s two seasons, the increased power is much more apparent. If we look at Castro’s 2010 ISO, we see that it stabilizes at .108. In 2011, Castro’s ISO stabilized at .125 - a 17 point increase over the course of a season, which is tied for the 22nd highest positive ISO change of last season, (among batters with over 550 PA). Castro’s 2012 ISO rates will show us if these gains are permanent and whether or not he can continue to build upon his power improvements.

Look out for a preview of the rest of the 25-man roster - or as much of it as I can get to - over the course of the next few weeks. In the meantime, let me me know (i) what you think of these three questions, and (ii) if you have any question suggestions for the rest of the 25-man roster.

* Thanks to FanGraphs for the catcher aging curve.

* Thanks to Pizza Cutter for his research on stabilization of statistics.

Cubs 2012 Season Preview

Tue, 10 Apr 2012 23:10:00 -0400

I put together some player previews over at Bleed Cubbie Blue. When I initially thought about constructing player projections, I quickly realized that there were other projections that were far better than anything I could produce, and that we were all likely projectioned-out anyway. That said, I decided to address one meaningful question regarding each Cubs player in advance of the upcoming season.

I will post one preview per day on each of the next six days. Here is a list of the previews and when they’ll be up.

April 10 | Middle Infield: Geovany Soto, Darwin Barney, and Starlin Castro

April 11 | Corner Infield: Bryan LaHair and Ian Stewart

April 12 | Outfield: David DeJesus, Marlon Byrd, and Alfonso Soriano

April 13 | Starting Rotation Part I: Matt Garza and Jeff Samardzija

April 14| Starting Rotation Part II: Ryan Dempster and Paul Maholm

April 15 | Starting Rotation Part III: Chris Volstad and The Rest

Value of Various Plate Approaches

Sun, 29 Jan 2012 22:53:00 -0500

Analysts and commentators frequently rave about a player’s ability to hit to the opposite-field. Extreme pull-hitters are often knocked by many fans who consider hitting to the opposite field a key indicator of a great hitter. However, some of the best hitters in the game - Albert Pujols, Alex Rodriguez, Ben Zobrist, Carlos Beltran, Paul Konerko, Mark Teixeira, and Ken Griffey Jr. - could be considered pull-hitters: hitters who have pull rates above the 84th percentile, or one standard deviation above the mean, among all players. Thus, I wanted to understand the value of hitters with extreme split tendencies versus hitters without any extreme split tendencies, (spray hitters).

I looked at the past seven years worth of data, evaluating 310 hitters in the process. These 310 hitters had at least 300 plate appearances that resulted in balls that were pulled, hit up the middle, and hit to the opposite field, (so a total of at least 900 plate appearances per player).

I started off by studying the correlation between a player’s pull wOBA, up-the-middle wOBA, and opposite-field wOBA against his overall wOBA. Below are the scatterplots with the directional wOBA on the x-axis and the overall wOBA on the y-axis, followed by the correlation coefficient - the measure of the strength of linear dependence between two variables - of the data.*

r = .6027

r = .7042

r = .5057

It’s interesting to see that a player’s up-the-middle wOBA has the strongest relationship with a player’s overall wOBA, (r=.7042). However, this analysis doesn’t bring about many tangible results. While it’s an interesting conclusion, there is a glaring issue with this analysis: directional wOBA does not include walks or strikeouts - it only records a player’s wOBA on the balls that he puts in play to each part of the field - so these correlation tests aren’t very meaningful.

Once I realized the relatively fruitless analysis I had just performed, I tweaked my methodology in the hopes of finding something more relavent. Instead of looking at directional wOBA, I looked at the relationship between the directional frequency of their plate appearances - how frequently these 310 hitters pulled the ball, hit it up the middle, and hit it to the opposite field - and their overall wOBA. Below are the scatterplots with the directional frequency on the x-axis and the overall wOBA on the y-axis, followed by the correlation coefficient of the data.

r = .2032

r = -.1858

r = -.1730

Here, pull frequency has the strongest positive association with overall wOBA, while both up-the-middle frequency and opposite-field frequency have negative associations with wOBA. In other words, the more frequently a player pulls the ball, the higher his wOBA likely is; however, the more frequently a player hits the ball up-the-middle or to the opposite field, the lower his wOBA likely is. This makes a lot of intuitive sense - players who can pull the ball will have an easier time hitting extra base hits and home runs, resulting in higher overall wOBAs. On the flip side, players who hit up-the-middle and to the opposite field will have a harder time hitting home runs, (the centerfield fence is usually the deepest, and hitting home runs to the opposite field is significantly more difficult than pulling home runs), and extra base hits, (hitting to the opposite field with power is significantly more difficult than pulling the ball with power), resulting in lower overall wOBAs. Let’s see if this logic applies when we test it on individual players and their overall wOBAs.

To do this, I needed to test the relationship between players with extreme directional frequencies and wOBA. I began by calculating the distribution of each directional frequency. I then categorized each of the 310 hitters into four plate approaches: pull, up-the-middle, opposite-field, and spray. Those who were categorized within one of the pull, up-the-middle, and opposite-field approaches had to have a directional frequency greater than one standard deviation above the mean, (higher than the 84th percentile), in that specific frequency. So, for example, in order for a hitter to be categorized as a pull-hitter, the hitter must have a pull frequency greater than 45.5%, (the 84th percentile of pull frequency amongst the 310 hitters). Those who did not fall into any of the first three categories, fell into the spray category - these hitters did not have extreme directional tendencies and are the ones who essentially hit to all fields. Once the players were categorized, I calculated the average wOBA of each category and compared it to the weakest wOBA of the four categories. Here are the results:

Pull hitters have the highest wOBA, followed by spray hitters, opposite-field hitters, and up-the-middle hitters. When compared to the weakest category, pull hitters were worth, on average, an additional win over the course of 600 plate appearances.* As we found in the correlation study, hitters who pull the ball more frequently tend to have higher wOBAs than those who hit the ball up-the-middle and to the opposite field.

Thus, we can conclude that, on average, pull-hitters are significantly better than up-the-middle and opposite-field hitters, and only slightly better than spray hitters.

* The higher the correlation coefficient, the stronger the relationship between the two variables.

* Assuming that 10 runs equals a win.

A Graphic Look at the Window to Win: Cubs

Wed, 25 Jan 2012 14:37:27 -0500

fungraphs:

Doesn’t look like they have all that depth in the higher levels of the minors.

Really neat look at the Cubs’ Window to Win. Great work as usual by Dave at FUNGraphs.

WAR Walk Through: Ben Zobrist

Tue, 24 Jan 2012 03:13:01 -0500

As I mentioned in my recent post on Wins Above Replacement, I will be walking through the calculation of a specific player’s WAR in this post. The player that I will use as an example is Ben Zobrist, not only because I’m a big fan of his, but also because he’s a good example to run this calculation on.

I will mirror the format of the aforementioned WAR post in order to make the following calculations easy to follow. Here we go.

Batting

First, we need to convert Zobrist’s wOBA to wRAA. To do that, we just use the following formula:

wRAA = ((wOBA - lgwOBA)/Scale) * PA

wRAA = ((.360 - .316)/1.15) * 674

wRAA = 25.8 runs

Zobrist’s wRAA, unadjusted for the ballparks that he played in, was 25.8 runs.* Therefore, Zobrist’s batting was worth 25.8 runs.

Fielding

Zobrist is what you would call a super-utility player; in the past four years, Zobrist has played every position except for catcher. Not only has he played seven defensive positions, but he has also provided above average defense at four of those seven positions in his career. In 2011, Zobrist primarily played played second base, (118 games started at second base), with a few starts in right field, (33 games started in right field). Zobrist’s UZR at second was 6.8, while his UZR in right field was 3.4; we just add the two UZRs to get the runs Zobrist was worth in the field. Therefore, Zobrist’s fielding was worth 10.2 runs.

Defensive Position (or Positional Adjustment)

Zobrist played 118 games at second base, and 33 games in right field. His positional adjustment is calculated below:

Positional Adjustment = (+2.5 * 118/162) + (-7.5 * 33/162)

Positional Adjustment = (1.82) + (-1.53)

Positional Adjustment = 0.3

Therefore, Zobrist’s positional adjustment was worth 0.3 runs.

Replacement Level Adjustment

We need to credit Zobrist for how frequently he played in 2011. The replacement level calculation is as follows:

Replacement Level Adjustment = (20/600 *PA)

Replacement Level Adjustment = (20/600 * 674)

Replacement Level Adjustment = 22.5 runs

Therefore, Zobrist’s replacement level adjustment was worth 22.5 runs.

The Rest

We now add the runs above average from each of the four components that we evaluated: Batting, Fielding, Defensive Position, and Replacement Level Adjustment. Below is a chart that summarizes Zobrist’s component run values calculated by both us and FanGraphs:

As you can see, Zobrist was worth 58.8 runs above average in 2011. After converting these runs to wins using the 10 runs to 1 win ratio, we find that Zobrist was worth 5.9 WAR.

In actuality, FanGraphs has Zobrist at 6.6 WAR; as we can see by comparing the two previous charts, the key differences in the numbers stem from the fact that: (i) FanGraphs gave Zobrist 27.0 runs in his batting component, which is higher because it accounts for the tough ballpark conditions that Zobrist had to play in, (ii) FanGraphs now calculates a base running component of WAR in which Zobrist scored positively, (iii) FanGraphs gave Zobrist 0.0 runs for his positional adjustment instead of 0.3, (iv) FanGraphs used a slightly different runs to win ratio. Once we account for base running (.3 WAR), and the ballpark adjustment (.1 WAR), we get within a couple tenths of the actual WAR.

Despite some inconsistencies, our hand calculated WAR of 5.9 was very close to Zobrist’s actual WAR of 6.6. With the inclusion of the base running component, the addition of a ballpark adjustment on the batting component, and a more accurate runs to win ratio, we would be able to perfectly calculate WAR.

* I have not been able to find how the ballpark adjustment is made. If I ever do manage to come across this, I will update this post to include the math.

Evaluating General Managers

Fri, 20 Jan 2012 00:13:00 -0500

My younger brother came up with the following concepts – I just filled in the logical gaps.

Winning in baseball is about optimization and efficiency. Sure, you could go out and spend $23 million a year on Prince Fielder - he posted 5.5 WAR, which was valued at $24.6 million in 2011 - but would he bring back any excess value on a 6-year contract? Probably not.

Why is excess value important? Well, if you were looking to build a 90-win team and paid market value for each player, you would end up with the following payroll:

Payroll = Cost of Replacement Level Team + Cost of Marginal Wins

Payroll = (# Replacement Level Players * League Minimum) + (# Wins Above Replacement * Dollar Value of WAR)

Payroll = (25 * $425K) + (42 * $4.47M) = $198.4M

This results in a team payroll that is over the luxury tax of $189 million dollars. While it’s possible to pay market value for players, as long as you’re willing to pay a luxury tax, it’s not realistic. That’s why payroll efficiency is important.

Efficiency

Let’s start with a basic measure of payroll efficiency: dollar per win, or the number of dollars team X had to pay per win.

Below is a chart detailing how much each team paid per win in 2011:

However, we can do better than this. The replacement level team would <link to fangraphs> win 48 games. We want to know how much teams are paying for wins above this replacement level. How much are teams paying for the wins that actually matter – the marginal wins? We arrive at a slightly more advanced measure of payroll efficiency,

Efficiency (rEF) = (rWAR * $/WAR)/Payroll

Where rWAR is WAR calculated by (Team Wins – 48), or the number of wins a team had above replacement level. This is different from summing the WARs of the individual players. I use rWAR instead of WAR because a team’s final win-loss record is more important than a hypothetical win-loss record based on player’s WAR values.

rEF > 1 = Positive Efficiency

An efficiency value that is greater than one indicates that a team’s 25 players are worth more than what they are paid.

rEF < 1 = Negative Efficiency

An efficiency value that is less than one indicates that a team’s 25 players are worth less than what they are paid.

Below is a chart detailing each team’s rEF in descending order.

As we can see, only five teams had an rEF of less than 1: the Mets, Mariners, Cubs, Twins, and Astros – all teams within the top 2/3 of all teams in terms of payroll, and the bottom 2/5 in terms of wins, which is not a winning combition by any measure. However, the takeaway here is that teams are generally efficient; therefore, we should look at relative efficiency.

Relative Efficiency (rREF) = Team’s rEF/League Average rEF

rREF > 1 = Positive Relative Efficiency

A relative efficiency value that is greater than one indicates that a team is more efficient than league average.

rREF < 1 = Negative Relative Efficiency

A relative efficiency value that is less than one indicates that a team is less efficient than league average.

Below is a chart detailing each team’s rREF in descending order.

Relative Efficiency measures how efficient a team is relative to the league. For example, the Rangers had an rREF of 1.237, which means that the Rangers were 1.237 times as efficient – as good at getting more value from players than what they pay players - as the average major league team. Five of the eight playoff teams had an rREF above 1, with two of the remaining three posting REFs above .850.

Another interesting data point: the Tampa Bay Rays. The Rays were 2.563 times as efficient as the average major league team. That is phenomenal. If we look at standard deviations of rREF – one standard deviation is .482 – the Rays were above the 99.7^th percentile in efficiency, i.e. three standard deviations above the average.

General Manager Value

Evaluating the decisions of general managers can be very difficult, but using the efficiency ratings that we have created, we can attempt to place a value on general managers. While this is by no means a comprehensive analysis of a general manager’s value, it can potentially be one among a number of tools used to evaluate a general manager. We can evaluate a general manager’s value, or GMV, by calculating the change in his team’s efficiency rating over his tenure as the team’s general manager. So the GMV formula is,

GMV = (Most Current Year rEF – rEF Prior to First Year)/(Number of Years as GM)

As an example, let’s look at former Cubs GM Jim Hendry. Hendry became the general manager in the middle of the 2002 season, but since he didn’t have much of a hand in architecting the 2002 team, we will use 2002 as Hendry’s baseline efficiency, or if you’re following the formula, the rEF prior to first year. The Cubs 2002 EF was 0.653. The Cubs 2011 EF – the last year of Hendry’s tenure, or Hendry’s most current year – was 0.772. Hendry’s GMV is calculated below.

GMV = (.772 - .653)/(9) = .013

In a vacuum, this number isn’t very useful; however, it becomes much more useful once you compare it to the GMVs of other general managers.

Let’s now look at the Rays’ Andrew Friedman. In 2005, the year before he took over, the Rays’ EF was 2.176. In 2011, the Rays’ EF was 4.588. Friedman’s GMV is calculated below.

GMV = (4.588 - 2.176)/(6) = .402

We can now compare the two GMVs: Hendry’s .013 and Friedman’s .402. As we can see, Friedman has been much better at acquiring more value than he pays for. How much better? Friedman’s GMV is 30.4x that of Hendry’s.

While GMV does contain value in and of itself, it is most useful when it’s being used to compare GMs.

General Manager Reasoning

The efficiency rating can also naturally be applied to individual players. For example, Albert Pujols’ efficiency rating in 2011 was 1.425 - he was worth $22.8M and was paid $16M.

Taking this player efficiency rating into consideration, another way to evaluate a general manager is to look at the moves that he makes and evaluate them at that point in time, instead of in retrospect. While some contracts can look very good or bad in retrospect, it is important to evaluate a general manager’s decision based on the information that he had at the time. One way to do this is to project the player the general manager acquires using the ZiPS projection system over the life of his contract. For example, we can use ZiPS projection of Pujols’ value over his 10-year contract and evaluate it against his annual salary. This should help show a general manager’s reasoning when signing a player.

We will call this statistic a general manager’s reasoning, or GMR. GMR evaluates a general manager’s decision given the information that he had at his disposal during the time of his decision. The GMR formula is,

GMR = Present Value of Player’s Projected WAR/Present Value of Contract

The present value of a player’s projected WAR is the value of the player’s production over the course of his x-year contract to the team as it stands today. All things equal, you’d rather have four 5.0 WAR seasons now than in the future. In order to account for this, you have to discount future WAR. I typically use a 5% discount rate. At the same time, you must discount the player’s contract value in order to account for the fact that money today is worth more than money tomorrow. I tend to use a 5% interest rate to discount contracts.

As an example, let’s take a look at Paul Maholm recent contract with the Cubs. Maholm looks like he should post about 2.0 WAR per year during the life of his contract. Let’s assume that the Dollar Value of a WAR stays at $4.5 million over the next two years, and that the Cubs pick up Maholm’s club option. Hoyer’s GMR on the Maholm signing is calculated below.

Present Value of Player’s Projected WAR = [((2.0 WAR * $4.5M)/((1+.05)^0)) + ((2.0 WAR * $4.5M)/((1+.05)^1))] = $17.57M

Present Value of Contract = [$4.5M/((1+.05)^0)] + [$6.25M/((1+.05)^1)] = $10.45M

GMR = $17.57M/$10.45M = 1.68.

While this GMR does tell us that Hoyer paid less than what Maholm will likely be worth, it’s much more useful when compared to the GMRs associated with similar transactions from the same offseason.

Conclusion

GMV and GMR both evaluate a general manager’s value through the use of the efficiency ratings that we’ve outlined. In our eyes, GMV is a retrospective macro-level look at a general manager’s effectiveness, while GMR is a prospective micro-level look at a general manager’s effectiveness. While there are many other factors that could have been considered, and some potential logical problems, (small market teams are more likely to have high efficiency ratings, larger market teams are expected to spend big bucks on big name free agents, depressing their efficiency ratings, etc.), they all add layers of complexity that can’t be completely measured. Even after considering these potential shortcomings, GMV and GMR offer a simplified glimpse of a general manager’s performance.

The Best and Worst Men on Base Splits of 2011

Wed, 18 Jan 2012 23:10:21 -0500

While I was surfing the FanGraphs leaderboards, I stumbled upon the splits section which allows you to view a player’s performance based on certain situations. I flipped through a couple of splits until I came to these three: Bases Empty, Men on Base, and Men in Scoring Position. Now I know that it has been proven a few times - most notably in Baseball Between the Numbers - that there is no such thing as clutch hitting ability; however, I was interested in trying to find players with the most extreme men on base splits of 2011 - a proxy for how a player performs in more important situations. Essentially, I wanted to see which players stepped up their games with men on base and which players fell flat in 2011.*

I decided to compare a player’s offensive performance with men on base versus his performance with the bases empty instead of his performance with men in scoring position versus his performance with the bases empty, because players drastically change their approach when a man is in scoring position as opposed to when the bases are empty, at times sacrificing their at-bat for the good of the team in the form of a sac-fly, or a ground ball to the right side of the infield. Naturally, some of these sacrifices will have a negative impact on a player’s offensive performance with men in scoring position. While the men on base stat has the same problem, the problem isn’t as extreme because it also includes situations that are less likely to force a player to sacrifice an out or drastically alter his offensive approach.

Let’s first look the ten best men on base versus bases empty splits.

Aaron Miles, he of the career .296 wOBA, produced .143 wOBA points better with men on base than with the bases empty. With that, we crown Aaron Miles the extreme positive split king of 2011, which naturally means that he is the best clutch hitter amongst these 10 hitters. Er… not so fast. Miles is first on that list because he was awful in bases empty situations - in this case, it pays to be bad in bases empty situations. To correct for the fact that players with bad bases empty numbers could be seen as some of the best clutch hitters of 2011, I compared a player’s offensive performance with men on base to the average bases empty performance. Let’s look and see how the order of our top 10 list has changed.

And the cream of the crop rises. When we compare the player’s performance with men on base relative to the average bases empty situation, we are essentially negating the advantage that the players with terrible bases empty numbers had. We can now see that while Aaron Miles was a lot better with men on base given Aaron Miles standards, he was only a handful of points better given league average standards. We would be remiss to glaze over the actual top clutch hitter among the players with the most extreme positive splits, Victor Martinez. Martinez hit .141 wOBA points better with men on base, and when compared to league average, he hit .103 wOBA points better. (Detroit will miss his bat in the middle of their lineup, but in no way does his injury affect their status as the AL Central favorites, and the team that has the best chance of winning their division).

Let’s switch our focus to the ten worst men on base versus bases empty splits.

We see some very good hitters, and some very bad hitters in an order that we wouldn’t quite expect, e.g. Mike Stanton has a worse reverse split, (worse with men on base than with the bases empty), than Yuniesky Betancourt, who is always in the running for worst player in baseball. However, the same problem that plagued our first list rears its ugly head again in this list. In this case, just like the last one, it pays to hit terribly in bases empty situations. If you start out with a bad bases empty line, then you have the advantage over players who have average to above average bases empty lines. That’s exactly the reason why it looks like Yuniesky Betancourt’s reverse split is not as bad as Mike Stanton’s. To correct for this, I compared a player’s offensive performance with men on base to the average bases empty performance. Let’s take a look and see how the order of our bottom 10 list has changed.

That looks much better.* By comparing the player’s performance with men on base relative to the average bases empty situation, we are essentially negating the advantage that the players with terrible bases empty numbers had. We can now see that while Yuniesky Betancourt did not have the worst reverse split given Yuniesky Betancourt standards, he did have the worst reverse split once we adjusted for league average standards. Furthermore, Mike Stanton’s “horrific” reverse split is now avenged - with men on base, he essentially hit the same as the league average player did in bases empty situations.

Not only was that a fun exercise, but it was also a valuable example of how dangerous it can be to take numbers at face value.

* For this exercise, I will define a clutch hitter as a player who raises his level of offensive performance in men on base situations. While I know that there are other factors that should be looked at when evaluating how clutch a hitter is, defining clutch in the manner that I have defined it makes following this article easier.

* Any worst 10 list with Yuniesky Betancourt at the top of the list is bound to be somewhat accurate.

Nota bene: League average wOBA with men on base numbers were only taken from qualified hitters, so it isn’t really the league average, but the average amongst all qualified hitters.

It’s been eighty six days and this picture still makes me...

Sun, 15 Jan 2012 23:05:33 -0500

It’s been eighty six days and this picture still makes me giddy.

Stat of the Week: WAR (Wins Above Replacement)

Sun, 15 Jan 2012 00:04:23 -0500

In the past two weeks, we looked at two offensive statistics that evaluate a player’s overall offensive contribution, wOBA and wRC+. This week, we will attempt to evaluate a player’s entire contribution - including a position player’s offensive and defensive value, and a pitcher’s run prevention value. This will be a two-part series: one part will be dedicated to position players and another to pitchers.

Wins Above Replacement (WAR) attempts to evaluate a player’s entire contribution. It essentially represents the value that a team receives from a player above and beyond the value that a replacement-level player would bring. A replacement player is usually considered a AAAA player - a player that is better than a AAA player, but not good enough to be a major league player - one that can be picked up as a minor league free agent, or via a cheap trade. A position player’s value above replacement is determined by four components - batting, fielding, defensive position, and a replacement level adjustment. Sum up the run values of these four components, and you arrive at a player’s WAR.

Batting

In order to arrive at the number of runs above average that a player was offensively, you convert the player’s wOBA to wRAA, which represents offensive runs above average. The conversion formula is as follows:

wRAA = ((wOBA - lgwOBA)/Scale) * PA

The formula essentially subtracts the league average wOBA from a player’s actual wOBA in order to calculate the player’s contribution above the average contribution. It then divides the difference by a scale factor that is meant to adjust for the specific season’s offensive environment. Finally we multiply the quotient by the number of plate appearances the player accumulated during the season to arrive at his wRAA (Weighted Runs Above Average).

Once you have a player’s wRAA, you have to make s slight adjustment to it to control for park effects. A player who calls Petco Park his home will see his wRAA adjusted to reflect the fact that runs are more valuable at Petco than, for example, at Fenway Park; his batting value will be higher than his wRAA. Similarly, a player who calls Fenway Park home will see his wRAA adjusted to reflect that runs are easier to come by than the average park; his batting value will be lower than his wRAA.

That’s batting value in a nutshell. Now let’s move on to fielding.

Fielding

In order to arrive at the number of runs a player was worth in the field, you just sum up a player’s UZR values from each position that he played during the year.

While this part seems very simple, there are some important things to note about the fielding component; but first, let me describe UZR. UZR, or Ultimate Zone Rating, evaluates a player’s range and error rate and packages them together to arrive at the number of runs above or below average a fielder is relative to the league average at the player’s position. The last few words of that last statement were important because a shortstop with a +10 UZR is not equivalent to a second baseman with a +10 UZR. Therefore, we need to adjust these UZR values in order to account for these positional differences. However, for the sake of clarity, sabermetricians decided to break up a player’s value into as many clearly defined parts as possible. They wanted to strip this positional adjustment factor away from any of the other factors - batting and fielding - and gave it it’s own section in the WAR formula.

Without further delay, we will move on to the defensive position (or positional adjustment) section.

Defensive Position (or Positional Adjustment)

The purpose behind valuing a player’s defensive position stems from the fact that all positions are not created equal - some positions are significantly more difficult to play than others. For example, it is much more difficult to find a +5 shortstop than it is to find a +5 first baseman. We need to represent this when we compile WAR.

Here are the positional adjustments that FanGraphs uses:

Catcher: +12.5 runs

First Base: -12.5 runs

Second Base: +2.5 runs

Third Base: +2.5 runs

Shortstop: +7.5 runs

Left Field: -7.5 runs

Center Field: +2.5 runs

Right Field: -7.5 runs

Designated Hitter: -17.5 runs

The adjustments essentially represent (i) the difficulty of defense at the given position, and (ii) the level of scarcity associated with that position at the major league level. For example, (i) catcher is a more difficult position to play than first base, and (ii) it is more difficult to find a major league catcher than it is a major league first baseman. Because of these two facts, a catcher is given an additional 12.5 runs, while a first baseman is docked 12.5 runs.

For more on how exactly these run values were determined, FanGraphs points us to these threads at The Book blog.

We’re not entirely done with the positional adjustments yet. Since the adjustments are calculated per 162 defensive games, we must multiply a player’s positional adjustment by the proportion of games he played in a season. For example, if a shortstop played 140 of his team’s 162 games, his positional adjustment would be (+7.5 * (140/162)), which equals 6.48 runs. This correction for playing time also helps provide a more accurate picture of the value of players who play multiple positions. If a player played second base, shortstop, and third base in a given season, we would calculate a positional adjustment for each position and then sum them up to arrive at the player’s overall positional adjustment.

Now that we have adjusted for the player’s defensive position, we have thoroughly evaluated a player’s value above or below average. However, in order to get a complete picture of a player’s value, we must define what average means, and add that value to the value that we have thus far calculated. Remember, it is Wins Above Replacement not Wins Above Average.

Replacement Level Adjustment

If we knew how much a league average player was worth, then we could just add that value to what we have thus far and we would be done calculating a player’s WAR. Unfortunately, we currently don’t have a fixed level for what a league average player is worth. Thus we have to look for the next lowest standard. That brings us to the league minimum player. $400,000 is the least any player in the major leagues can be paid. We peg this value as replacement level.

Now all we need to complete our WAR system is to find the difference between an average player and a replacement level player. As I mentioned earlier in this post, a replacement level player is someone who has more ability than an average AAA player, but not enough ability to play in the major leagues. Thanks to some research by Sean Smith, we know that the expected value of a replacement level player is about -20 runs for every 600 PA. Therefore, the formula for calculating the replacement level adjustment is simply (20/600 * PA). Every additional plate appearance that a player collects during a season, means that the team will give one less plate appearance to a replacement level player. Therefore a player is credited this adjustment based on how frequently he plays, and consequently how infrequently a replacement level player plays in his place. For example, if a player collected 500 plate appearances during the course of a season, his replacement level adjustment would be (20/600 * 500), which equals 16.67 runs.

With the replacement level adjustment we have now adjusted the scale so that the baseline value is $400,000 at zero wins. We have filled the value gap between replacement level and major league average, and can now appropriately evaluate a player’s contribution above replacement level.

Next up, we convert these runs above replacement to wins.

The Rest

In order to understand how runs are converted into wins, we will briefly look at the pythagorean formula for expected win-loss records. The Pythagorean Winning Percentage formula states that you can get a good estimate of a team’s winning percentage by the following:

Pythag Win % = (Runs Scored^2)/(Runs Scored^2 + Runs Allowed^2)

Now let’s say that a team scored 800 runs and allowed 800 runs. The team’s Pythagorean Winning Percentage would be .500, which translates to 81 wins. Now let’s say that the team scored 10 fewer runs, so it scored 790 runs and allowed 800 runs. The team’s Pythagorean Winning Percentage would now be .493, which translates to 79.98 wins. As we can see, a win is effectively worth 10 runs; when the team scored 10 fewer runs, it lost 1.02 wins. This 10 runs per win ratio has become a standard within the sabermetric community.

Now, In order to convert a player’s runs above replacement value to Wins Above Replacement, all you have to do is divide the runs above replacement by 10. Voila! We have now calculated a player’s value above replacement in the form of wins.

In my next post, I will put this method to the test and walk us through the calculation of a specific player’s WAR in all its mathematical glory.

A Look at Paul Maholm

Fri, 13 Jan 2012 00:34:00 -0500

I wrote the following piece for Bleed Cubbie Blue - a Chicago Cubs blog. I’ve posted it here in order to keep all of my work in one place.

Paul Maholm is the latest in a long list of acquisitions made by TheoJed. Maholm, now 29, was selected by the Pirates with the 8th overall pick in the 2003 draft.

Since 2006 - his first full big league season - Maholm has averaged 183.7 IP per season, which ranks 22nd of all pitchers that pitched between 2006 and 2011. While he has displayed great durability in the past, his 2011 season was cut short as a result of a shoulder strain. Fortunately, it doesn’t seem like it was much as he was cleared for workouts on October 24th. Maholm’s ability to stay on the field will be a breath of fresh air for a Cubs team that had a variety of injuries plague it’s rotation last year.

Let’s take a look at what Maholm has produced in the past, and what he could produce moving forward.

Over the course of the past six years, (not including the 41.1 innings that he pitched in 2005), Maholm has posted a wide range of pitching lines. His line has been as bad as a 4.76 ERA/4.81 FIP/4.59 xFIP, (his first season), and as good as a 3.66 ERA/3.78 FIP/4.03 xFIP, (his 2011 season). Below is a chart with Maholm’s career numbers.

In general, Maholm has been improving - aside from 2010, Maholm’s FIP has been decreasing year-by-year. Unfortunately, some of this decrease may be a result of his below average HR/FB rates over the past few years. If you take a look at his xFIP, (the same as FIP excepts it uses the league average HR/FB rate instead of the pitcher’s HR/FB rate), you’ll see much more varied results.

That said, let’s look at something Maholm is clearly good at: inducing ground balls. Since being called up to the majors, Maholm has shown a knack for getting ground balls. Below are his ground ball rates by season:

At his best, Maholm induced ground balls at a rate that would put him in the 90th percentile amongst all pitchers. While his ground ball rate has been trending slightly down for the past couple of years, it is still well above average, and ranked close to the 80th percentile amongst all pitchers in 2011.

On the other hand, I do have a couple of concerns with some of Maholm’s peripherals. His SwStr% has fallen every year since his career high of 8.4% in 2008; it stood at 5.7% in 2011, (well below the 8.6% league average). Given his declining SwStr%, Maholm’s Contact% has increased since 2008, rising to a career-high 86.9%, (well above the 80.7% league average). Furthermore, Maholm has had a history of high HR/FB rates. He posted three straight seasons with a HR/FB rate above 12.0%. Fortunately, in the three years since 2008, Maholm’s HR/FB rates have hovered around 7.5%, (well below league average, which was 9.5% in 2010). While some of this may have been a result of luck, Maholm did change his pitch selection after 2008. He cut back on throwing his fastball in 2009 - throwing it 8.1% less than he did in 2008 - and instead chose to throw his CB% (15.9% in 2008 | 17.7% in 2009) and CH% (10.1% in 2008 | 16.2% in 2009) more frequently in 2009. This change in pitch selection as an explanation for the decreased HR/FB rates is somewhat reassuring.

Maholm’s ability to induce ground balls is his most valuable skill. If he can continue to keep his GB% high, Maholm can continue to be a league average starter, (his career FIP- of 100 is the definition of league average).

At $4.75 million for one year with a club option for $6.5 million in 2013, Maholm comes at a bargain. He has averaged 2.1 WAR per year over his career, and 2.5 WAR per year over the past four years. At 2.5 WAR, Maholm has, on average, been worth anywhere between $10 and $12 million dollars a year. Maholm could conceivably be worth his entire contract, (assuming the club option is picked up) in one year.

While Maholm isn’t necessarily the young pitcher that you’d expect a team to build around, signing Maholm opens up a few different possibilities:

1. Maholm could fill a spot in the rotation left by a Garza trade.

2. Maholm could fill a void left by Garza or Dempster in 2013.

3. Maholm could be traded this July, or next off-season, and net a prospect or two.*

4. Maholm could become a long-term fixture at the back-end of the rotation.

Maholm’s another asset in the cupboard, and at the cost that he comes at, is another shrewd move by TheoJed that opens up a bunch of possibilities.

* It might not be in our best interest to consider trading a bunch of the free agents that we have singed, (this matters more with a pitcher like Maholm or a player like DeJesus as opposed to someone like Sonnanstine or Corpas), for the following reason: if we sign people to major league contracts with the intention of flipping them at the deadline, or in the middle of their deal, free agents may be wary of signing with us in the future and may end up choosing a different team to sign with because they’re scared that they’ll just be another asset that we leverage in a trade. I’m not sure how important this effect is - it might be the case that certain players don’t mind being traded - but I think it’s something worth mentioning.

A Look at Chris Volstad

Thu, 05 Jan 2012 00:54:00 -0500

I wrote the following piece for Bleed Cubbie Blue - a Chicago Cubs blog. I’ve posted it here in order to keep all of my work in one place.

Chris Volstad, who just turned 25 at the end of this past season, was drafted out of high school with the 16th pick in the 2005 draft. In 2006, he was named the Marlins’ #1 prospect by Baseball America, and just cracked the Top 100 prospects list - he came in at 97. In 2007, he jumped up the Top 100 prospects list and landed at #40, subsequently falling to #58 in 2008.

I’ll be looking at each year of Volstad’s career, so the following chart should help you follow along.

Volstad was called up to the majors in 2008, and has had mixed results since. In the 84.1 innings that he pitched in 2008, Volstad put up a 2.88 ERA/3.82 FIP/4.55 xFIP line, which was worth 1.5 WAR. As you could probably tell by his line, he was pretty lucky in 2008. His .271 BABIP, (career average .295 BABIP), and 3.9% HR/FB, (career average 12.3% HR/FB), have been the lowest of his career, while his 77.1 LOB%, (career average 70.4% LOB%), has been the highest of his career.

His luck dried up in 2009 - he actually ended up being unlucky - and he posted a somewhat atrocious line: 5.21 ERA/5.29 FIP/4.29 xFIP and a .3 WAR in 159.0 innings pitched. While his BABIP and LOB% came closer to his career averages - and league averages - his HR/FB% spiked to 17.5%. To put that a couple of different ways: his HR/9 increased from .32 to 1.64; he gave up 3 HRs in 2008 and 29 HRs in 2009, (albeit in roughly twice the innings).

In 2010, his line improved to the tune of a 4.58 ERA/4.34 FIP/4.43 xFIP due in large part to his decreased HR/FB rate.

While Volstad’s HR/FB spiked once again in 2011, he had arguably his best year in the majors from a peripherals standpoint. Volstad posted his best K/9 and BB/9 numbers, 6.36 and 2.66 respectively, and he induced ground balls at a very high rate of 52.3%, which according to 2010 league numbers, would rank close to the 90th percentile amongst all qualified pitchers.

While some may be concerned about how his HR/FB and HR/9 numbers will translate to Wrigely Field, here is a collection of statistics, statements, and images that should help quell your fears. HR/FB rates are highly variable from year to year and tend to regress toward league average, so Volstad will likely have a lower HR/FB rate moving forward. In terms of Park Factor, Sun Life Stadium had a .991 runs factor, while Wrigely had a .934 runs factor in 2011. Furthermore, Sun Life Stadium’s HR factor was .941 while Wrigley’s HR factor was .987, not a terribly large difference, and one that could be offset in the aggregate by the aforementioned difference in runs factor. The last reassuring point will come in the form of the following image:

The above image maps all of the hits and outs Chris Volstad recorded at Sun Life Stadium onto Wrigley Field.* Of the seven home runs that Volstad gave up at Sun Life Stadium, five would have been home runs at Wrigely, (I’m counting the one that’s on top of the left field wall as a home run), and only one non-home run in Sun Life Stadium would have been a home run at Wrigley, (the double to deep center field). So, of the hits and outs that Volstad recorded at Sun Life Stadium, he gave up 7 home runs at Sun Life, which would have theoretically been 6 home runs at Wrigley. Volstad’s move to Wrigley should not result in an increase in his HR/FB rate; in fact, Volstad will likely have a lower HR/FB rate going forward.

If Volstad continues to improve upon his K/9 and BB/9 numbers, and if his BABIP and HR/FB rates regress to the average - which isn’t a huge “if” - he could become a very valuable middle of the rotation starter over the course of the next three years. In my opinion, Volstad is a pretty impressive return for Zambrano given the situation. Well done, TheoJed.

* These plots are taken from Gameday hit-location data, which track where the ball was fielded, not where the ball landed.

Thanks to MLB Gameday BIP Location.

Team Composition of World Series Winners

Fri, 30 Dec 2011 13:12:00 -0500

As I was flipping through a friend’s copy of Flip Flop Fly Ball, I came across a very interesting infographic titled “World Series Winners: How the Players Were Acquired, 2000 - 2010.” It essentially color coded the players on each of the World Series winning teams according to the way that they were acquired. I found this fascinating, and decided to convert the infographic into numbers. I also added 2011 to the data set. Below is a summary of the numbers, followed by a graph highlighting an interesting trend:

The trend of World Series winning teams acquiring more players from the amateur draft is quite apparent. Aside from the 2002 Angels, none of the World Series winning teams between 2000 and 2005 had more than 3 players that they acquired via the amateur draft. Between 2006 and 2011, every World Series winning team had at least 6 players that they acquired via the amateur draft.

The trends regarding free agents and players who were acquired via trade are not as clear. While trades seemed to be on the decline between 2005 and 2010, the Cardinals acquired 9 of their players via trade. Free agency has been all over the place, and is likely more of a function of a team’s individual situation rather than league-wide trends.

While there is no one way to go about creating a World Series winner, the rising prevalence of player’s from the amateur draft is an interesting trend to note.

At some point, I’d like to further this discussion with (i) a study of the composition of World Series winning teams prior to 2000 in order to see if the rise of the amateur draft is a brand new phenomenon, or something that has already occurred in the past, and (ii) a study of the composition of all 30 teams on an annual basis in order to determine the relationship between specific attributes of team composition and winning percentage.

Nota bene: Any analysis of a dataset with 11 points has to be taken with a grain of salt as it’s quite a small sample size.

Playing with a Decade's Worth of Line Scores

Wed, 28 Dec 2011 21:02:45 -0500

I downloaded the line scores all of the games that were played between 2000 and 2010. I removed all of the extra inning games, and games that contained innings of 10 or more runs from consideration because of the difficulty in working with them in Excel. Fortunately, that still left me with 24371 games.

At first, I was interested in quantifying home-field advantage, which is a relatively simple task. According to my results, the home team won 54.5 percent of the nine-inning games between 2000 and 2010. After doing all of the work to set up the data set of games within Excel, I felt it a shame to stop there. So I quantified another advantage of sorts: scoring first. How often do teams that score first win?

According to the data set, teams that scored first won 67.0 percent of the time. What’s more interesting though, is the breakdown of win expectancy based on the number of runs that were scored in the first run-scoring inning - the first inning that a run was scored in. How valuable is scoring one run first versus scoring two runs and so on. Below is a chart that sums up the results.

It’s interesting to see that the second run is the most valuable run from a marginal value standpoint.* A team that scored one run in the first run-scoring inning won 59.2 percent of the time, while a team that scored two runs in the first run-scoring inning won 70.4 percent of the time. The 11.3 percent change in win expectancy is the highest change among all consecutive pairs of runs. The marginal value of the second run is followed very closely by the marginal value of the fourth run, which has a change in win expectancy of 11.0%.

The least valuable run from a marginal value standpoint was the 8th run, which actually had a negative effect on win expectancy; the 8th run had a change in win expectancy of -0.2 percent. Teams that scored run number 8 in the first run-scoring inning had a lower win expectancy than teams that scored 7 runs in the first run-scoring inning. While the value of the 8th run is definitely low, it doesn’t make logical sense for it to be below zero. This is most certainly the result of a small sample size, as there were only 33 games in which 8 runs were scored in the first run-scoring inning. It is much more likely that the change in win expectancy of the 8th run is between 5.9 percent, (marginal value of the 7th run), and 2.9 percent, (marginal value of the 9th run).

The first chart below shows win expectancy as a function of the number of runs scored in the first run-scoring inning, while the second chart shows the diminishing marginal returns of runs scored in the first run-scoring inning.

While the returns to the runs scored in the first run-scoring inning are jumpy, the general trend of diminishing marginal returns of runs scored in the first run-scoring inning is quite apparent, and certainly confirmed once the trendline is considered.

While numbers like these have certainly been derived by many before, deriving these numbers for oneself is always a rewarding experience.

* With the assumption that the baseline for win expectancy is 50.0 percent.

Stat of the Week: wRC+ (Weighted Runs Created plus)

Tue, 27 Dec 2011 11:52:31 -0500

Last week, we took a look at Weighted On-Base Average, wOBA, which represents a player’s total offensive value in the form of a percentage. This week, we will attempt to both index a player’s total offensive value to the league average and adjust it for ballpark factors with Weighted Runs Created plus, or wRC+.

wRC+ was created in response to OPS+, which measures On-Base plus Slugging Percentage, OPS, against league average and adjusts it for ballpark factors. Measuring OPS against league average essentially adjusts for the run-scoring environment in a given year. In 1925, the league average OPS was .765, while the league average OPS in 1967 was .664. Let’s take two hitters, hitter A and hitter B. Hitter A played in 1925, while hitter B played in 1967. Both hitter A and hitter B each had a .765 OPS. However, hitter B did it in a season where the average OPS was .664 as opposed to .765. Hitter A was a league average player, while hitter B was approximately 30% better than league average, according to OPS+, where,

OPS+ = 100 * [(OBP/lgOBP) + (SLG/lgSLG) - 1].

As you can see, adjusting for the run-scoring environment of a given year is important in evaluating a player’s true offensive value. OPS+ also adjusts OPS for ballpark factors - hitter C benefitted from playing in the Ballpark at Arlington, while hitter D was hurt from playing in PETCO park. You can also see that adjusting for ballpark factors is important in evaluating’s a player’s true offensive value.

However, since OPS is aflawed statistic, sabermetricians decided to create a more accurate statistic to evaluate offensive value adjusted for run-scoring environment and ballpark factors. As we saw last week, wOBA is much better at evaluating a player’s offensive value than OPS; thus, we will use wOBA to create a league adjusted and ballpark adjusted statistic that encompasses a player’s offensive value.

Weighted Runs Created, wRC, measures a player’s total offensive value by runs. It uses wOBA to calculate the total runs created as a result of a player’s offense.

wRC = [((wOBA - lgwOBA)/wOBAScale) + (lgR/PA)] * PA.

It essentially takes a player’s wOBA, subtracts the league average wOBA, and then divides the difference by wOBAScale - a multiplier that converts wOBA to runs per plate appearance; it then adds the league average runs per plate appearance, and multiplies the resulting sum by the number of plate appearances the player had.* We now have a player’s wRC.

In order to get wRC+, you simply divide a player’s wRC by the league average wRC, and multiply it by 100. A wRC+ of 100 is average. A wRC+ greater than 100 is above average, and every point above 100 is a percentage point above league average. For example, a 130 wRC+ means a player created 30% more runs than the league average. Likewise, a wRC+ less than 100 is below average, and every point below 100 is a percentage point below league average. For example, a 70 wRC+ means a player created 30% fewer runs than the league average. wRC+ translates wOBA into a run-based measure of a player’s offensive value, while adjusting for both the player’s run-scoring environment and for ballpark factors.

With wRC+, you can now compare Babe Ruth and Albert Pujols, even though they played in different run-environments and different ballparks.

* In other words, wRC converts the player’s excess wOBA into runs per plate appearance above league average, adds league average runs per plate appearance, and multiplies by plate appearances to get the total runs created.