### Evaluating Outfielders’ Defense Using Fieldf/x

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 / √[(a _{2}- a_{1})+(b_{2}- b_{1})]^{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 / √[(a _{2}- a_{1})+(b_{2}- b_{1})]^{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.