THE BOOK--Playing The Percentages In Baseball

Monday, November 29, 2010

Gameday slice bias

How much is the hit location biased based on where a fielder is normally positioned?  The following is a starting point, and as a result, will use a crude estimate.

From 1B to 3B line is 90 degrees.  The circumference of a circle is 2PI*r, or PI*r/2 for a quarter circle.  If we treat the radius as around 115 feet (meaning a spot somewhere between the 1B/3B bags and the 2B bag), then the distance from 1B to 3B bags, along a circular path is 180 feet.  Or, 1 degree = 2 feet.  I know it’s not a circle, but, we just need crude approximations.

Also remember that a SS / 2B are positioned around -16 / +16 degrees, where 0 degrees is 2B. 

Peter provided us with this data from HITf/x (FX) and GameDay (GD), based on spray angles in 4 degree slices:

rate is FX / GD.

We see that at -16 (meaning -14 to -18 degrees), groundballs are recorded by Gameday far more frequently than HITf/x is recording.  We see an enormous bias in the holes as well.

Now, let’s try an experiment.  Let’s say that the Gameday scorers agree with HITf/x perfectly on half of the batted ball locations, and are off by 4 degrees (8 feet) on the other half?  Let’s start with the 314 balls up the middle (-2 to +2 degrees).  Gameday marks 157 of those up the middle, and for the other 157 record half to the left (-6 to -2) and half to the right (+2 to +6).

At the -4 degrees (-6 to -2), HitF/x had 329 balls, of which half Gameday agrees with, and the other half are all more toward the SS side (at -8 degrees). 

So, this is what we have at -4 degrees as per Gameday:
164.5 balls that HITf/x marked at -4 degrees
78.5 balls that HITf/x marked at 0 degrees

That’s a total of 243 balls marked by Gameday at -4 degrees under this illustration, compared to the 329 actally recorded by HITf/x… but still a far away from the 204 actually recorded by Gameday.

The same thing happens at -8 degrees: of the 328, 164 are properly marked by Gameday, the rest are marked toward the SS side (at -12 degrees).  And we go on until we get to -20 degrees, where the shift happens toward the 2B bag.  This is the result of all that:

My illustration here shows that my model bridges some of the gap.  The standard deviation of the original FX/GD is 42%, while the Tango/GD is 34%.

And trying different inputs didn’t make much better difference.  If I treat anything between 50% and 75% of the HITf/x data as being perfectly recorded by Gameday, the remain balls in play are about 4 degrees (about 8 feet) biased toward where the fielder is positioned.

I think we can try to construct a more elaborate model, and we’ll probably end up at the following: about half the data from Gameday will match HITf/x, and the other half will be off by 2 to 8 degrees (4 to 16 feet).  The amount it will be off will be biased by either where a fielder is normally positioned, or whether a play was made or not, or how much space between fielders (the holes).

This is the framework I’m proposing.  Implementations will vary.