Baseball Musings
Baseball Musings
November 26, 2007
Does a Good Offense Improve a Defense?

One criticism leveled at the Probabilistic Model of Range this year is that due to building the models based on the visiting team fielders, teams with good offenses get a bonus defensively. The example given is the Yankees, but there are other high offense teams ranked high in terms of PMR.

The idea is that since the Yankees hit well, their opponents DER must by definition be low. A ball put in play by the Yankees must have a lower probability of being turned into an out. This causes the model to underestimate the fielding ability of opponents, and over estimate the fielding ability of the Yankees. If the model contained one parameter, ballpark, then this would be absolutely true. However, there are six parameters, including a vector indicating the direction of the ball. I propose that the Yankees hit better than their opponents not because a random ball in play has a higher probability of falling for a hit, but because the Yankees do a better job of hitting balls where they are tough to field.

The following table shows the number of ground balls hit by the Yankees and their opponents by vector:

Vector Yankees Opponents Predicted DER
254 4 0.000
261214 0.000
273726 0.766
2811857 0.898
29175118 0.706
30193156 0.671
31148119 0.844
3211182 0.934
33164136 0.868
34114105 0.585
3510074 0.535
36117124 0.624
37101108 0.617
38116150 0.838
39119131 0.865
40163139 0.764
41165174 0.550
42110130 0.688
436155 0.847
443540 0.572
457 13 0.010
465 5 0.000

As you can see, the low probability vectors are 29-30, the shortstop hole, 34-37, up the middle, 41-42, the second base hole, and 44, right down the first base line. I'm not looking at the foul vectors where a ball is always a hit. Breaking these down:

Ground ballsYankeesOpponents
In Holes11101029
At Fielders882895

So the Yankees hit more grounders where they are less likely to be fielded, and fewer grounders where they are more likely to be fielded than their opponents. Later I want to look at how the Yankees field home and road. If they field much better at home, then the objection still my have some validity.


Posted by David Pinto at 08:27 AM | Defense • | Probabilistic Model of Range | TrackBack (0)
Comments

David,
back in one of your earliest posts about PMR, you said that you computed the probability of an out for a set of parameters using a maximum likelihood estimate. Does this mean that the predicted DER shown for a particular vector is not independent of the results for surrounding vectors? Can you explain this aspect of PMR in more detail? [Or can you point me to a more detailed exposition if I missed it?]

Also, I don't have the raw detailed data which you do, but I've aggregated pbp data from fangraphs' playlogs, which use BIS data, and can report that the yankees batted .261 on ground balls at home, compared to .236 on the road. Yankee pitchers allowed a .238 average at home and .240 at home. [In 2007, MLB averages were .243 by the home team and .236 by the visiting team] . There was a similar profile on line drives; yankee hitters batted .832 at home and .769 on the road; yankee pitchers allowed a .743 average at home and .755 on the road. [MLB averages, .771 at home and .769 on the road.]

Everything looks pretty average except the performance of yankee hitters at yankee stadium. The skew in hitting direction which you document may still overlap heavily with the park ... [If yankee hitters had more success on batted balls specifically at home, that should involve some combination of hitting the ball in tougher directions, and just hitting the ball harder.]

Posted by: joe arthur at November 26, 2007 06:47 PM

David:
If I've done the calculations correctly, I don't think the table makes the point you want. If you calculate the two overall DERs for GBs, the Yankees are .725 and opponents are .714. So the Yanks hit into vectors where balls are easier to field, not harder.

In any case, I think the most important comparison is the Yankee hitters' actual DER at home in each vector compared to the MLB average for that vector. If Yankee hitters tend to have a lower DER, then they must be hitting the ball harder. (The fact that an incredible 62% of the Yanks' PAs went to LHHs may play a role too.) And in a visitor-model, that would in turn make Yankee infielders look better than they are.

Posted by: Guy at November 26, 2007 10:43 PM

Guy,

you're right. The extra balls hit to the holes are more than completely cancelled out by the extra balls hit to the "easy" vector 28.

Posted by: joe arthur at November 26, 2007 11:35 PM
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