F/X Visualizations January 22, 2010
How Do Pitchers Change Their Approach Against Good Hitters?

Nick Steiner, who over the last couple months has been producing some great pitchf/x content, had an interesting piece asking how many HRs Albert Pujols would hit if he saw the same pitches as Juan Pierre. He wrote the piece in mid-September and concluded he would have hit 62 HRs up to that point in the season. It is a very cool question, and implicit in it the question is the understanding that pitchers pitch differently to good hitters than they do to not-quite-as good hitters.

I think this is a very interesting idea to explore further, and the PITCHF/X data set is a great tool for it. To do that I created two groups of hitters. First the twenty regulars with the top wOBAs in 2009 (wOBA is a stat of TangoTiger's construction that measures overall offensive impact), and second the twenty regulars with the lowest wOBAs in 2009.

One common assumption is that good hitters see fewer fastballs and this analysis bears this out. The top-wOBA group saw 58.4% fastballs versus 61.5% for the bottom-wOBA group. But that actually understates the difference. The top group saw many more pitches in hitter's counts and pitchers throw more fastballs in hitter's counts. It is best to consider the difference in each count.

```Fastball Frequency by count
top   bottom
0-0   0.626    0.663
0-1   0.551    0.545
0-2   0.549    0.511

1-0   0.587    0.664
1-1   0.542    0.559
1-2   0.497    0.484

2-0   0.659    0.780
2-1   0.579    0.679
2-2   0.530    0.528

3-0   0.717    0.848
3-1   0.735    0.823
3-2   0.591    0.705
```

Here you can see the difference is largely driven by hitter's counts (e.g., 1-0, 2-0, 2-1, 3-0, 3-1) where the top group saw on average 10% fewer fastballs than the bottom group. Interestingly in pitcher's counts (e.g., 1-2, 2-2) the differences are very small.

The next thing we can look at is where those pitches end up. Here I plot the location of fastballs to the two groups. Areas where the top-wOBA group sees more pitches are red and where the bottom-wOBA group are blue.

Not surprisingly the top group sees many fewer balls in the strike zone. The extra pitches end up inside more than they end up outside, which is a little surprising to me. This also shows that the pattern of good hitters seeing fewer pitches in the zone is not just a result of them seeing fewer fastballs, which are more likely to be in the zone. That is good hitters see fewer fastballs AND the ones they do see are less likely to be in the strike zone.

Overall the top group saw 47.6% of their pitches in the strike zone, compared with 51.8% for the bottom group. But again this 4% difference understates the difference because the top group gets more hitter's counts in which pitchers should be around the zone. Breaking up by count we see:

```Proportion of pitches in the strike zone
top   bottom
0-0   0.507    0.548
0-1   0.428    0.473
0-2   0.325    0.325

1-0   0.505    0.575
1-1   0.478    0.526
1-2   0.376    0.424

2-0   0.505    0.592
2-1   0.545    0.580
2-2   0.443    0.489

3-0   0.471    0.554
3-1   0.607    0.646
3-2   0.553    0.598
```

Here the difference increases to 4% to 7% in each count. It is clear the pitchers avoid the heart of the zone, and the zone as a whole, against the better batters.

This is another example where the pitchf/x data support the prevailing assumptions: good hitters see fewer fastballs and fewer pitches in the zone. But there are some interesting patterns: the smaller frequency of fastballs seen by good batters is largely driven by a much smaller frequency in hitter's counts -- not all counts across the board -- and the out of zone fastballs that good hitters see are more likely to be inside than outside.

Very, very cool.

Good stuff, Dave. I didn't know good hitters saw more fastballs in 0-2 and 1-2 counts than bad hitters.

Bad hitters will chase when the pitcher is ahead in the count, so throw them a breaking ball away from the center of the plate.

Great work, but I would be careful claiming that better hitters see more pitches out of the zone. You have a selection bias because you are choosing players who are known to take pitches and draw walks. This might lead to some confounding in the results. One way to get around this would be to select based on a measure that represents a hitters ability without considering their ability to draw walks/have a good eye (e.g. Slugging?). The proportion of fastballs in each count seems fine and insightful to me, given all the counts have a large enough sample size.

Sully and Jeremy, thanks guys.

Brian, that is a very good explenation for the small to nonexistant difference in fastball frequencies between good and bad hitters in pitcher's counts. Thanks. I always appericate your readership and comments.

James. I think you are right that slugging would have been a better way to break up batters than wOBA -- MGL had the same suggestion over at the book blog. But I am not sure if I understand your first comment about selection bias. The better hitters do take more walks, but I am not looking at whether the pitch was a ball or a strike, but whether it was in or out of the strike zone regardless of whether the batter swung or what it was called.

I agree with James-

For the 182 players in the 2009 MLB season who had at least 450 plate appearances, the correlation between wOBA and fastball % is about .132 while the correlation between iso and fastball % is .5; a larger sample size should help as well.

Very cool Dave. That graph in the middle is very powerful.