Home field advantage on pitch calls, by count

Did a bit of last minute research before putting together my presentation on home field advantage (HFA) for the SABR convention.

In "Scorecasting," Toby Moskowitz and Jon Wertheim wrote that HFA on ball-strike calls varies with the importance of the situation. They said that in clutch plate appearances, HFA is very high -- but, when it doesn't matter much, HFA actually goes the *other* way, and visiting pitchers actually get the benefit of more called strikes than home batters. They concluded that biased umpires are favoring the home team, but trying to compensate the visiting team by calling more strikes for them when it's not as important.

A few months ago, MGL did a study, and found some confirmation for Scorecasting's results. He did find that HFA went up with leverage. However, he didn't find any situations in which the home team actually had an advantage -- just situations in which they had less of an advantage than usual.

So I tried the same thing today (but not as rigorously). I used 2000-2009 Retrosheet data, and I got similar results.

Overall, not looking at leverage yet, the home pitchers got 0.6 percentage points more strikes than the visiting pitchers. (Specifically, the visiting team had 31.2% of their called pitches ruled strikes, but the home team had 31.8% of theirs ruled strikes.)

In certain higher-leverage situations (for which I used 8th inning or later, score tied), the difference was higher -- 1.2 percentage points. In another higher-leverage situation (9th inning or later, tying run at the plate), the difference was also higher -- 1.0 percentage points.

But in lower-leverage situations (one team leads by 5 runs or more), the difference was only 0.3 points.

Summary:

0.3 -- one team leading by 5+ runs
0.6 -- all situations
1.0 -- ninth inning+, tying run at bat
1.2 -- eighth inning+, score tied

Another thing I did is, for all these situations, I computed the HFA in terms of the outcomes of the plate appearances. Here are the home team advantages by wOBA points:

.0010 -- one team leading by 5+ runs
.0013 -- all situations
.0018 -- ninth inning+, tying run at bat
.0025 -- eighth inning+, score tied

As expected, an excellent correlation between HFA on ball/strike, and HFA on eventual outcome.

But here's something interesting: the home/road difference on what percentage of pitches were swung at (including foul balls and balls in play):

0.48 -- one team leading by 5+ runs
0.54 -- all situations
0.88 -- ninth inning+, tying run at bat
0.59 -- eighth inning+, score tied

For instance, overall, home teams swung at 44.9 percent of pitches, but road teams swung at 45.4 percent of pitches.

So, not only did home teams have fewer strikes *called* against them (first table), but they also had fewer *swings* (third table). That suggests that visiting teams actually throw fewer strikes than home teams, since this results holds even on pitches where the umpire has no say.

But, you could argue otherwise. It's possible that the swing difference is because the home batters know they're going to get more marginal calls in their favor, so they don't swing on iffy pitches in order to work a walk. It's also possible that batters are worse on the road, and they can't tell a good pitch from a bad pitch quite as well as they can at home.

So I'm not sure if we can draw any conclusions from this, but I thought it was worth mentioning.

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Anyway, that does confirm the "Scorecasting" basic findings. But it occurs to me that what might be causing this is just the different ball/strike counts.

As I said above, when an umpire called a home pitch, it was a strike 31.8 percent of the time. But, I checked, and when an umpire called a home pitch *on an 0-0 count*, it was a strike 43.0 percent of the time. That's a big difference. Maybe it extends to home/road differences too?

It does. The HFA was also much bigger on 0-0: instead of 0.6 percentage points, it was 0.9 percentage points.

So maybe HFA is lower in low-leverage situations just because when a game is a blowout, teams pitch differently and you get a different frequency of the different counts. So, what I did was break down all pitches by count, and by leverage group. The leverage groups were:

High ..... 8th inning or later, 0-1 run difference
Low ...... One team leading by 6+ runs
Average .. All other plate appearances.

Here are the results, in percentage points of HFA (called strikes as a percentage of all called pitches). Standard errors are in parentheses.

-------------------------------- Leverage -----------------
----------------- Average -------- High ----------- Low ---
-----------------------------------------------------------
0-0 count ..... 1.03 (0.09) ... 1.02 (0.20) ... 0.66 (0.28)
0-1 count ..... 0.63 (0.14) ... 0.77 (0.31) ... 0.79 (0.43)
0-2 count ..... 0.51 (0.20) ... 0.62 (0.45) .. -0.13 (0.64)
1-0 count ..... 0.92 (0.14) ... 1.54 (0.31) ... 0.38 (0.44)
1-1 count ..... 0.65 (0.15) ... 0.35 (0.34) .. -0.22 (0.48)
1-2 count ..... 0.83 (0.17) ... 0.72 (0.37) ... 0.56 (0.53)
2-0 count ..... 0.98 (0.23) ... 1.11 (0.52) ... 1.18 (0.75)
2-1 count ..... 0.80 (0.20) ... 0.75 (0.46) ... 0.22 (0.65)
2-2 count ..... 0.56 (0.18) ... 0.44 (0.40) ... 1.05 (0.58)
3-0 count ..... 1.07 (0.37) ... 2.35 (0.86) ... 1.15 (1.20)
3-1 count ..... 0.90 (0.30) ... 1.31 (0.69) ... 0.64 (0.97)
3-2 count ..... 0.56 (0.22) ... 1.25 (0.50) ... 1.77 (0.72)

Is there evidence here that HFA depends on leverage? If you compare the average leverage to the high leverage, you get that the high-leverage situations have a higher HFA in 7 out of the 12 cases -- not much more than average. Comparing average to low, you get more HFA for the average situations again 7 out of 12 times. And, comparing high to low, the "high" only win 8 out of 12.

Doesn't seem like much. But I think I've just diced up the data so finely that you can't see the real pattern any more. It looks like all three of the three lowest differences do appear in the low-leverage column (although that could be partly because the SDs are high there, so you expect extreme more values than in the other columns).

Here's the equally weighted average of all three columns, each column weighted by the smaller of the frequencies (home, road) in column 1:

0.82 (~ 0.04 SD) overall
0.92 (~ 0.10 SD) high leverage
0.58 (~ 0.14 SD) low leverage

So there is something there, although smaller than it looked before adjusting for count. But the differences are not statistically significant, although the low-leverage one is close.

Conclusion: from 2000 to 2009, home teams were somewhat more likely to get a strike call in higher-leverage situations than in lower-leverage situations. This is significant only at approximately p=0.1.