How likely are walks and strikeouts by count?

Now that baseball is back (for now, at least…) I thought it would be fun to do another look at some stats! Specifically, from a given ball-strike count, what are the odds that the plate appearance ends in a walk or a strikeout?

Like last time, I extended the parsing code of my baseball win expectancy finder to gather these statistics. (it’s available on GitHub, see CountsToWalksAndStrikeoutsReport in parseretrosheet.py) Without further adieu, here are the numbers!

0-0
walk: 8.2%
strikeout: 17.1%
0-1
4.6%
25.1%
0-2
2.8%
41.3%
1-0
14.7%
13.4%
1-1
8.5%
21.9%
1-2
5.3%
37.8%
2-0
30.3%
9.7%
2-1
17.6%
17.1%
2-2
11.6%
32.3%
3-0
64.4%
5.0%
3-1
41.8%
9.7%
3-2
30.1%
22.3%
Chances that a plate appearance ends in a walk or a strikeout from a given ball-strike count

Here are some interesting observations:

  • From any given count, getting a ball doubles your chances getting a walk. This isn’t exact, but it does almost hold at every count, which is interesting. At first I wondered if you could model this as there being a constant chance of getting a ball or a strike from any count – this would also explain why from a 0-0 count a strikeout is twice as likely as a walk. (since you only need 3 strikes for a strikeout but 4 balls for a walk) But there doesn’t seem to be a similar relationship for strikes.
  • The 1-0 and 2-1 counts have basically the same probability for a walk as a strikeout, which seems reasonable since it takes the same number of balls to get a walk and strikes to make a strikeout. But for a 3-2 count there are significantly more walks than strikeouts. I’m not really sure what to make of that.
  • 3-0 is a weird count. There is evidence (not from this data) that the strike zone gets wider at this count, so the same pitch that might have been a ball some other time will be a strike here. But you still have a 2/3 chance of ending up getting a walk, which is very high! It’s rare to get a strikeout after getting to this count (5.0%), but not as rare as getting a walk after getting to 0-2 (2.8%)
  • You’re significantly more likely to get a walk from 3-0 than a strikeout from 0-2. This kind of lines up with the 3-2 weirdness – maybe balls are just a bit more likely than strikes, all else being equal?

This is a sample of just under 6 million plate appearances, although the numbers for counts other than 0-0 are fewer. The least common count was 3-0 – there are just under 300,000 of these. This is all pulled from Retrosheet data that have pitches recorded which range from 1957-2019, but it’s heavily weighted from 1988-2019 (where all games have pitch data, I believe); before that seasons had 1,000-10,000 plate appearances with pitch data, after that it was more like 160,000.

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