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% |

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.