I forgot all about this spreadsheet I put together in May. Since 1990 - which is as far back as I felt like going - there have been 53 instances of a team replacing its manager with another in-season, with each manager lasting at least 20 games. The numbers:
Manager #1:
- 1600-2153
- Total win percentage of 42.6%
- Average win percentage of 41.6%
Manager #2:
- 2140-2394
- Total win percentage of 47.2%
- Average win percentage of 46.8%
Naturally, we can assume that a big part of this is simple regression to the mean. Teams generally end up firing their managers when they're underperforming relative to expectations, and teams that are underperforming relative to their expectations tend to regress north over time. We must also be aware that (1) 53 instances isn't an enormous sample size, and (2) teams change over the course of a season, and manager #2 will not be leading the exact same team as manager #1.
Still, it's interesting. Manager #1's average winning percentage corresponds to a full-season record of 67-95. Manager #2's average winning percentage corresponds to a full-season record of 76-86.