The impact of managerial mistakes

This postseason, there's been a surprising dearth of managerial criticism, especially given that the managers competing into October included Ned Yost, Don Mattingly and Mike Matheny, who have generally not been viewed in the kindest light by analytical fans. It could be a result of improved decision making, or just fewer bad results following the same bad process, but either way, it's been somewhat refreshing to have less bullpen- or lineup-related fury flying around the internet as a result.

The constant criticism gets tiring quickly; everyone reading it understands the basic concepts, it doesn't change how the managers do their jobs, and the actual impact of managerial decisions is relatively small. This can be hard to accept, since the points that stick in our mind are when something goes horribly wrong, and it's easy to criticize those decisions retrospectively. At the time, however, the expected difference between the actual choice and the alternative was, in all likelihood, quite small.

To demonstrate this, I'm going to go through the Royals-Blue Jays game from Saturday, picking out a few managerial decision points and trying to estimate their expected impact on the game. This game seems like a good choice, as it featured a few big swings in win expectancy and stayed competitive until the end. Obviously this can't cover every decision, since whether to bunt or not is technically a choice every batter, so I picked three that seemed impactful at the time.

Situation 1

Inning: T6
Score: KCR 0 - 1 TOR
Outs: 0
Runners: _ _ _
Pitcher: Y. Ventura
Batter: J. Donaldson
KCR Win Expectancy: 34.3% (using this calculator for ease of hypotheticals, set to 2010-2014)

This is the first notable non-move in this game, as Yost left Ventura in to pitch to the heart of the Blue Jays order for the third time. Everyone should be familiar with the times-through-the-order-penalty (hereafter TTOP), since we talk about it all the time in October, but if not, sabermetrician Mitchel Lichtman wrote a great explanation at Baseball Prospectus. The simplest takeaway is that starters are expected to be about .35 runs per nine innings worse than their overall performance would suggest on their third time through an order.

Ventura, in the regular season, had an RA9 of 4.13. He ended up getting pulled later in the inning, and was replaced by Luke Hochevar, who had a regular season RA9 of 4.09. If we bump Ventura's RA9 up by .35, to 4.48, the expected difference between him and Hochevar for the 7th was about 1/25th of a run, worth roughly 0.6 percent in win expectancy. If you put in a much better reliever, however, like Kelvin Herrera and his 2.97 RA9, the difference grows to about 14.5 percent. That obviously has an impact later in the game, so using Herrera this early might not be feasible, but it's worth noting that who gets put in as a reliever can matter much more than whether a reliever comes in or not.

Assuming it would've been Hochevar coming in, the difference is fairly slight. Teams obviously want any advantage they can get in the playoffs, but it's easy to inflate the impact of this move with the benefit of knowing how the top of the 6th actually went. The denizens of the Jays' murderer's row, Donaldson, Bautista, and Encarnacion, all reached, and after Ventura struck out Chris Colabello, Troy Tulowitzki doubled and Russell Martin walked. At that point, when Hochevar entered, two runs had scored and the Royals' WE had fallen 24 points, to 8.0 percent. It's easy to attribute all that decline to Yost leaving Ventura in, but it turns out the Blue Jays are really good at hitting. Without the benefit of hindsight, the difference between Ventura and Hochevar, or even Ventura and Herrera, is not nearly that large. Was it a bad move? Probably, but also probably not as bad as it looked.

Situation 2

Inning: B7
Score: KCR 0 - 3 TOR
Outs: 0
Runners: _ _ _
Pitcher: D. Price
Batter: B. Zobrist
TOR Win Expectancy: 90.5%

This is a very similar situation, but for the Jays and John Gibbons instead, so I won't spend as much time on it. Zobrist, like Donaldson, was hitting second, and was up for the third time. Price had been pitching well, striking out 7 and walking none, and also very efficiently. It was easy to understand why Gibbons wanted to leave him in for the 7th, if also pretty clearly wrong. MGL's research above showed that the TTOP affects high- and low-pitch count pitchers similarly. It's not merely a question of fatigue, but of batter familiarity, meaning leaving Price in was probably asking for trouble.

Doing the same analysis as above, Price's 2015 RA9 was 2.86, compared to 3.41 for Aaron Sanchez. You might note that, even with the TTOP, Price is still expected to be better than Sanchez, another suggestion that mechanically removing the starter after 18 batters is probably not the right move. But Sanchez also made 11 starts at the beginning of the year, and performed much better after moving to the bullpen, so let's give him the benefit of the doubt and use just his bullpen RA9 of 2.39. In that case, the difference between third-time-through-the-order-Price and Sanchez would be .09 runs per inning, or roughly 0.9 percent in win expectancy. Was Price at this point worse than Sanchez? Almost definitely. Was Toronto very likely to win either way? Yep! Just because they didn't doesn't mean this was an awful move.

Situation 3

Inning: T8
Score: KCR 5 - 3 TOR
Outs: 1
Runners: 1 _ _
Pitcher: A. Loup
Batter: E. Hosmer
KCR Win Expectancy: 96.2%

Lorenzo Cain was the runner on first, having just walked, but he wasn't for long, getting thrown out trying to steal second. Kansas City at this point was overwhelmingly likely to win, but Toronto's lineup is terrifying, so it's plausible to think Yost badly wanted one more insurance run, and the steal was his idea rather than Cain's.

Cain, this year, stole 28 bases and was caught 6 times, good for an 82.4 percent success rate. The Royals' win expectancy would've fallen 1.3 percent had he been caught, and... fallen 0.2 percent had he succeeded. Not really, but since 2010, home teams with a 3-run lead in the bottom of the 8th have won slightly, slightly more often with a runner on 1st and 1 out than with a runner on 2nd and 1 out. This isn't just a quirk of the time frame, either; if expanded to 1994-2014, a successful steal gives a 1 percent bump, but a caught stealing gives a 0.3 percent bump!

Clearly, it's not actually better to have a runner on first than on second; the takeaway is that a successful steal here would've done essentially nothing to the Royals' likelihood of winning the game, and an unsuccessful steal would've done just barely more than essentially nothing. If we set the impact of success at exactly zero, then the decision to send Cain cost KC about two-tenths of a percent, dropping them from 96.2 percent to 96.0 percent. You might be noticing a common thread: Was it a bad decision? Almost certainly! Was it a big deal? Absolutely not.

Again, I could keep going, but I hope the point is clear. When this game was happening, these felt like three pivotal decision points, where the game had the potential to be lost or won based in part on mistakes made by the manager. That's technically true, but as these three cases show, it's in very small part. Managerial tactics matter, but not much.

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Henry Druschel is a Contributor at Beyond the Box Score. You can follow him on Twitter at @henrydruschel.