Yer out of here

Manager ejections have long been a fascination of mine. There are those who think that a manager needs to have that fire. That getting ejected is going to light a fire under the players’ asses and is going to spur them on to victory. Go Lou Piniella on them. Go Bobby Cox on ’em. That’ll show ‘em!

Others, like me, think ejections are for show. Sure, teams might be successful with a fiery manager but we shouldn’t confuse the impact of an ejection with the talent of the team.

So I wanted to dig into manager ejections a bit more. Thankfully, the Retrosheet people maintain a database of elections that spans a considerable period of time. For parsimony, I’ve selected the 1990–2020 period (2021 data isn’t yet available).

I’ve taken the ejections database and paired it withRetrosheet game data, allowing me to append ejection data to game-sheet data. The number of ejections is really low. In my dataset, each game from 1990–2020 forms its own row. I’ve limited the data for the months of April-September. Less than one percent of games have an ejection — this makes probability models (logit, probit, LPM) difficult because the events are rare. To be frank, I’m not sure if there’s a way to do it, so this is going to be pretty descriptive, top-line kind of stuff.

Some basics. From 1990–2020, managers were ejected 2,463 times. The top 10 were:
1. Bobby Cox: 124 times (shocking, I know)
2. Ron Gardenhire (83)
3. Bruce Bochy (76)
4. Clint Hurdle (64)
5. Jim Leyland (58)
6. Joe Maddon (56)
7. Tony LaRussa (54)
8. John Gibbons (53)
9. Charlie Manuel (52)
10. Lou Piniella (52)

Figure 1 plots the number of manager ejections per season. Note the upward trend in ejections beginning in 1993 (this includes the 1994 strike season) and the sharp decline represents the COVID-shortened 2020 season.

This got me thinking: can we nail down what makes managers more likely to get tossed? Not quite, unfortunately, because of the rarity of the event. But we can peel back the layers a little bit.

First, does being at home, being riled up by the crowd, have an impact? Strictly speaking, no. Home-team managers were ejected 1,238 times whereas visiting managers were ejected 1,223 times — 50.2% to 49.7%.

Second, for what reasons do managers get ejected? I broadly re-coded some of the categories in the ejection dataset (I combined arguing a call at first, second, third, and home into a single “arguing the base call” variable; I also combined “argued called third strike” into a “argued called strike”). The top 10 reasons were:
1. Balls and strikes (37.97%)
2. Call on base (17.05%)
3. Check swing (5.97%)
4. Intentional HBP (4.67%)
5. Fair/Foul call (2.3%)
6. Balk (2.1%)
7. Replay ruling (< 2%)
8. Interference non-call (< 2%)
9. Ejection of player (< 2%)
10. Warning to both teams (< 2%)

Figure 2 plots the frequency of ejection per top-5 reason in each season. Note the increase in balls and strikes and the, unsurprising, drop off in base calls with the implementation of the review system. Note, as well, the peak in intentional HBP that has since petered off.

Does the reason for which a manager gets ejected vary based on the inning in which the event occurs? Looks like it. Figure 3 plots the number of ejections in the inning in which they occurred. It plots only the top-five most frequent ejection types in the above list.

Figure 3 limits ejections to only full-length, nine inning games — extra innings are excluded. Here we can see that not only does the number of ejections increase as the game goes on but managers are more likely to be tossed for arguing balls and strikes and calls on the bases. Not entirely surprising given that these are probably high-leverage situations when teams are on edge.

Third, are manager more likely to be tossed later on in the game? Yes. Figure 4 plots the frequency of ejections by inning in which they occur and confirms Figure 3. The number increases nearly linearly as we get later into the game before dropping off into the 9th (I imagine because some games have one half inning less played). This makes sense — leverage, high-leverage, tense situations in circumstances where managers believe that a bad call can have a negative impact on their team. Of course negating the effect that calls earlier on might have had.

Fourth, does game time matter? Yes. 65% of all managers were ejected during night games.

Fifth, what about score? Score is a bit complicated. On the one hand, the ejection database identifies the inning in which a manager was ejected but doesn’t identify the specific play, nor when in the inning did the manager get tossed, nor the score of the game when the manager got tossed.

To get around this, I took the Retrosheet boxscore variable for home and away teams and made a running score based for each inning. I then summed the score up to the inning in which the manager got ejected. Cards on the table, this is problematic because it imputes the score after the inning as the score at the time the manager got ejected. It’s a rough approximation so I wouldn’t put too much stock into it.

The data show some interesting patterns. First, managers generally get tossed when losing, regardless of managing the home or away team. At ejection, 58.8% of home managers were ejected when losing, 24.5% when winning, and 15.5% tied. 62.2% of away managers were ejected when losing, 22.2% when winning, and 15.3% when tied.

Second, I wondered what the outcome of an ejection might be. This, again, is difficult given the parameters of the data. Broadly, the win/loss split isn’t as dramatic as I expected: 51% percent of managerial ejections ended with the ejected manager’s team winning compared to 49%. This does not give evidence to the idea that ejections will fire up a team and spur them on to victory — the difference is marginal.

I was then curious to see if teams generally add more runs when the manager gets ejected. Table 1 demonstrates that this isn’t necessarily the case. The findings are pretty intuitive. The average number of runs scored post-ejection dwindle as the game goes on. Obviously. When a manager is tossed in the first inning, there’s still 8 more innings to score runs. The opportunity to score runs decreases as your outs run out.

So what comes from all of this? The findings are bit hodgepodge and pretty descriptive. Overall, I think till will be a larger research project that I will develop on an individual basis. I’m a Mariners fan and one of the more insufferable parts of being a Mariners fan (besides the losing) is the people who want Scott Servais to get ejected more to show some fire. So, next I think I’ll compare Mariner-specific outcomes.

But anyway, I’ve demonstrated, at least at the surface level, that ejections don’t necessarily light a fire up players’ asses. They’re nuanced. They happen for a lot of reasons but it seems like the most obvious finding is important: it’s just baseball. Ejections don’t necessarily seem to spur a team on to victory but they also don’t necessarily hurt. They might have a team-building benefit, they might be dramatic, they might be necessary at times, but it doesn’t really seem like there’s an obvious payoff to them.