How much is that closer worth anyway?

Let’s mess around with the save rule, shall we?  Let’s pretend that every inning of the game (not just the ninth) was eligible for a save (yes, I know exactly what the save rule says… he doesn’t have to enter in the ninth, but that’s usually what happens).  A team would have to enter their turn on pitching/defense with a lead between one and three runs.  The goal is to escape the inning with the lead still intact.  I can think of no logical reason why this goal would be any different in the third inning or the seventh or the ninth.  The goal is always to protect a lead when on defense/pitching.
It’s also not a mystery that managers use their bullpens in a very specific way, basically in order, with the pitcher whom he believes to be the best used in the ninth, the second best in the eighth and so on, especially when the game is close.  The manager might use more than one pitcher in an inning, but the rules of the seventh inning are the same as the rules in the ninth inning: don’t let the other team score.  So, if the closer pitches the ninth, how often is he successful?  What about his eighth inning brethren?  Come to think about it, what about the guy who’s pitching the fourth inning, most likely the starter?
I isolated all innings from 2000-2006 in which the defending team was leading by a score of between 1-3 runs.  If it were the ninth inning, that would be a save situation.  I then checked to see whether they exited that inning still in the lead (if it were the ninth, a save would be awarded) or if the other team had either tied or gone ahead (if it were the ninth, a blown save would be “awarded”).  I looked at the results for each inning, bottom and top, with the exception of the top of the 1st.  In the top of the first, the pitching team hasn’t yet been to bat, so it’s impossible for them to be in the lead.  For anyone interested in replicating my analyses, I used Retrosheet’s game logs.
The best “save” conversion rate in an inning: The top of the ninth with only 13.0% of all leads under three runs disappearing, followed by the bottom of the ninth with a 13.9% success rate.  What about “blown saves” in the eighth inning?  14.8% in the top of the inning, 15.8% in the bottom.  So, closers (9th inning pitchers) are about two percentage points better than 8th inning pitchers.
The full chart:
Inning      Top        Bottom
1st             —          24.6%
2nd          19.5%     19.9%
3rd           18.1%     19.1%
4th           20.0%    20.6%
5th           17.0%     19.3%
6th           19.0%     19.2%
7th           16.9%     17.6%
8th           14.8%     15.8%
9th           13.0%     13.9%
A few patterns to note: it gets harder to overturn a lead as the game goes on.  Given the reverse order bullpen strategy that most managers use, that’s not a shock.  It’s based on slowly trying to close off the game based on time (inning, as opposed to situation) and the need to always be seen as increasing the certainty of winning the game.
Another pattern, more leads are overturned in the bottom of the inning than the top (when the home team is batting).  This is pretty uniform across innings.  The home team does, in general win the game 53-54% of the time, although by definition, they are the better team 50% of the time.  Home teams are a little better at rallying than are their visiting counterparts.  Maybe there’s something to be said for all those rally caps out there.  Or that monkey.
But back to the closer issue.  A ninth inning save situation (pitching team up less than three in the ninth) occurred for the home team in about 26.3% of all games in the seven year period under study and 24.2% for the visitors.  Some quick math tells us that’s about 41 save situations for the average team.   The 9th inning pitchers are generally 2% better than the guys from the eighth inning and 4% better than the guys from the seventh and 6% better than the guys from the sixth (who might be the starter or a mediocre reliever).  But, what would happen if you had a “sixth inning” pitcher closing games for your team (all else being equal)?  Since we’ve seen that he converts “save” chances at a 6% lower rate than the actual ninth inning guys, he’d blow an extra two and a half saves, but… given that he converts those chances in the sixth inning at roughly an 81% rate, he’d also have 33 saves applied to his name if he just pitched in the ninth.  So, a guy who really is nothing more than a sixth inning guy, put in the right role, can easily save 30 games and suddenly, become a multi-millionaire because people believe he is something that he is not.  A “closer”.
One other (vastly over-simplified) thought experiment.  Suppose that the average ninth inning guy (alias, “closer”) goes down with a season-ending injury on the night before the season opener while washing his car or just suddenly retires for no apparent reason.  What would the effect be on the team?  Well, let’s say that the starter generally goes 5 and the team has a some guys who pitch the sixth and seventh, an eighth inning guy, and a closer.  Everyone moves down a notch.  So, now the eighth inning guy pitches the ninth, the seventh inning guy pitches the eighth, and so on, with some AAA replacement coming up to be one of the sixth inning guys.  The guys who are pitching in the sixth are usually pretty replacement level anyway and half the time it’s the starter (no data there, just an educated guess), so we’ll say that there’s no change in the sixth inning.  
A seventh inning “save” situation appears 28.8% of the time for the home team and 27.9% of the time for the visitors.  Assuming a 2% conversion efficiency drop, the effect of the sixth inning guy pitching the seventh is .92 blown saves over a season.  But this has a chain reaction effect on what we can expect in the 8th inning.  Those .92 save opportunities have been blown and won’t be there for the unfortunate closer-less team in the eighth inning (assuming that the team’s offense doesn’t compensate in some way.)  However, to keep from having to program a Markov model this late at night, let’s just pretend that chain effect is not there.  In the eighth inning (I’ll spare you all the calculations), the effect is .88 blown saves, and in the ninth, it’s .8 blown saves, for a grand total over the season of 2.6 blown saves.  The average team blows about 20.6 saves from the seventh inning on during a year, so the closer is worth about a 12.6% uptick in blown saves per season.

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3 Responses to How much is that closer worth anyway?

  1. DanC says:

    So, a guy who’s worth somewhere between 1-2 wins per year gets millions of dollars. In that, I’m accounting for the fact that your stats only discuss blown saves, not changes in outcome (loss instead of win).
    I would love to see you discuss the perceived psychological advantage a closer may or may not have, and then also relate this to the playoff atmosphere. Are teams really paying closers because of some sort of intimidation factor, or because some guys are thought to do better under pressure or in the playoffs? And is there any way to statistically show that perceptions of closers have any basis in terms of closer performance?
    Anyway, good piece on an area of the game that needs some changing, as Kyle said.

  2. Kyle J says:

    Good piece. If I could make a single change to the world of baseball, it would be to abolish the save statistic.
    But applying it to every inning of a game is a second-best alternative. As you have done, this shows that most saves aren’t all that difficult to earn.
    I’ve also been wondering if we couldn’t come up with something comparable to the quality start statistic. A quality relief appearance would be an appearance in which innings pitched are equal to or greater than twice the number of runs allowed (1 IP, 0 R; 2 IP, 1 R; etc.).
    Of course, this doesn’t account for the ability to stop runners already on base from scoring. But there has to be a better way to measure the effectiveness of relief pitchers with a relatively simple stat.

  3. Pizza Cutter says:

    Dan, I’ve thought of doing a piece on that very subject. I’ve thought of two ways to approach it, and I may do both. One is to use the same approach we use for measuring “clutch” for hitters on closers. Let’s see if that . The other is a little less sophisticated (but easier to present): compare how a closer does in save situations vs. the occasional mop-up job he pulls in a 13-4 game when he just needs some work.
    I thought about looking at it from a win-probability perspective, but I couldn’t quite figure out how. My guess is that the average closer is probably worth two extra wins or something around that, assuming an average bullpen behind him.

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