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How have the Cleveland Indians fared under different managers (and other Pythagorean expectation questions)?

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In this, the second part of an article in what will hopefully become a new Tribe sabermetrics series, we continue our discussion on Pythagorean expectation - the number of wins a team "should" record based on its run differential.

David Richard-USA TODAY Sports

In part I we discussed the concept of Pythagorean expectation - using run differentials to estimate how many wins and losses each team "should" record. In the second (and final part) we shall be looking at some other interesting questions relating to Pythagorean expectation. We start by discussing the role of managers.

Is it a "manager" thing?

It is sometimes claimed that the difference between good managers and bad managers lies in their ability to win close games. Thus good managers are able to defy the Pythagorean win expectancy by winning more than their fair share of the close ones. Let's take a look at the Tribe's managers from 1996 to the present:

Manager Total wins above Pythagorean expectation
Hargrove 1996-99 +8.74 wins
Manuel 2000-02 +3.41 wins
Wedge 2003-09 -27.66 wins
Acta 2010-12 +9.41 wins
Francona 2013-14 +4.31 wins

* Manuel was replaced during the 2002 season and Acta towards the end of the 2012 season. For the sake of this article, we have assumed that they were responsible for the whole season.

I'll leave it up to you to decide whether Eric Wedge was one of the unluckiest managers of all time, or one of the worst...

The role of the closer (and the bullpen as a whole)

Another theory is that the effect of having a top closer may not be revealed properly by the broad sweep of run differentials, because the skill of the closer is in squeezing out a few extra very close wins. Marchi and Albert (see below) supply some code in their book which suggests that for for 2001-13, top closers added 0.8 wins over and above those predicted by the Pythagorean formula. For our slightly longer period of 1996-2014, this figure actually rises to 1.2 wins. In two of the three years (1998 and 2001) that the Tribe had what Marchi/Albert regard as a "top closer" (over 50 games finished with an ERA below 2.50), the Tribe outperformed their expectancy, whereas in 2005 even having a top closer couldn't help the Tribe fade the "Wedge factor".

This effect isn't limited to just the closer either. In an article so old that I genuinely did have to use the Wayback Machine to find it, Rany Jazayerli suggests that "good" bullpens win around 1.3 games more than Pythagorean methods predict, whereas "poor" bullpens win roughly 1.6 fewer games than expected: "The difference between having a great bullpen and a terrible one is nearly three games in the standings over the course of a year."

If indeed, the Pythagorean expectation isn't properly capturing the effects of the bullpen (either in relation to "top closers" or in general) this may also have important ramifications in the post-season. When people ask "Why doesn't Billy Beane's shit work in the playoffs?" it may be that the bullpen is where the discrepancy lies. Teams that have amassed very good run differentials over the course of the season might become unravelled in the playoffs if they don't possess a strong bullpen.

During the playoffs there are enough rest days for the top relievers to be available to pitch in practically every medium/high leverage situation, and this will certainly magnify any bullpen effects. Over the course of the season most teams rely on 7-8 relievers on a regular basis, but in the playoffs you really don't need that many relievers to win – five premier contributors will suffice. Perhaps the fact that the Royals reached the World Series last year on the back of an 89-win season, whereas the Tigers crashed and burned at the first hurdle, shouldn't have been as surprising as it was.

2014's winners and losers

So, while we're on the subject, what about the 2014 regular season? Who were the biggest gainers and losers relative to Pythagorean expectancy?

Team Actual wins Pythagorean wins Difference between actual and Pythagorean
Athletics 88 99.15 -11.15
Rockies 66 74.80 -8.80
Twins 70 74.58 -4.58
Mariners 87 91.18 -4.18
Mets 79 82.27 -3.27
Reds 76 78.77 -2.77
D-Backs 64 66.72 -2.72
Rays 77 79.31 -2.31
Blue Jays 83 84.94 -1.94
Nationals 96 96.91 -0.91
Red Sox 71 71.77 -0.77
Marlins 77 77.56 -0.56
Astros 70 70.33 -0.33
Phillies 73 72.98 +0.02
Rangers 67 66.29 +0.71
Giants 88 87.01 +0.99
Pirates 88 86.86 +1.14
Braves 79 77.79 +1.21
Dodgers 94 92.44 +1.56
Angels 98 96.37 +1.63
Padres 77 75.15 +1.85
Brewers 82 80.10 +1.90
Orioles 96 94.04 +1.96
Indians 85 82.77 +2.23
White Sox 73 70.40 +2.60
Cubs 73 70.20 +2.80
Tigers 90 86.36 +3.64
Royals 89 84.16 +4.84
Yankees 84 77.27 +6.73
Cardinals 90 82.92 +7.08

Surprisingly (to me), the Royals weren't the luckiest team, as the model expects them to win 84 games whereas they actually won just five extra games. It was actually the Cardinals who were the most fortunate – they were predicted to win 83 games and actually won 90, whereas the A's "should" have won 99 games but only managed 88 victories.

At this point it is worth mentioning the "Johnson effect", a term coined by Bill James in his 1985 Baseball Abstract. James observed that when a team significantly departs from its Pythagorean expectation, there is a two-thirds chance that they won't record the same number of wins the following year. Thus a team that recorded 88 wins when it was expected to score 99 (such as the 2014 A's) is likely to record at least 88 wins the following year, whereas a team like the 2012 Orioles, which exceeded its expectancy by 11 games after recording only a +7 run differential, wouldn't be likely to reach 93 wins again in the following year (they actually won 85).

Tribe 2015 targets

So, in a run environment of (taking last years' figure) 9.117 runs to 1 win, what does all this mean for the Tribe? Let's say that they might need 90 wins for a playoff spot. Naturally that requires a run differential of (90-81)*9.117 = +82 - the Tribe needs to score around 82 more runs than they concede to get to 90 wins. In the grand scale of things, it doesn't really matter hugely whether they score 800 runs and concede 718 or score 700 runs and give up 618, although as we have seen, the lower run-scoring scenario is definitely slightly preferable.

And what about 95 wins, enough to almost certainly clinch the division? That would require a run differential of +128, so (compared to the 90-win calculations) the Tribe would have to find a further 46-run upgrade either on offense or defense or some combination of the two.

Given that the Tribe had a run differential of only +16 runs in 2014, they clearly need to find a fair amount of improvement from somewhere, be it offense, pitching or fielding, or a combination of all three.

Note that this is the exact same process that is described in the book Moneyball, where Paul DePodesta ascertained that to achieve 95 wins in the 2002 season, the A's would need a run differential of 135 (obviously there was a higher run environment in those days). He believed they would achieve this by scoring 800-820 runs and giving up only 650-670 runs – and he was spot on, they scored 800 and conceded 654 (the book is actually out by one run), but wound up winning 103 games instead of the Pythagorean expectation of 96.


We have discussed the idea of Pythagorean expectation, identifying it as useful but far from flawless tool in assessing win/loss records. Certain factors may be in play that aren't captured well by the formula, notably bullpen strength and the fact that all runs don't carry equal significance. Although it's not desirable for teams to be too imbalanced towards hitting or towards pitching, a great pitching/average offense team is slightly favored over a great hitting/average pitching team – and for winning teams an extra run saved is worth fractionally more than an extra run scored.

As for Eric Wedge? He was probably just unlucky...

Incidentally, if anyone is interested in exploring win expectancy in more detail, I would strongly recommend Analyzing Baseball Data with R by Max Marchi and Jim Albert (CRC Press). I based some of my analysis in this article on chapter 4 of their book. Marchi was hired last Spring to join the analytics team at the Cleveland Indians, so he is obviously a good egg.