RESEARCH: Expected Wins

A few years ago, this writer was looking at projections for the Reds' pitching staff. While the exact numbers are part of history, they looked somewhat like this:

Arroyo, with the highest projected ERA and fewest IP, was projected for the most wins. And Volquez, with the lowest ERA and most IP projected, was projected for the fewest. Now, this made sense given the win totals for each player over the prior three years, but it didn't make intuitive sense. Surely, lower ERA and more innings should lead to more wins, all things being equal. (And all things were equal—these pitchers had the same offense and defense behind them, and the same bullpen). Yet, there we were.

We've tackled the subject before. Last year, Patrick Davitt took a look at unlucky pitchers. He found that lucky wins were rather rare, but unlucky losses (or no decisions) were somewhat common. Ed DeCaria also weighed in a few years ago with a ranked list of factors that explained a pitcher's Win %, but ultimately wasn't able to produce a usable forward-looking projection with then-available data.

Background and methodology

First, we need to specify that we are looking strictly at starter wins; reliever wins are much more situational, as a pitcher can record as little as one out and still be credited with a win. To that end, we examined only pitchers with no bullpen appearances. In a quest for reasonable sample sizes and to capture the current environment, we only looked at pitchers with 15+ starts from 2010-2014. That yielded 531 pitcher-seasons encompassing over 15,000 starts, so that's a good place to, er, start.

Factors affecting wins

We hypothesized that wins would be affected by:

  • Pitcher ERA
  • Team offense
  • Team defense
  • Bullpen quality
  • Innings pitched per start

In order to properly compare pitchers with more playing time, we checked each of these against wins per game started (W/GS) rather than total wins. We found that none of these factors had a particularly strong correlation:

Not the breakthrough we had hoped for. ERA and innings per start are the closest, and they are themselves correlated to each other (-0.67 correlation). So a complex formula with multiple factors, such as xBA or xERA, isn't likely to yield concrete results. Of course, in a multifactor regression, some of the terms might become more significant, but without a strong starting point, it's probably wasted effort.

Is there an alternative?

Yes, there's an alternative—a very simple one. So simple, in fact, that we had our doubts going in: the Pythagorean Theorem of Baseball. Developed by Bill James, it's a fairly robust method to check a team's winning percentage, based strictly on runs scored and runs allowed. Teams that outperform or underperform their Pythagorean estimated wins typically show strong regression in the following season. Would it work for individual pitchers?

As a reminder, here is the Pythagorean Theorem:

We tried it. And the results didn't look right. For example, Clayton Kershaw had 27 expected wins for his 2013 season. Errors were high, insults were thrown, and we were tempted to give ourselves the Hook.

Okay, not so much. There were actually two flaws in our first attempt. First, research has shown that the correct exponent for the theorem is closer to 1.80 than to 2. Various researchers have pegged it at 1.83 or 1.81, and a few have even derived a formula for deriving the exponent. In looking at all teams from 2010-2014, the lowest mean squared error (MSE) resulted from using 1.80 as the exponent, so that's what we used.

Second, while a team either wins or loses every game, starting pitchers have a third option: the no decision. So before we can apply the Pythagorean factor, we have to project how many no-decisions a starter should be expected to have. (If you want to skip the next section, you can).

No decisions

We'll keep this simple, though we'll include a chart (because we like charts):

  • The average no-decision percentage in our sample was 28%. In other words, 28% of starts resulted in a no-decision.
  • There was no correlation in no-decision percentage between pairs of pitcher-seasons (we had 260 such pairs).
  • Nearly 70% of pitchers who were above average in one season saw their no-decision percentage move towards (or past) the average in the subsequent season.
  • While there are outliers, no-decision percentage is roughly normally distributed and clustered in the center:

Based on this, we concluded that individual pitchers have little control over their no-decision percentage, allowing us to use the league average (28%) for all pitchers.

The final formula

Putting it altogether, we have the following formula:

Of course, a model is only as good as its accuracy. Here are the results:

According to this, our expected wins formula explains nearly 70% of the variation in pitcher wins. Funny how that number matches up with our rule of thumb that the best projections are no better than 70% accurate. Coincidence, for sure, but an interesting one.

Furthermore, 70% of pitchers whose expected wins varied from actual wins from 2010-2013 showed regression in wins per start in the following year.

Statistically, a 70% R-squared is a pretty darned good fit, and frankly better than we had hoped for. Time will tell how will employ this statistic, but the results are noteworthy.

Looking at 2015

We'll end with the (nearly) obligatory list of pitchers from 2014 who defied our model. These pitchers would be expected to see improved or declined winning percentage in 2015*:

Consistent with Patrick Davitt's research, the unlucky outnumber the lucky, and the luck is more extreme on the "unlucky" side. We can expect the outperformers to see a small drop in wins/start, and the underperformers should see improvement there (the emphasis on "should" takes into account the Whirlpool Principle, where underperformers are more likely to lose their jobs before they can get back on track).

*Pitchers who did not have a relief appearance in 2014 and started at least 15 games.


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  For more information about the terms used in this article, see our Glossary Primer.