Runs, Win Expectancy, and the 2016 Seattle Mariners
Friday, June 17, 2016
Pythagorean Theory 101
No, no, no….not high school geometry. This is basic sabermetrics.
Going all the way back to Henry Chadwick at the dawn of the 20th century, those who have studied the game of baseball have realized that the path to the ultimate goal of winning is to score more runs than your opponent. The more runs, the more wins. And winning is good, right?
Fast forward to Bill James in the late 70s and early 80s. James began to formulate theories of how scoring runs and preventing runs correlated to wins. This culminated in his original “Pythagorean theorem” which set out to explain the relationship between run differential and wins. The resulting formula and subsequent tweaks to the formula are easily found with a simple Google search. But essentially the various formulas boil down to roughly this - start with a .500 record and add or subtract wins based on increments of ten run differentials.
So, for instance, the Chicago Cubs are 44-20 through 64 games, with a run differential of 159. A .500 record would be 32-32. Add 16 wins based on the run differential of 159 (rounding by one) and the expected record would be 48-16. The Cubs, as great as they are this season, are actually underperforming slightly.
A team at the other end of the spectrum might be the Baltimore Orioles. As of Thursday morning, the O’s sat atop the AL East, tied with the Red Sox, with a 37-27 record. However, their run differential was 26 compared to 86 for the Sox. Take a .500 record of 32-32, add three wins by rounding up the 26 run differential and you could expect 35-29, whereas the same formula for Boston yields an expected 41-23 record. It’s why most projections sill have the Red Sox, not the Orioles, winning the division at the end of the season.
It’s also important to note that James’ Pythagorean theorem is intended to be applied to a full season. The smaller sample size – there’s nearly 100 games left to go – creates more noise than over a full season. Historically, James’ theorem is accurate to within about two games. Run differential matters.
Cluster Theory + Pythagorean Theory = 2016 Seattle Mariners
So, starting with the Pythagorean theory, the Mariners should have around 38 wins. Their actual record is 35-31. Underperforming slightly. Cynical, long suffering Mariners fans might be tempted to chalk that up to “karma” or some other superstitious nonsense. But keep reminding yourself that Mariners teams of the last fifteen years have absolutely no effect on this 2016 version, no matter what obscure historical statistic the announcer on your television may evoke.
What’s interesting about the M’s this year is how different the box score looks in a win from what the box score looks like in a loss. Have you ever seen a box score where one team has maybe 9 hits and 3 runs and the other team has 7 hits and 5 runs? If you’ve monitored even one season of box scores, the answer is a resounding, “of course.”
In small samples, hits don’t always translate into an even distribution of runs. Clustering of runs has a strong influence over fewer games. Hypothetically, a team could grind out 27 hits, all singles, three per inning, and never score.
Normally, there is a relatively strong correlation between batting average and runs scored. There’s an even stronger correlation between on base percentage and runs scored. But those correlations are meant to play out over the course of an entire season. In small samples like 60 or so games (yes that’s small in baseball), clustering of hits and runs can sometimes skew the results.
Runs in Wins v. Runs in Losses
It goes without saying that teams tend to score more runs in victories and fewer runs in losses. So far in 2016, the Seattle Mariners have taken that truism to the extreme.
The Mariners have scored more than ten runs in seven games this season, including two games with sixteen runs (both against the hapless San Diego Padres). The M’s own an incredible 14-6 record in blowouts, games won by 5+ runs.
While Seattle has averaged around five runs per game over the course of the season, a closer inspection reveals a team that is averaging slightly over seven runs per game in wins but under three, 2.7 to be precise, in losses. Might this be normal? Well, not exactly. Opponents are averaging 2.97 runs per game in losses to the Mariners and 5.57 runs per game in wins. This is a differential of about two and a half runs in wins versus losses for opponents while the Mariners’ differential is over four runs.
Who are “The Real Mariners?”
What isn’t exactly clear at this point is which Mariners offense is the real Mariners offense - the one that scores runs in droves in victories, or the one that struggles to score in losses?
The Pythagorean model would tend to suggest the Mariners are underperforming, oh so slightly. But a closer look at clustering of hits and runs might suggest their current record is about right or even slightly inflated.
One thing is for sure, the Cinderella, feel good story that accompanied the M’s in May with a 17-11 record has at least temporarily turned into a Miyazakiesque nightmare of a 5-15 June. Stay tuned for the continuing story of Pythagoras v. Cluster.
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