What does it take to have luck in baseball? The bounce of a ball or gust of wind through the stadium can turn the tide of a game. Bill James, often credited as the father of sabermetrics (the analytics of baseball), found that runs scored by and against a team strongly predicts a team’s record. Let’s use his analytics, Pythagorean Expectation, to give a sense of the winners and losers of the 2017 MLB season and peer into the possible post-season.
First, let’s learn the formula. A fraction will estimate the percentage of games a team will win. The numerator equals the square of the number of runs scored by the team. The denominator equals sum of the square of the number of runs scored by the team and the square of the number of runs allowed by the team. Consider the 2002 Oakland A's. The team scored 800 runs and allowed 654 runs during the regular season. So, the Pythagorean expectation equals
(800)^2/(800^2 + 654^2) = .5994, indicating the team is expected to win 59.94% of their games.
The team played 162 games and 59.94% of 162 is 97.1. The team won 103 games and thus exceeded their expectation by 5.9 games. Teams that exceed their Pythagorean Expectation are sometimes called lucky.
Note, you can also take a team’s current figures for runs scored and allowed and project how many games they will win by the end of the season. In early June, the Yankees had won 44 games and lost 39. They’d scored 464 runs and given up 362. Using the Pythagorean Expectation, they were expected to win 51.6 games but had only won 44. They’d been unlucky. Did their luck change? One way to measure is to project out to 100 games. Our formula predicts the Yankees should have won 62.2% of their games in early July. At the 100 game milestone, the Yankees had won 54, still struggling on the unlucky side of the formula. Want to try yourself? Look up the data and click here to use this interactive calculator.
Chances are you didn’t get an exact prediction. Bill James' formula isn't perfect. It won't be. Sports are unpredictable, but not entirely unpredictable either. So, how solid is the foundation for this formula? Let’s plot the expected wins versus the actual wins over the last 10 seasons. If you want to explore this plot interactively, click here.
Teams denoted by green dots were lucky and exceeded their expected wins. We also see the unlucky teams. In terms of the model, the Pythagorean Expectation explains 92.11% of the variation in the actual games won.
What else can we learn from a decade of MLB data? First, MLB has been on the unlucky side of its overall record. However, the National League is much less affected by luck with the American League’s statistics accounting for almost 95% of MLB’s unlucky record. Could this be karma for not making the pitchers bat?
Looking team by team over the past ten years, the luckiest team has been the Los Angeles Angels, winning 20 games more than their Pythagorean Expectation. Other lucky teams include the Baltimore Orioles, Seattle Mariners, and Pittsburgh Pirates.
The unluckiest team over the same period has been the Oakland Athletics, losing 34 games more than expected by James’ formula. Other unlucky teams include the Boston Red Sox, Toronto Blue Jays , and Colorado Rockies.
What about your team? For the teams given, how did their luck change over the past decade? Click here to explore the interactive graphic that produced the image below to see a team’s luck over the past ten years .
So, where do we stand today? All of the teams] leading the standings are close to their expected wins with the Red Sox falling behind the most, at 1.6 games below their expectation. The Dodgers have the greatest boost at 0.47 games above their expectation. What about the teams in second place in the standings? Notably, the Yankees, not that far back given the time of year, are still struggling with lack of luck. They are now 8.5 games behind their expected wins. To catch the Red Sox, they’ll need to find some luck or score more relative to runs allowed to improve their record.
So, here we are in the baseball season’s 7th inning stretch. Summer's heat dwindles as we inch toward crisp evenings and the fateful days of October. Each game marches us closer to the playoffs. Could luck change? Time will tell. In the end, all will be determined with balls, strikes, hits, outs, and runs. As three time Cy Young Award winner Tom Seaver stated, "If you dwell on statistics, you get shortsighted. If you aim for consistency, the numbers will be there at the end." Until that final out is called on the playoff clinching games, much is possible and we tune in to watch it all unfold.
This article is co-authored with Scott Teal and Mitchell Stanek. Scott works for Tableau. Mitchell is a first year student at Davidson College.