Sunday Morning Sabermetrics: Pythagorean W-L

Image Credit: Fangraphs

The Pythagorean Won-Loss Formula is a simple regression test that forecasts a team’s winning percentage based on the number of runs that team scores, and the number of runs that team allows. The formula is as follows:

Winning Percentage = (RS2)/(RS2 + RA2)

162 x Pythagorean Winning Percentage = Pythagorean Wins

1 – Pythagorean Wins = Pythagorean Losses.


Bill James developed the Pythagorean Won-Loss Formula in 1977. James, often considered the father of sabermetrics, developed the formula, as well as a few other statistics that we’ll cover in subsequent weeks, while working as a night watchman at a Stokely-Van Camp’s pork and beans cannery in Lawrence, Kansas, and now works for the Boston Red Sox as a senior advisor within the organization’s baseball operations department.

One of the most popular applications of the Pythagorean Won-Loss Formula is in determining how effective managers are at winning close games. A team that is excellent at winning close games will have a better actual record than Pythagorean record, because these teams are able to win games that do not amount to a full Pythagorean win. On the other hand, teams that struggle to win close games and chalk up a lot of frustrating one-run losses over the course of the season can look at their Pythagorean record and understand their frustration. Their Pythagorean record depicts them as a much better team than they actually were, but they could not win the close games.

The closer the ballgame is, the more of an impact a manager can have on the outcome of the game. Think of it this way: in a ten-run blowout, the manager can essentially put in whichever relief pitcher he chooses without affecting the ultimate question of which team will win that game. He can pinch hit, order players to lay down a sacrifice bunt, or attempt to hit and run without affecting the ultimate question of which team will win that game. But if the game is tied in the eighth or ninth inning, which pitcher the manager chooses to call in from the bullpen, whether or not to pinch hit for a player, or whether to bunt, steal, or hit and run can and does directly impact whether his team will win or lose. In essence, the nature of a close game gives the manager a greater role in determining the outcome of the game.


The 2012 Baltimore Orioles were fantastic at winning close games, in part due to the superb in-game management by three-time Manager of the Year Buck Showalter. The O’s accumulated an astounding 29 one-run victories during the 2012 season. Baltimore scored 712 runs and allowed 705 runs for a Pythagorean record of 82-80, hardly a winning team. However, the fact that they were so good at winning close games enabled the team to post an actual record of 93-69, good for making the 2012 playoffs.


The 2016 Major League baseball season is a third of the way complete. The Chicago Cubs are rocking, on pace to win 116 actual games. What is even more mind-boggling is the Cubbies’ runs scored and allowed. Based on their runs scored and runs allowed thus far, their Pythagorean W-L record extrapolated over 162 games would be 128-34. And yes, the Cubs really are this good. They get on base like there’s no tomorrow and pitch the lights out night in and night out. No other team in the National League can stop the Cubs, or even come close, not even the talented squads in Washington and San Francisco. When you lead your league in both runs scored per game and runs allowed per game, and by two landslides at that, it makes sense that you’ll only lose a quarter of your games. And it’s been this way for two whole months on the North Side. Barring injuries, the Cubs will win 120 games this year.

The St. Louis Cardinals, the rival of the Cubs, are another interesting case study for 2016. The Cardinals are on pace to win 82 games, not enough to make the playoffs. However, the Cardinals are one of the most talented teams in baseball, and their Pythagorean W-L record extrapolated over 162 games is 95-67, good for playoffs. The Cards will progress towards closer to 95 wins as opposed to 82, seeing as they have lots of young talent and are coming off a 100-win season in 2015.

Don’t be teased by the decent start of the rebuilding Philadelphia Phillies. Trust me, the Phils are not contenders. They may be around .500 currently but have allowed significantly more runs than they have scored. Their pace Pythagorean W-L is 60-102, ahead of only the lowly Atlanta Braves in the NL East.

The Texas Rangers are red hot, and the Seattle Mariners, who have led the AL West for most of the season, have cooled off and fallen to second place. The Rangers are younger, and they made the playoffs last year, and their manager, Jeff Bannister, won Manager of the Year, while the Mariners, a team with overpaid veterans and an underachieving franchise for most of the past decade under a new manager this year after firing Lloyd McClendon in response to a laughable 2015 campaign. The Rangers are the team to beat in the AL West, right? Wrong. The Mariners are scoring more and allowing fewer than the Rangers. The Mariners may not be on pace to win as many games (93) as the Rangers (96) based solely on wins and losses, but in the long run, the Pythagorean run, based on runs scored and runs allowed, a more accurate valuation model, the Mariners can be expected to win more games (99) than the Rangers (90).

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