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A Pythagorean examination of Tony La Russa

White Sox have three fewer wins than their runs for/against projection suggests, but it’s nothing abnormal.

For his career, White Sox manager Tony La Russa entered the season essentially right on his Pythagorean projection.
For his career, White Sox manager Tony La Russa entered the season essentially right on his Pythagorean projection.
Steph Chambers/Getty Images

A 32-20 record through Sunday, just a game behind the MLB-leading 34-20 records of the Padres and Rays, hasn’t halted critics of White Sox manager Tony La Russa.

Controversies about unwritten rules aside, the Sox have won three fewer games than their runs scored and allowed suggest is average. Could the shortfall lie with La Russa?

You can’t prove that by the numbers. It’s normal to be a few games above or below the Pythagorean projection.

Baseball’s Pythagorean projection has been with us since the first mass-marketed Bill James Baseball Abstracts in the early 1980s. The formula is runs squared divided by (runs squared plus runs allowed squared) equals winning percentage.

Through Sunday, the Sox had scored 258 and allowed 178. Square 258 to get 66,564. Square 178 for 31,684. Divide 66,564 by (66,564 plus 31,684), and the expected winning percentage is .6775.

Multiply .6775 by 52 games played, and the average expected win total is 35.23. The Sox’ Pythagorean projection is a 35-17 record.

Unusual runs of clutch hitting, for better or worse, can move records away from projections. So can lockdown or leaky bullpens.

But differences between records and projections largely are put down to chance. At Baseball-Reference.com, the column displaying distance between a team’s record and projection is labeled “luck.”

Occasionally, a pennant can be won by a team with a record far better than its projection. The 2005 White Sox won 99 games when the formula suggested 99 wins.

But teams that finish far above or below Pythagorean tend to be closer to the projection the next season. The 2006 Sox, in winning 90 games, were only two games above their projected 88. There’s no proven ability to win more games than projected on any consistent basis.

Managers have years above and below projections, and that includes La Russa.

La Russa managed 5,014 games before returning to the Sox this season and had a .535 winning percentage vs. a .533 projection. He’d won just under 11 games more than projected. That’s about a third of a win per 162 games, so essentially right on Pythagorean.

There were ups and downs. His 96-win A’s of 1992 were about seven games above Pythagorean, but his 86-win Cardinals of 2010 were six wins below. Both showed a return to norms the next year, with the 1993 A’s and 2011 Cards one game above projection.

La Russa’s first 33 years of managing included 15 with fewer wins than projected.

Among longtime managers of recent vintage, Bobby Cox had a career .556 winning percentage in 4,505 games. Runs data projected to a .558 percentage, so Cox’s teams won just under 12 fewer games than projected. Entering 2021, Dusty Baker had a .532 winning percentage and .529 projection for a surplus of six victories.

Ups and downs balance, and no one with a long career varies from Pythagorean by as much as a single game per season.

That’s not to absolve La Russa of any blame. Fans can debate mistakes at will. There’s just nothing in the Pythagorean record that looks abnormal.