Blogging The Boys
In a recent article here on Blogging The Boys, we looked at Wins Over Average (WOA) and which NFL quarterbacks were winning games for their teams. In the course of the ensuing discussion, some readers wondered whether WOA was something that could be applied to head coaches as well.
Traditionally, coaches are evaluated by their winning percentage, and an easy way to calculate a head coach’s Wins Over Average (WOA) would be to subtract the league’s average winning percentage (.500) from the coach’s career winning percentage, then multiply that difference by their total games coached.
This baseline formula would isolate how many actual victories the coach secured compared to what a perfectly average (.500) coach would have achieved over the exact same number of games.
But that just gives you a souped up version of the winning percentage. What if there was a way to isolate the head coach’s impact more effectively?
So instead of using 0.500 as the baseline, we‘ll use the Pythagorean Expectation to create a custom baseline derived entirely from the team’s points scored and points allowed. This isolates the head coach’s impact by comparing a team’s actual wins against how many wins the team’s point differential says they should have had. So instead of Wins Over Average (WOA) we get Wins Above Expectation (WAE), which we’ll use for the rest of this post.
If you’ve been on this blog for a while, you’re familiar with the Pythagorean Formula. If not, here is what it is: The formula was originally developed by the godfather of baseball stats, Bill James, who surmised that a team’s true strength could be measured more accurately by looking at points scored and points allowed, rather than by looking at wins and losses. And here’s why we’re using it:
Winning percentage treats every victory and defeat identically, regardless of how the game was played. A 1-point win secured on a lucky, deflected pass at the buzzer looks exactly the same on a record sheet as a 35-point blowout where a team dominated from the opening kickoff. Winning percentage tells you what happened, but it tells you nothing about how it happened.
The Pythagorean expectation shifts the focus from volatile win-loss records to a team’s underlying point differential. In the NFL, points scored and points allowed are far more stable and mathematically predictive of future success than a raw win-loss record. By calculating how many games a team should have won based on their total points, the Pythagorean formula establishes a highly accurate baseline for the true talent level of the roster.
NFL games decided by eight points or fewer are historically highly volatile and prone to random variance (e.g., a bad referee call, an unusual bounce of a fumble, or extreme weather).
