If we’re talking about fantasy football sabermetrics, then the Pythagorean Win Expectation has to be a part of the discussion. The PWE is a way to look at the points scored to points against differential and see how that correlate to wins. Bill James is credited for creating it as a way to show which teams were most influenced by luck in baseball.
Mr. James created the following formula to discern the expected win percentage for any given baseball team:
Wins = Runs Scored^2 / (Runs Scored^2 + Runs Against^2).
Using this formula, he was able to get a pretty accurate predictor of total wins. He proved it by applying the formula to past teams, and seeing how close it was to the actual result. It just so happened that the most accurate exponent was 2.
When I applied this formula to every single team we’ve ever had in my fantasy football league’s 10 year history, my predicted wins were off by around 2-3 on average. So, I did what other folks did for the National Football League and NBA – I played around with my exponent until I got the smallest possible average difference from actual results.
So the smallest possible number I could come with for average difference between real & predicted wins was 1.16353 wins. Now, Bill James and the rest of the Sports Numbers People aren’t too helpful to fantasy football sabermetrics amateurs, so I have no idea how much more accurate their numbers are. I think the more seasons (and bigger sample size), the better off we’ll be in getting this number accurate.
Anyway, after fiddling around with the exponent, the most accurate formula came out to:
Wins = Runs Scored^4.55 / (Runs Scored^4.55 + Runs Against^4.55).
Weird, right? Turns out the most accurate number for basketball is 13.91, as well.
So, how do you do this for your league? Now you can be a fantasy football sabermetrics master in seven easy steps!
- You’ll need to copy and paste every team’s Points Scored and Points Against for each season. That’s easily done in a Yahoo! league, but I’m not so sure about ESPN.
- Once those numbers are loaded into excel, create a formula in the spreadsheet for each team like the one I listed above.
- That will give you the expected win percentage, so you’ll have to multiply that by the amount of games in each season to get expected wins.
- Once you’ve got that, enter in the actual wins for each of these teams.
- Subtract actual wins from expected wins to get your difference.
- Now that you have a “difference” number for each team, enter the function (=STDEV(*enter selection of “difference” numbers*). That result is how many games off your formula averages in its predictions.
- Play around with the exponents until you can get the lowest number possible!
With this method, I was able to create a spreadsheet that showed the luckiest and unluckiest teams of all time. Managers in my league found it interesting, and it gave us much to talk about. Likewise, if you’re able to find a smaller average difference from expected wins, let me know your sample size and if you did anything differently.
Much like the PWE for baseball, this can also tell us which fantasy teams are outperforming or under-performing expectations due to luck. With this knowledge we can see if our teams are truly “for real” or not. Although this is probably my least practical piece on fantasy football sabermetrics, it’s certainly lead to the most conversation and received the best reaction among the managers in my league!