Weekend Report: The Ten Run Rule

on 09/05/2003


No, I'm not talking about the mercy rule in softball. I'm referring to the widely used estimation that if your team could score 10 more runs or allow 10 fewer over the course of the season, your team would be expected to win one more game. This handy estimation is based off the Pythagorean winning percentage I talked about a few weeks ago. That formula is: (runs scored^2) / [(runs allowed^2) + (runs scored^2)]. This generates a winning percentage. For those of you who forgot over the course of a season, most teams will be within three games of this prediction and from season to season it predicts future records better than actual records do.

It stands to reason that if you start taking runs scored and allowed totals, you can create a chart that shows how the Ten Run Rule tracks with various run totals. I've wanted to do this for a while, just to see how this estimation behaved over what could be considered normal season totals. I was particularly interested in how the estimator held up as you got to more extreme run totals.

Runs scored Runs Allowed Pythagorean wins
500 600 66
510 600 68
520 600 69
550 600 74
560 600 75
570 600 77
600 600 81
650 600 87
660 600 89
670 600 90
700 600 93
710 600 95
720 600 96
800 600 104
810 600 105
820 600 106
900 600 112
910 600 113
920 600 114
600 500 96
600 510 94
600 520 93
600 550 88
600 560 87
600 600 81
600 610 80
600 620 78
600 700 69
600 710 67
600 720 66
600 800 58
600 810 57
600 820 56

That's the handy chart I ran. I wanted to cover as broad a range as possible without making a huge chart. Now I expected that for teams closer to .500, the Ten Run Rule would hold best. After all, most teams cluster closer to .500, so you would predict a common estimator would work most accurately for those teams. If you're looking at the chart though, you're bound to notice that for many of the 10 run intervals, the change in wins is two and not one. In fact, only for 12 out of the 22 ten run intervals on the chart does the win total change by one. For the other 10 it changes by two. Looking deeper, it appears to be the case that the estimator actually works better for more outlying teams. In contrast, the reality is that in going from 500-600 runs allowed or scored nets you 15 wins. This is to say that the real estimate for teams near .500 is that every 10 runs are worth 1.5 wins. This is clearly significant when you're talking about major team changes. The most natural use for this estimator is for comparing players and their various values and converting that into a win improvement.

Player of the Week

This is another good week to be a Brewer fan. I had this spot all reserved for Luis Martinez, but unfortunately he didn't grab the torch in his debut. We shouldn't hold that against him. Looking at other performances this week, no pitcher stood out though Kolb could have. A number of offensive players had good weeks - Podsednik and Sexson just chugging along and Ginter was no slouch either, but nothing that grabbed me and screamed Player of the Week except Brady Clark with his near cycle performance and four total multi-hit games. We like to reward little guys when possible and Clark was an underused talent in Cincy for a number of years. He hasn't shown the plate discipline so much this year, but limited playing time and fighting for recognition tends to make players more aggressive then normal. The final word - go Beloit, Huntsville, and Helena!