For the last couple of days, we’ve been talking about the different components of the Win Value system. However, you may have noticed that we’ve been dealing entirely in runs. wRAA, UZR, the position adjustment, and replacement level are all expressed in terms of runs, not wins, and that’s why the sum of those numbers is categorized under Value Runs.
So, if all of our metrics deal in terms of runs, but we want to get to wins, we need to know how many runs it takes to make a win. This is actually quite a bit easier than it sounds, thanks to the pythag formula for expected win-loss records. For those not aware of pythag, you can get a good estimate of a team’s winning percentage by dividing the square of runs scored by the sum of the square of runs scored and the square of runs allowed. Or, in formula terms:
RS^2/(RS^2 + RA^2) = Pythagorean Winning Percentage. So, if a team scored 775 runs and allowed 775 runs, they’d have a .500 Pythag Win%, or 81 wins and 81 losses – even amounts of runs scored and runs allowed should lead to something like an even record. Not as scary as it sounds.
What happens if we subtract 10 runs from the runs scored column, so that we now have a 765 RS/775 RA team? Pythag spits out a .4935 win%, and .4935 * 162 = 79.95 wins. So, instead of 81 wins, you’re now expected to win just barely less than 80. By subtracting 10 runs, you lost a fraction more than one win.
Same thing happens if you add 10 runs to the runs allowed column – 775/785 RS/RA spits out .4935 as well. How about if you add 10 runs, so we have a 785/775 team? .5064 win%, or 82.03 wins. Again, 10 runs added equals one win gained.
For an even more precise look at the issue, you could use the improved PythagenPat method, which places a better exponent in the calculation, but the conclusion is going to be the same; 10 runs = 1 win.
So, when you see value expressed in runs, but you want it in wins, just divide by 10. Likewise, if you see it in wins but you want it in runs, multiply by 10. It might sound like a cheap trick, but it’s reality – 10 runs add up to a win. A +20 run player is a +2 win player.
Dave is the Managing Editor of FanGraphs.