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Run Distribution

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There's been quite a bit of talk about the Brewers' luck, or lack thereof, with regard to actual vs. expected records. However, I think that everyone intuitively understands that blowouts, like the ones the Brewers laid on the Cubs the past two days, can distort the picture provided by looking at runs scored and allowed. With that in mind, I thought I'd take a closer look at the Brewers' run distribution:


(Click to enlarge)

The pink line tracks the number of times each amount of runs was scored by all the teams in the National League combined last year. The blue line tracks the same for the Brewers this year. Obviously, the '06 Brewers have played far fewer games than the '05 NL, so the line is quite a bit spikier, but it's still interesting to look at. Even more interesting is the Brewers' winning percentage when scoring a given amount of runs, again compared to the '05 NL:


(Click to enlarge)

Obviously, there are a few problems with the graph, as the Brewers have yet to score 6, 10, or 13-15 runs this year. Nevertheless, you can see that they're winning more games when scoring 3-5 runs than expected, which is counteracted by their underperformance when scoring 7, 8 and 12 runs. I subtracted the baseline winning percentage when scoring each amount of runs from the Brewers' winning percentage in those same games and then multiplied that number by the total number of games the Brewers have played with each run total:

Runs '06 Brewers '05 NL Diff Total
0 .000 .000 .000 0.00
1 .000 .077 -.077 -0.08
2 .000 .274 -.274 -0.27
3 .500 .351 .149 0.89
4 .667 .513 .154 0.46
5 1.000 .613 .387 1.16
6 n/a .702 n/a 0.00
7 .667 .814 -.147 -0.44
8 .500 .874 -.374 -0.75
9 1.000 .949 .051 0.05
10 n/a .902 n/a 0.00
11 1.000 .983 .017 0.02
12 .000 1.000 -1.000 1.00
13 n/a 1.000 n/a 0.00
14 n/a 1.000 n/a 0.00
15 n/a 1.000 n/a 0.00
16 1.000 1.000 .000 0.00
Total 0.04

Sum up the net differences and you can see that the Brewers technically come out ahead, by 0.04 games.

Basically, everything cancels out so far this season. They're winning more low-scoring games than they should and losing more high-scoring ones. The way their runs have been distributed has caused their hypothetical record when looking at runs scored and allowed to be inflated.