Friday, September 12, 2003

ayayay! of the tiger...

if it's true that when the tigers get good hitting, they don't get good pitching, and vice-versa (such that they are truly the victims of bad luck), then it stands to reason that the team's winning percentage should be fairly constant across the runs scored continuum. in other words, as the theory goes, when they score a lot of runs, they allow even more runs, and when they allow few runs, they score even fewer runs, such that they tend to lose regardless of however many runs they may score. thus, the theory suggests that the team should be winning at a fairly constant rate independent of variation in offensive production.

overall, the tigers are now 37-108. thus, they have won 25.5% (37/145) of all their games. therefore, the bad luck theory suggests that this winning percentage should hold relatively constant across changes in run production. now here's a look at how their winning percentage actually varies across their runs scored distribution:

runs scored frequency wins winning %
0 16 0 0.0%
1 16 2 12.5%
2 27 3 11.1%
3 27 5 18.5%
4 15 4 26.7%
5 12 4 33.3%
6 11 5 45.5%
7 8 5 62.5%
8 4 2 50.0%
9 7 5 71.4%
10 2 2 100.0%

from this distribution, it seems fairly obvious that their winning percentage
drastically improves when they score more runs. and if we collapse the above distribution into three categories, the trend is even more apparent:

runs scored frequency wins winning %
0,1,2,3 86 10 11.6%
4,5,6 38 13 34.2%
7,8,9,10 21 14 66.7%

thus, if the tigers were to score 7-10 runs/game every game they played,
they would win about 2/3 of all their games and have about 97 wins right now; good enough to put them in first place in their division and have the best record in the american league (about 8 games ahead of the yankees, in fact). however, the tigers don't score 7-10 runs/game every game they play. instead, they only do this 14.5% of the time. more commonly, they score 0-3 runs/game (59.3% of the time), or 4-6 runs/game (26.2% of the time).

in conclusion, it appears that the tigers are not the victims of circumstance, but instead, are a bad team that doesn't hit very well. future research should replicate this approach focusing on the pitching/defense of the tigers. i will speculate right now that when the tigers allow fewer runs, their winning percentage increases.

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