We've seen that, in the situation of a batter reaching third with two outs, that all runners score at the same rates for each of the subsequent events, and therefore that the variation in run scoring from that position reflects the variation in talent of the subsequent hitters.
What happens if we keep the outs constant, but advance the batter to a different base?
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The first thing to note is that the number of events we track here goes up by a factor of 6 or so. Part of this reflects the fact that doubles are more common than triples, although there is the secondary effect that it may take two hits to bring the runner home from second, rather than one.
It should be no big surprise that the scoring rate on extra base hits is effectively uniform - 2208 doubles scored the runner 2205 times, which is essentially unity.
On singles, the scoring rate is nearly uniform at 80%, but there are some interesting points. First, the number 9 hitters are only scoring 70% of the time. There are a couple reasonable theories here. Perhaps the pitchers (who dominate the 9th spot) don't run as well, or perhaps the singles hit by the top of the lineup aren't as deep, making it more difficult to score. Controlling for the pitchers might illuminate this better - perhaps a future study.
Looking more closely, the top two lineup positions have a slightly higher scoring rate, perhaps 2%. With 1075 trials and an 80% true success rate, the standard deviation would be something like 1.2%; so while this hints at a difference in ability, the sample is too small to trust that conclusion to closely.
Oddly enough, the third hitter scores more frequently, about 83% of the time. If this is a real effect, it could reflect the fact that singles by the number 4 hitter tend to be deeper than those of the rest of the lineup. But again, the sample size doesn't give us much confidence in this result.
(The 9th spot, with its 70% scoring rate, is more than 6 deviations out - we should feel very confident that this effect is real - although the cause is uncertain, as noted before).
On errors, the linup scores about 48% of the time. The number 9 spot is low man on the totem pole again, although the number 8 hitters aren't much better. The extreme outliers at the top of the chart are the number 2 and 3 hitters. However, the samples are very small, which means the standard deviations are much larger (relatively speaking) - the variation here could certainly be chance.
In short, with the exception of the performance of number 9 hitters on singles, the evidence is consistent with the conclusion that run scoring in this position is independent of running skill.
If we look at the batter advancing to first base with two outs, the situation becomes messy. The number of events jumps by another factor of seven, which again reflects that singles, walks, etc are more common than extra base hits, and also reflects the fact that it can take multiple events to get the batter around the bases.
First the good news - everybody scores on triples and home runs.
On doubles, the lineup scores roughly 67% of the time. The sample size tends to be around 1700, which means that our standard deviation should be around 1.15%, and we should suspect a real effect if we see more than a 3.4% deviation from the mean. The number 9 spot is well past that limit on the low end - which is consistent with our earlier results - and the top two linup spots are just over the edge at the high end.
Looking at singles, we see scoring rates around 24%. Remember, this does not suggest that runners score from first on a single 24% of the time, but rather that the runners score on 24% of the singles hit while they are on base. Given the sizes of the sample, a 1.5% difference is likely to be significant. With that hint, it makes sense to divide the run scoring into three bands - 29% for the leadoff hitter, 25% for the second and third spots, 22% for everybody else - including the #9 hitter.
One might reasonably suspect that the balance of power in the lineup favors the top three hitters, as does the stolen base ability of the leadoff hitter.
Scoring rates on errors are pretty uniform around 22.5%, although the number two spot sores about 32.6% of the time here. Definitely significant, given the sample size, though I am stumped as to why that should be so.
The retrosheet data also indicates that the leadoff hitters are getting a real advantage on ground balls, and the two and three hitters on fly balls. Presumably these are ground ball and fly ball errors. I believe these are the numbers reflected in the error scoring rates above.
May 11, 2004 12:31 AM
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