The underlying (unpresented) table contains the average number of runs that scored, from that base/out state and event, to the end of that inning. The next step was to take the run expectancy, by base/out/event, and subtract the run expectancy by base/out. The resulting figure is roughly equivalent to the run impact of the event for that base/out state. That is, Linear Weights, by the 24 base/out states.

We could have used different (better) techniques, such as look at the state before and after the PA, and using the already published RE by the 24 base/out states, and attributing that difference to the events. That is kind of mixing part empirical and part Markov.

Because the two figures being subtracted are both samples of different data sets, you will get sometimes strange results, like a value of 1.04 for the HR with the bases empty and 0 outs. To expand on this particular event/state, consider that the run expectancy with bases empty and 0 outs is .555 runs. The run expectancy following a HR on a bases empty and 0 outs is 1.591. These are all samples. There's nothing inherent about the .555 other than that's essentially the average number of runs scored per inning. There's nothing inherent about the 1.591, other than that's the actual number of runs that scored starting from the HR with bases empty and 0 outs. Subtracting the two, and you get 1.04 runs. We expected exactly 1.00.

One sampling issue is that you probably have a better batter at the plate following a HR, since the batter who hits the HR probably is a good hitter, and is surrounded by other good hitters. A bad pitcher is more likely to give up more HR, and therefore, the sample in which the HR is drawn is not random. This issue is much more apparent when comparing the HBP, NIBB and IBB. The Markov article cited in the next paragraph shows them all as equals. Since IBB are almost always issued to a better batter to face a worse batter, you will see very strange empirical results.

If you were to run a Markov chain, you would get exactly 1.00, as I've shown previously. I strongly recommend a full Markov approach, but tailored to the run environment in question. That previous article was based on the run environment from 1974-1990, using a Markov approach. This current article is based on empirical results (which is subject to sampling issues) from 1999-2002. The reader is advised to be careful when using either of these two charts.

All data is from 1999-2002. Note: All partial innings are excluded. All home innings in the 9th or later are excluded. In instances where there were no events that occurred at that base/out state, a "---" will show. In instances where less than 30 occurrences exist, a "..." will show.