from Amazon
Friday, April 09, 2010
Starting Run Expectancy
Two people sent me an email this week asking how I calculated the starting run expectancy in The Book.
Let’s look at Table 3, which shows “runs to end of inning” (REOI) for the regular walk of 0.845 and for the non-intentional walk of 0.849. What this means is that from the time the batter received a walk, there was an average of 0.845 runs that scored from that point to the end of the inning. This includes all future batters AND all runners already on base.
Now, you and I both know that IBB are issued in much different circumstances than a regular walk. What we need to do is quantify that context into a single number: the starting run expectancy. Table 3 does that for us. The base/out situation when the IBB was given was .743 while for the regular walk it was .520. Where did those numbers come from? Well, you start with the standard run expectancy 24 base/out chart (Table 1), and weight that table based on the frequency that an IBB and a regular walk was handed out. IBB are disproportionately given out with 1B open and 2 outs. As an example, with 1b open and 1 out, the RE is either .725 or .983 (or 1.467 to load the bases). With 2 outs, it’s between .344 and .634. The weighted average is .743. For the regular walks, the base/out situation leans heavier toward the bases empty, and the weighted average of Table 1 is .520.
That gives you the starting run expectancy, the situation that the batter faced. We also know how many runs were scored when the event occurred (including the runners on base = the situation that the batter face = the starting run expectancy). The difference is the run impact.
That’s one way to get the Linear Weights values. The Book details other ways.