The most popular way of measuring the run impact of a batting outcome is called linear weights, first introduced by Pete Palmer in the 1980’s and discussed at length in the Sabermetric Wiki.

Using linear weights, you can compare the impact of a single to a double, or a walk to a home run. The linear weight value of an intentional walk, for instance, is usually stated as being between .16 and .18 runs. That’s what you get when you calculate the expected runs for the BaseOut situation that exists after each intentional walk, subtracting the expected runs for the BaseOut situation that existed before the intentional walk, and dividing by the number of intentional walks.

This “Expected Runs” method is the most common method for calculating the linear weight of any event. But it isn’t the only method, and for some events like intentional walks, steals, caught stealing, and bunts, it isn’t the best method.

The alternative method for calculating linear weights is described in detail in The Book (Tango, Lichtman, and Dolphin) on pages 17-22 and the values for events is shown in their Table 4. Simplified, the alternative method substitutes the actual runs scored after an event in the remainder of the inning for the expected runs for the resulting BaseOut state used in the “Expected Runs” method.

Usually the Expected Runs method is preferable because it normalizes to an average lineup for most events, and removing the context of lineup improves the predictive ability of the linear weight. But for strategic events, like intentional walks attempting a steal or bunting, it is better to include the context of the actual lineup, because that context is a major factor in the strategic decision to attempt that play.

For example, the defensive team can elect to intentionally walk any batter, even the leadoff batter, if it wants to. But the intentional walk is usually reserved for certain BaseOut situations, types of batters and places in the lineup.

Both methods of calculating linear weights take into account the actual BaseOut situation in which it occurs (that is why both methods have a value for the intentional walk that is lower than a non-intentional walk), but only the actual runs method includes the factor of the actual lineup position in which the intentional walk occurs.

Here are the linear run values calculated by both methods over the last four years. As you can see, the “Actual runs” method yields a result that is typically a tenth of a run lower than the “Expected Runs” method.

Intentional Walk Linear Weight Value Year N Total Exp Runs Total Exp Runs Total Actual Runs LW EXP Runs LW ACT Runs Before After After 2005 1216 932 1148 1038 0.177 0.087 2006 1410 1067 1318 1217 0.177 0.106 2007 1323 1016 1249 1129 0.176 0.085 2008 1310 974 1220 1065 0.187 0.069 Total 5259 3990 4935 4449 0.180 0.087

Whether the particularly low value for 2008 calculated by the actual runs method is just a sample size aberration or whether it is a result of better insight by teams into when to intentionally walk a batter will take several more years of data to figure out. I suggest that the average linear weight value for the last 4 years by the “Actual Runs” method , .09 runs, be used for all analysis of a batter’s offensive value.

Peter Jensen said...

For some purposes you are correct Dan. If you are trying to calculate whether an intentional walk is the right strategic decision or not, win expectancy is what you want. But many of the win expectancy tables are based on Markov chain simulations that use a constant probability for the intentional walk and therefore make the same error in its win value that I describe here for run value.

Also, if you are using a value for the intentional walk in a linear weight or wOBA formula to calculate a player’s offensive value you should use the value I give in the article, not 0 which is close to an intentional walk’s win value.

dan said...

For IBB, I am of the opinion that calculating linear weights runs doesn’t matter much—Win Expectancy is what I feel you should care about in this case.

dan said...

Also, standard Markov chains obviously don’t have ability to know the abilities/tendencies of the hitter and the pitcher. So if you’re evaluating a specific situation, using something like THT’s new win expectancy tool won’t do you much good anyway.