First off, the ideas presented forthwith are the result of some joint discussions with Graham, so credit or blame goes to him as well.
There were some lingering questions that Graham and I had after looking at how pitcher's hit a few days ago. Chief among them was the issue of run environments. A typical batter has little effect on his run environment and the situations he bats in are for the most part normally distributed around a 1.00 LI. Pitchers however have a huge effect on the run environment of the particular game itself and we should attempt to account for it.
Consider this, lets say that we have a hybrid player who pitches like Tim Lincecum and hits like Carlos Zambrano. And lets say that in our hypothetical situation, every NL pitcher is a Tim Lincecum clone, imbued with the same talent and ability. In this case, the league average wOBA wouldn't be .333 anymore, it would plummet to something like .310 or whatever Lincecum's wOBA-against was in 2008. Scoring league-wide would be down about two runs per game. That means that each individual run would become more valuable since there are now fewer of them. Now, compare our hybrid Lincecum-Zambrano player to any of the Lincecum clones and you can hopefully see what we're driving toward here. The Zambrano-batting player is now much more valuable than any of the clones because the difference in hitting skill has been made more important.
To put it in a more basic and understood way, just look at park effects. We all know that a run in Texas, Philadelphia, Colorado, etc is not as valuable as a run in Seattle, Oakland or San Diego. That's because those parks have differing run environments. Over the course of a full season they will see enough combination of pitchers that, like the batters, it evens out and the determining factors for parks becomes their dimensions, altitude, weather, etc.
But in an individual game, the pitcher matters a great deal and because of that, we feel that it would be pertinent to give them credit for that on the hitting side. Now, in order to approximate run environment, I am going to use tRA. Specifically, the league average wOBA (.333 in the NL, where pitchers hit) will by divided by a factor which is defined as: tRA+/200 + 0.5. The reason for this is that we want to take the percentage a pitcher bettered the league (tRA+ / 100) and because a specific pitcher only controls half of the run environment for the game (the opposing pitcher, after all, has an equal effect), we add one to account for a league average and then divide by 2 to get back to scale. In unsimplified form: [(tRA+/100)+1] / 2.
What this boils down to is that pitchers that are above average at pitching will get a boost to their hitting value, no matter how good or poor it is because he will be batting in lowered run environments, while the opposite holds for below-average pitchers.
Another factor to consider is leverage. As mentioned, low run-scoring environments mean that each marginal run is more valuable than in a high-scoring environment. That means that each plate appearance in an offensively suppressed situation is going to have a fractionally higher leverage. That can affect our model by magnifying or attenuating the importance, to a small degree, of how the pitcher bats in his turns at the plate. If the pitcher is especially good, like Tim Lincecum, his plate appearances might carry a larger leverage index than those of Kyle Kendrick and thus how Lincecum performs in those at bats is slightly more valuable, either positively or negatively.
To test if this effect exists, I would need a large amount of information on the leverages encountered by pitchers in their at bats since they have such small samples individually. It does me little good to point to the above example, but note that Lincecum does indeed have a higher LI on average than Kendrick. In fact, just by looking through the numbers of some long time NL hurlers, their LI seems to be more connected with their hitting ability than their pitching. The better the pitcher is at hitting, the higher his leverage is, theoretically because the manager will let him bat in higher leverage situations. Again though, that is nowhere near confirmed.
Either way, pitchers do face an overall lower leverage in their at bats, to the tune of about a 0.90 average, so we should knock off 10% of their hitting value to account for this.
Here are the top 25 starting pitchers in terms of wins (encompassing all mentioned above):
wOBA is park-adjusted, BRAA is the straight hitting value, PosAdj is the position adjustment for pitchers (roughly 9.8 wins per 700 PA in 2008), Runs is the addition of the preceding two values, BRAA^ is BRAA adjusted for the run environment, Diff is the difference between BRAA^ and BRAA, Wins is Runs^ / 10 * 0.9 [for leverage].
Bottom 10 in wins:
Top
and bottom 10
in terms of Diff, seeing the spread in how the pitcher's pitching ability affects his hitting value. As you can see, the spread here is not as large, roughly ten runs, compared to the overall values, which have a spread of 20-25 runs. Still, it's a worthwhile addition to the model and provides a far more complete picture.
Once again, to be clear, the value presented as wins is not the pitcher's hitting ability in WAR. It's the pitcher's hitting ability plus a positional adjustment plus a leverage adjustment plus a run environment adjustment. For example, Brandon Backe is a better hitter than Tim Lincecum, but because Lincecum is such a better pitcher, Lincecum's hitting is more valuable because his poor at bats do less damage in a low run environment.
Of course, that is just the hitting component, so why not go ahead and add the pitching wins to those? Good idea, Matthew! Here's the top 21 (so that you could see Zambrano) and bottom 20 in overall wins. As far as I can figure, this represents a complete measure for everything except a pitcher's ability to field.
Top 21:
Bottom 20:
Note that these are separated by team-seasons, so CC Sabathia has separate entries for his time in Milwaukee and Cleveland. Altogether he was worth a little over 9(!) wins in 2008.