From Bryan Cole at Beyond the Box Score:
From this analysis, we conclude that the efficacy of "saving the bullpen" is overstated, and that there is little if any carryover effect on the bullpen from a longer outing by a starter. Admittedly, there are some improvements to the methodology described here, including developing a probit model (as opposed to a simple linear regression) and using statistics that more directly measure bullpen performance. However, the results here serve as a first approximation showing that any potential dynamic effects from a long outing are most likely too small to contribute to player valuation models such as wins above replacement (WAR).
This conclusion is counter-intuitive and in some ways unsatisfying, as it suggests that innings-eaters have no value beyond their performance. Yet given the choice between a starter who contributes two WAR over 200 IP and one who contributes two WAR over 150 IP, I believe most front offices would prefer the starter who throws more innings. This suggests that we should continue to work to improve our player valuation models to account for such dynamic effects.
This off-season, I've seen Oriole fans bemoaning the lack of starting pitchers going deep into games. Pitchers who average 7+ innings a start are rare. They can be counted on one hand. But that's another story.
The most interesting part to be is that potential effects of a long outing are just too small to have any meaning in WAR. WAR certainly isn't perfect but it's still the best all around indicator that we have to determine overall player value.
As we are in the Hall of Fame season, you have someone like Jack Morris, who ate up innings but also was much less productive later in games. He potentially "saved the bullpen" but at what cost to the game or the overall course of the season?
Does a pitcher who goes 6 innings and lets up 2 runs mean as much as a guy who goes 8 innings but lets up 4?
In a perfect world, you want your starter to go 9 innings and let up 0-1 runs. Most of the time, that gets you a win. But the world isn't perfect and I would be ecstatic about any member of the Orioles starting staff producing 6 IP/2 runs a start.