The cost of a long first inning

On Thursday night, I posed a question to our Twitter followers unsure of the response. I hadn't spend a great deal of time thinking about the question and I certainly hadn't taken the time to delve into any relevant data. The question was simple, and to be honest, I expected someone to point out an obvious solution and send us on our way. Instead, the feedback was pretty split.

Would you rather have your starting pitcher throw 40 pitches (SP40) during the first inning without allowing a run or would you rather your starter throw ten pitches (SP10) but allow one run?

There are many variables at play, and I won't pretend to consider them all, but it comes down to the fundamental question: would you rather get to the bullpen sooner or get there later having allowed an extra run?

If you assume the average starter is going to give you about six innings, the starter who threw 40 first inning pitches is probably only going to make it through four. That certainly isn't a guarantee, but it's a good place to start. Normally you need three innings from your bullpen, but here you will need five. This likely means two extra innings from your long man or an inning a piece from your fourth- and fifth-best guys.

We could generate probabilities to help, but there are so many variables at work that any estimate is going to be lacking. Instead, let's simply talk through the factors at play and potentially set up a future analysis.

SP40 has a run to give on SP10, but the fact that he threw 40 pitches during the first inning might indicate that he does not have his best stuff and will be more likely to allow runs in later innings that we would expect before observing the first inning. So in theory, we might trust the bullpen guys to perform within a run of the starter over the course of the replacement innings, but SP40 might have already given away the advantage.

Building on that factor, it matters who the pitchers are and what your prior expectations were. If Clayton Kershaw throws 40 pitches in the first inning, you should be less concerned about him going forward than if Mike Pelfrey needed forty pitches to escape the first. The odds of Kershaw settling in and being his usual self are higher because the 40-pitch inning was more likely an outlier. The same is true for the 10-pitch inning in reverse. If you get an efficient inning from someone who usually needs many more pitches, it's less likely that this 10-pitch inning is a sign of a special day.

Of course, it also matters who you have in the bullpen. If you have a dynamite group in there, you're more likely to prefer the absence of a run to the efficiency of a starter. But it also matters how well rested they are and where you are in the season. The effect of taxing the bullpen isn't just felt in the game in which you're doing it, you're also going to have some downstream costs from extra pitches.

You also need to consider the quality of the two offenses. If you're very likely to outscore the opponent going forward, you'd probably rather give up the run and save the bullpen while taking a chance that your starter is on his game than if you probably weren't like to score too many runs yourself.

This is all before you consider the actual quality of the inning. Was the 10-pitch inning a great inning in which Mike Trout crushed a pretty good pitch or did you happen to escape thanks to a really fortunate double play? The same is true of the 40-pitch inning. Did the defense give away extra outs or was the starter really struggling to find the zone and put hitters away?

I suspect there are variables I haven't considered and someone who had more time that I did this weekend could probably work out a strategy for solving the inequality. Under a certain set of conditions one is probably favorable and under another set of conditions you'd prefer the other. Feel free to post in the comments section with complicating variables and important considerations.

Prior to doing that type of complete analysis, my personal preference would be to take the guy who allowed the run over 10 pitches. Some of that is simple aesthetics. Watching a guy labor through 40 pitches can be brutal. Some of it is the hunch that a guy who threw a 10-pitch first inning is probably going to have a good day and you'd rather see what he can bring rather than turning to some of your worst relievers.

It's an interesting question because the more you think about it, the more you probably go back and forth between your choices. My guess is that the single game math will favor SP40, but just about every long term factor favors SP10, and that's before you factor in how much real information you can glean from that first inning. I'd also be curious to know what managers would prefer. My guess is that all 30 would pick SP10, but that doesn't necessarily mean it's the right call.

...

Neil Weinberg is the Associate Managing Editor at Beyond The Box Score, a contributor to Gammons Daily, and can also be found writing enthusiastically about the Detroit Tigers at New English D. Follow @NeilWeinberg44