Why should Bronson Arroyo pitch 160 innings instead of 200 this season?

John Sommers II

It turns out that being a League-Average Innings-Muncher is more lame than LAIM.

If you know one thing about new Diamondbacks starting pitcher Bronson Arroyo, know this: He’s a workhorse capable of delivering 200 innings every season. Over the past 10 years, Arroyo has thrown over 2,000 innings for the Red Sox and the Reds – only C.C. Sabathia and Mark Buehrle have thrown more.

(If you know two things about new Diamondbacks starting pitcher Bronson Arroyo, know this. But that’s hardly relevant at this time.)

When the Diamondbacks signed Arroyo to a two-year, $23.5 million contract last week, it’s possible that 200 (and all those innings) were the first and foremost number on Kevin Towers' mind. After all, if you look at almost any statistical reference, Arroyo’s not a top-flight starting pitcher. He's the guy you acquire when you can't acquire the other guy. During his better seasons, he’s average or slightly better. During his worst seasons -- most of which have come recently -- he’s below-average. By himself, Arroyo isn’t a difference-maker, but he’s the type of starter teams love to have as a consistent veteran presence to anchor the back end of a pitching staff.

So why is it that the Diamondbacks will probably be a better baseball team if they have Bronson Arroyo pitch fewer than his usual 200 innings? Why is that also the case for so many starting pitchers these days? If we assume that the D’Backs made the investment in Arroyo mainly for his ability to rack up innings, why on earth should they want to limit his one unique skill?

The first and most important is something called the "Times Through the Order Penalty" or "TTOP". TTOP tells us that the more times a hitter sees the same pitcher in a ballgame, the better the hitter does against that pitcher. And because of this penalty, pitchers like Bronson Arroyo shouldn't go quite as deep into games ... even if they're capable of doing so.

If you consider it for more than a minute, this concept rings true from a common-sense perspective: pitchers fatigue, hitters see more pitches and are able to recognize and time them more easily as the game goes on. But beyond common sense, there’s also some serious math to back it up. It doesn’t matter if you’re an elite starter like Clayton Kershaw or a journeyman like Kevin Slowey -- the data says that, on average, a pitcher's performance is going to decrease the second and third times through the batting order. Death, taxes, familiarity.

Christy_mathewson_medium A hundred years ago, pitchers like Christy Mathewson averaged over 300 innings a season, but they weren't necessarily all good innings. (Getty Images)

If you're a monster like Clayton Kershaw -- or even a lower-level ace or No. 2 starter -- or your starter is having a killer game, it may be worth it to leave a starting pitcher in the game as you venture into the third trip through the order. The penalty shows up as about an additional .35 runs added to a pitcher's overall ability, which in the case of an ace makes riding it out a no-brainer. However, since hitters benefit so much from seeing a starting pitcher a third time, it makes mathematical sense to pull your back-end starter before this happens in most situations. Unless your bullpen is truly awful (I’m looking at you, Houston Astros), the sixth and seventh innings are probably too much of a danger zone for starting pitchers these days.

It's one thing to want to ditch a starting pitcher before he hits that third-time-through-the-order wall, but what about the guy you're going to replace him with? Isn't the reliever going to be worse than even a tired back-end starter? The answer is, probably not. We are firmly entrenched in an era where relief pitchers are -- on average -- quite a bit more effective than starting pitchers. Take a look at the league averages for two stats: earned run average and fielding independent pitching for starting pitchers compared to relief pitchers for 2011, 2012, and 2013 below:

YEAR ERA - SP ERA - RP FIP - SP FIP - RP
2011 4.06 3.69 4.00 3.83
2012 4.19 3.67 4.13 3.79
2013 4.01 3.59 3.95 3.70
Data from FanGraphs.

Simply put, the average reliever gives up fewer runs (and home runs) and strikes out more hitters than the average starter. If you have an average starter and an average reliever, then you're probably going to wish the average reliever was pitching at any given time.

With this information in mind, let’s go back to the case of Bronson Arroyo for a moment. Imagine that he’s having an average outing at the beginning of the 2014 season. The score is tied at three, but Arroyo is set to face the top of a batting order for the third time in the middle of the sixth inning. The Diamondbacks didn’t have a great bullpen in 2013. Pre-season darling David Hernandez wasn’t any good, and the bullpen ranked 24th in baseball by sabermetric statistic FIP -- which measures walks, strikeouts, and home runs allowed. Nevertheless, at least five of those D’Backs’ relievers from last year were markedly better than Arroyo on a rate basis last year -- even before accounting for the fact that Arroyo is facing a lineup for the third time in a game. With Addison Reed in the fold, there are probably six or seven arms in the bullpen who could provide equal or better value if the team would simply pull the plug on Arroyo in this instance, and this doesn't even account for matchup situations like bringing in a left-handed pitcher to face a left-handed batter – a situation that brings its own advantages for the pitching team.

There are perfectly reasonable arguments to be made against having a quick hook for your starter. Here's one: if you pull Bronson Arroyo an inning (or maybe two) earlier than usual in each of his 32 starts next season, perhaps you need to find 40 or so innings somewhere else in your starting staff. And those innings won't be coming from one of your best pitchers, they're likely coming from the 14th-best pitcher in your system. But in this case, you're probably going to be able to find a guy who's usually considered "replacement-level", someone who pitches about as well as Heath Bell did in 2013 (4.11 ERA, 4.10 FIP in 62 innings), or slightly worse. Your mileage may vary -- maybe the guy you call up from Triple-A or find on the waiver wire will be better, maybe he'll be worse -- but that's what you're looking for, and the drop-off between some of Bronson Arroyo's worst innings and these doesn't seem like very much. That's not a good enough reason to stick with Arroyo or another fringy starter in the late innings.

Another possible counterargument is that a starter that goes deeper into games can "save" the bullpen for future days. Well, this may be counterintuitive, but there’s one study (performed by Bryan Cole over at Beyond the Box Score) that seems to indicate that this doesn’t have much, if any, effect on future bullpen performance. This is a dynamic question to try and answer, and you can’t do it with just one study, but there’s some indication that maybe this isn’t something that dramatically affects a team’s future chance of winning, so maybe there's an issue here, but maybe not.

Could having a quick hook for a starter reduce his confidence, and make him less effective in future outings? I suppose that’s a possibility, and it would be great to see data to support that assertion -- but I suspects that major league pitchers are mentally tough already, and being pulled early in games might not be a disaster -- especially if it means that their end-of-year pitching statistics are a little better since they didn’t get crushed the third time through the lineup.

If I’m the fan of a team, or part of the front office, I’m probably going to be in favor of the strategy that allows my team to win the most games. If limiting Bronson Arroyo to two times through the batting order each start forces the Diamondbacks to run more relievers out during each game, yet it also causes them to win an extra game or two and line up a wild-card berth, I think the fans and the front office are calling the tradeoff more than fair.

Unless a guy is a No. 1 or No. 2 starter, or is throwing a particularly great game, the math tells us to pull your starter early and hand things over to the guys in the bullpen. They're a better bet the third time through the lineup than an iffy starter.

Sorry, Bronson.

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