Does the order of the starting rotation matter? Or "Second is the best."

One of the popular talking points in the wake of the Masahiro Tanaka signing has been the ideal order of the Yankees rotation. The question of how Joe Girardi will line up Tanaka, C.C. Sabathia, Hiroki Kuroda, and Ivan Nova has been an object of speculation not only on talk radio, but even amongst the more sabermetrically inclined, including here at IIATMS. I was surprised by the intensity of interest in this topic because for quite some time I have been operating under the assumption that the order of the rotation does not really matter. At some point, I tallied this an established baseball truth. However, when I attempted to figure out why I was persuaded of this belief, I came up empty. (If anybody does know of a comprehensive study on this subject, please make reference to it in the comments.) So, I began doing some analysis myself. Those who argue about the order of the rotation premise that argument on two primary assumptions. First, pitchers at the top of the rotation get more starts. And, second, pitchers at the top of the rotation face tougher competition. I was most interested in this second assumption, which I wanted to analyze from two perspectives. First, in terms of intent: Do top of the rotation starters consistently face other pitchers at the top of the rotation? Second, in terms of results: Regardless of how they "rank," do top-of-the-rotation starters actually face competition that performs better?

The findings that follow are by no means comprehensive. To get truly convincing answers to these questions, a larger sample would be preferable, as would assessment based on more advanced metrics (for instance, FIP). But, alas, that requires time and resources I don't have. My cursory attempt does suggest it may be a project worth pursuing, because my results, though inconclusive, are intriguing.

Naturally, I started with the 2013 Yankees, and the vaunted "Ace" position. Sabathia, last season's Opening Day Starter, occupied the pole position for the first 95 games of the season. After the All-Star Break, as you may recall, the Yanks reset their rotation with Sabathia as the #3 and Andy Pettitte at the top. But, again, the identity and performance of Sabathia and Pettitte only matter to me in so much as they represent management's intention to match their "Aces" against similarly highly-regarded opponents.

To this end, the 2013 Yanks were somewhat successful. New York's "Ace" faced the opponent's "Ace" on twelve occasions. No other spot in the rotation faced the opponent's #1 more than seven times.

Ace Table 1A closer look at the data, however, reveals a potential flaw in this strategy. Though Sabathia/Pettitte matched up a disproportionate amount with the Verlanders and Prices of the American League, they actually faced pitchers from the top half of the opposing teams' rotation less than 50% of the time. They faced 18 opposing pitchers who were graded as fours, fives, or replacements (inserted into a rotation because of injury or ineptitude).

This is especially interesting as contrast to the Yankees #2 spot, the position Kuroda occupied all year.

#2 Table 1

As you can see, Kuroda faced substantially stiffer competition than Sabathia/Pettitte, matching up with somebody from the top half of the opposing rotation (#1-#3) approximately 75% of the time. Not only did the #2 position face competition which was "intended" to be tough, that competition performed accordingly:

Yanks OP ROT

Kuroda's opponents stayed in games a half-inning longer, allowed substantially fewer earned runs and baserunners, and had a far superior K/BB rate.

Reflecting upon this, there is a coherent reason the #2 position might consistently be the toughest in the rotation. As the season progresses, usually even before the end of April, it is inevitable that off days, skipped starts, etc. will ensure that some team's rotations turn over before other's, creating opportunities for a #1 to face a #5, etc. However, we might expect these shifts to happen somewhat incrementally, so that while a #1 might have equal chances of seeing a #2 or a #5 two weeks into the season, they are less likely to see a #3 or #4 (unless their opponent has chosen to go with four-man rotation). Thus, while an Ace is almost guaranteed to see the backside of several opposing rotations in May or June, the #2 is somewhat less likely, because it requires his rotation to be further out of sync with that his opponent. (This is exactly what happened with Kuroda. He did not face a single pitcher who began in the #4 or #5 spot until the 81st game of the season. Soon thereafter, everybody reset their rotation during the All-Star Break and he went another month or so before he lined up with somebody from the backend.)

At least based on the rotations I've analyzed, while there is considerably variance in performance among the top three positions, the pitchers teams choose for these positions are considerably better than those assigned a #4 or #5, as well as considerably less likely to be replaced (and the replacements are rarely any good). Thus, it would follow, if the #2 consistently faces more "top of the rotation starters" than the #1, even if he faces fewer so-called Aces, it might be strategically advantageous to put your best pitcher in this position, rather than at the very top. I wanted to test this theory across the AL East.

First, let's look at the intention component:

Rotation Chart 1

As you can see, the totals for the East are roughly consistent with those of Yankees, especially at the top of the rotation. Like Sabathia/Pettitte, the other AL East Aces saw a lot of each other and a lot of Aces throughout the league, but they saw relatively little of pitchers from the #2-#4 range. #2 starters matched up with each other as often as Aces did, but drew a #4 or #5 only 12% of the time. Aces throughout the AL East only faced "top of the rotation" starters 56% of the time, roughly the same as pitchers is the #3 (52%) and #5 (51%) positions. #2 starters, on the other hand, drew such opponents a full 72% of the time.

This disparity was not only true for the division as a whole, but for each team individually. The Red Sox #2 starters faced one of their opponents top three a staggering 88% of the time. Baltimore's #2 starters had the lowest such share, at 62%, which was still even with that of their Aces (63%). It seems pretty clear, if you want to assure the most starts against the most highly-rated opposing pitchers (in the 2013 Al East), you should pitch out of the #2 slot. But what about the results?

AL East Rotation Chart 2

The opponents of #2 starters led all other rotation slots in ERA, WHIP, BB/9, and IP/GS. They led by a wide margin in several of those categories.

I am tempted, based on evidence from the two preceding tables, to draw the following conclusion: your best pitcher, whoever you believe that to be, should be your #2 starter. Also, again, probably because #1 starters often mismatch with #5 starters, your worst (or most inconsistent) pitcher should probably slot in at #4.

However, returning to the caveat from earlier, this data clearly needs to be correlated with similar studies of rotations from throughout the league and from earlier seasons. The AL East's #2 starters in the first half of last season were Kuroda, Jeremy Hellickson, Clay Buchholz, Wei-Yin Chen, and Brandon Morrow. After the All-Star Break they were Kuroda, Hellickson, John Lackey, Miguel Gonzalez, and Mark Buehrle. I don't think that's a particularly awe-striking group, so I doubt they the disproportionate number of starts they made against each other swayed the stats too much to their advantage. More realistically, perhaps, down years from Sabathia, R. A. Dickey, Jason Hammel, and Jon Lester might have depressed the quality of the Aces.

How should this influence the debate about Tanaka? One of the familiar refrains has been to keep him free of the "pressure" of being the Opening Day starter. The temptation to avoid that single-game spotlight might lead the Yankees to unintentionally thrown him into the pressure-cooker for six months, as he pitches in closer, lower-scoring games and has few opportunities for "confidence-building" victories. Remember, Kuroda had an 11-13 record last year, despite having one of the best seasons of his career (4.1 WAR). Lackey had his best season since 2007, but after the All-Star Break was 3-7. Of all the #2 starters listed above, only Buchholz had a record that was better than two games over .500. None had more than 12 wins. The safest bet, in my opinion, would be to leave Sabathia and Kuroda at the top, in positions they've become accustomed to, and put Tanaka at #3, where he's likely to see a wide array of opponents.