Where should Robinson Cano bat in the order?

Let me say that Steven Goldman, over at the Pinstriped Bible, is one of my favorite sportswriters. Actually, he was numero uno, until he was dethroned by The Poz, but there is no shame in that, not at all.

What Goldman has in spades is writing chops — the guy knows how to put words together to make you understand the game. That is why I follow him religiously, even though his main subject matter is the hated (by me, of course) Yankees.

Goldman, who also moonlights over at Baseball Prospectus (or maybe that's his day job, I dunno), is pretty sabermetrically savvy, but I'm not totally on board with his recent blog post on Robinson Cano. In that post, Goldman essentially claims that:

1. Robbie Cano hits much better with the bases empty than he does with men on.
   
2. Given (1), batting Cano 2nd in the lineup would be smarter than batting him in his usual position lower in the order, the idea being that in the two-hole, Cano would bat more often with the bases empty.
   

Let's take these one at a time. When I see anybody claim that any hitter is better in a certain situation, e.g. with runners in scoring position, I immediately get skeptical. My, admittedly nerdy, working assumption is that batters hit the same in all situations. Now, before you get all huffy, let me make a disclaimer:

1. Obviously, one split that really is real is the platoon split. Nearly all batters hit better against opposite-hand pitching.
   
2. I'm not saying that there isn't any player in the world who truly hits better with the bases empty (or in night games, or in Cincinnati, or on Tuesday). I'm just saying that I believe that the vast majority of players do not hit better in these odd situations. Most everybody hits about the same most situations. That's my working assumption. I'll be wrong sometimes, but (I believe) I'll be right most of the time.
   

So, here are Cano's splits with nobody on and with men on base:

.
               PA   AVG   OBP   SLG
Bases empty  1580  .331  .363  .528
Runners on   1456  .280  .312  .425

Wow, Cano really does hit a lot better with the bases empty. I checked to see if these numbers might just be a statistical aberration and it seems pretty unlikely. For example, the probability that the 51 point difference in OBP is just a statistical fluctuation (i.e. that Cano's true OBP in the two situations are the same) is about 0.5%. Cano's propensity for hitting with the bases empty is especially curious, since on average batters fare better with runners on. (That's because the defense has to worry about the baserunners in addition to the batter.)

Ok, so maybe Robbie Cano really does hit worse with runners on. That's unfortunate for him, but so be it. But will batting Cano 2nd instead of 7th (his usual spot in 2009) make a difference? Goldman's take:

To get the most out of Cano, a manager might keep him out of RBI spots. Now, when you have one of the best offenses in baseball, your whole batting order is an RBI spot. That’s why the second spot in the order is a place he might prosper. Even if the Yankees get another .400 OBP from their leadoff man, Cano would be batting with the bases empty 60 percent of the time, do his best hitting, and be on base for Mark Teixeira, A-Rod, et al. The downside is that you might get a few extra Cano double-play specials when the leadoff man does reach base.

The following table shows how often Yankee batters came to bat with the bases empty for the different lineup positions in 2009:

+------------+-----+--------+------------+
| lineup_pos | PA  | noneOn | noneOnFrac |
+------------+-----+--------+------------+
|          1 | 785 |    496 |     0.6318 | 
|          2 | 772 |    392 |     0.5078 | 
|          3 | 753 |    358 |     0.4754 | 
|          4 | 732 |    341 |     0.4658 | 
|          5 | 715 |    356 |     0.4979 | 
|          6 | 699 |    402 |     0.5751 | 
|          7 | 682 |    371 |     0.5440 | 
|          8 | 668 |    361 |     0.5404 | 
|          9 | 643 |    336 |     0.5226 | 
+------------+-----+--------+------------+

The last column of this table shows the fraction of plate appearances that occur with nobody on base. Now, focus on the #2 and #7 positions: actually, the #2 slot batted with nobody on less often than the #7 position (51% compared to 54%). Putting Cano in the #2 slot would actually worsen his overall production (taking at face value the splits mentioned previously.)

Furthermore there is an additional cost of batting Cano 2nd: it likely moves Nick Johnson, you know, the .400 OBP guy, down in the order. (Goldman talks about Johnson possibly leading off and Cano batting second, but the Yanks have a guy who has always batted #1 or #2, fella name of Jeter.) Obviously, batting higher in the order gets you more PA's. A good rule of thumb is that each spot in the order gets 18 more PA's over the season than the next one. Anyway, what difference might we expect in Yankee offensive production if Cano bats second and Johnson bats seventh and vice versa? Well, it turns out the difference is quite small (I'll spare you the details), batting Cano 2nd and Johnson 7th would cost the Yankees about a run over the course of a season.

So, moving Cano up in the order will not really accomplish anything for the Yankee offense. In the end, careful analysis of batting order scenarios invariably leads to the conclusion we have here — it just doesn't make much difference. Goldman himself said it nicely:

First, many studies suggest that the difference between the optimal batting order and the least-optimal batting order is quite small. That said, there is a difference, and even if it’s as little as one win a season, you never know when you might need that one win.

It's just that the "win" he mentions is more often a small fraction of a win, but it's still true that you never know when you might need that one small fraction of a win.