After needing 11 starting pitchers in less than half a season, the Pirates could potentially be facing the opposite situation soon, with more starters than slots. While some people are thinking outside the box, the general consensus seems to be that Jeanmar Gomez will return to the bullpen, James McDonald will be dealt, DFAd, or go to the bullpen, and AJ Burnett, Francisco Liriano, Wandy Rodriguez, and Jeff Locke will hold the top four starting slots.
Some people claim it’s obvious that Cole should remain with the Pirates and Morton be sent to the bullpen. Others claim it’s obvious that Morton should start and Cole be optioned back to AAA. An analysis shows that it’s not at all obvious what the optimal decision is.
To simplify matters, let’s look at a simple decision: The Pirates can either (1) give Morton the fifth starter’s slot and option Cole to AAA, or (2) give Cole the fifth starter’s slot and move Morton to the bullpen. Assume that between now and August 31, the fifth starter gets 10 starts.
If no other starter is injured before August 31, we'll disregard any contributions from the pitcher who doesn’t get the starter’s slot - we’ll assume that Cole stays in AAA, or Morton provides the same contribution from the bullpen as Bryan Morris or whoever gets sent down to AAA.
If a starter does get injured before August 31 and Cole is in Indy, then we’ll assume he gets called up and takes the remainder of that starter’s games. If a starter gets injured and Morton is in the bullpen, we’ll assume that Brandon Cumpton gets called up and takes the remainder of that starter’s games. This leaves out more complicated possibilities like stretching Morton back out, giving Cumpton a spot start while Morton gets stretched out, piggybacking Morton and Gomez, and so on, but is a reasonable approximation.
The construction of the decision tree and the simplifying algebra is left as an exercise to the reader, but the result boils down to the following key factors:
1. The difference in "quality" between Cole and Morton.
2. The difference in "quality" between Cole and Cumpton.
3. The expected number of starts missed by any or all of the other four starters before August 31 (not including the games leading up to the point where Burnett and Rodriguez are back in the rotation).
The magic formula is: Give Cole the fifth starter slot iff:
E(SM) < 10 * [(WAR(Cole) - WAR(Morton)) / (WAR(Cole) - WAR(Cumpton))]
In words: If the expected number of starts missed by the other four starters is less than the ratio of the difference between Cole and Morton to the difference between Cole and Cumpton, times 10, give Cole the starter’s spot. (The factor of 10 is because in the event of injury, Cole or Cumpton will be called on to start some number of games out of ten games that the injured starter is otherwise scheduled for.)
For "quality", I used fWAR, normalized to a ten-game period. For Cole and Morton, I used the ZIPS ROS projection from Fangraphs. (The Steamer ROS projection from Fangraphs actually projects Morton to be better than Cole; if you believe that Morton will be better than Cole, then the decision really is a no-brainer.) For Cumpton, I used the Steamer ROS projection, as there is no ZIPS ROS projection for him on Fangraphs.
So let’s plug in the numbers.
WAR(Cole), normalized to 10 games: 0.6
WAR(Morton), normalized to 10 games: 0.375
WAR(Cumpton), normalized to 10 games: 0.125.
The difference between Cole and Morton is therefore 0.225 WAR, and the difference between Cole and Cumpton 0.475 WAR.
The key ratio is 0.225/0.475, or 0.47. Multiplying by 10 (for the ten "starter-games" between now and August 31) gives 4.7.
If Burnett, Liriano, Rodriguez, and/or Locke miss 5 starts or more (out of the 40 games they would be expected to start in July/August), then keeping Cole in AAA to fill in is the better decision. (Again, assuming that rotation slots work out for Cole to fill all of these positions, which is more likely in the case of a single starter getting injured and missing 5+ starts - but could also happen in the case of a couple of starters missing two or three turns, depending on timing.) If not, then keeping Cole in the rotation is the better decision.
The next question is, what’s the expected number of missed starts between Burnett, Liriano, Rodriguez, and Locke? While past performance is no indicator of future results, these four have started 50 of 76 Pirates games, or 66%. Liriano hasn’t missed a start since initially coming off the DL, so if you credit him for six additional starts, that’s 74%. So let’s assume each starter has a 75% chance of not getting injured. That works out to a 32% chance of all remaining uninjured, or a 68% chance of at least one getting injured. An injury resulting in a 15-day DL stint and a 30-day rehab assignment would result in a pitcher most likely missing about 40 games, or 8 turns in the rotation. 8 games missed times a 68% chance of injury gives 5.44 expected games missed - which is right around the breakeven point. (Note that an injury requiring a DL stint that happens after the All-Star Break will result in the rehab period extending past August 31, when Cole is almost certainly going to be called up, so the numbers shift a little bit - but this shifts them even closer to the breakeven.)
There are any number of other ways to guess at the expected number of games to be missed by the four Pirates starters, but they all seem to come out at around 5 expected starts missed. So it’s basically a coin flip.
The good news is that whether the Pirates send Cole to AAA and keep Morton in the rotation, or send Morton to the bullpen and keep Cole in the rotation, they’re not making an egregiously wrong decision.