(numbers are now all updated for the end of the regular season)
Mainstream media pundits have decided that Miguel Cabrera, if he wins the hitting triple crown, needs to be named the MVP of the American League. Statisticians have countered that Mike Trout has been worth at least 2-4 wins more over the course of the season, according to every mega-stat available and that the difference is not close enough to consider the Tigers third baseman. The mainstream have predictably replied by mocking or deriding those stats without understanding and then the blowback has become that there is no possible statistical case for Cabrera.
I think so. We will need to consider three things that mega-stats don’t to make that case, and it becomes quite context-specific (though not to the point where we’re considering team standings). First, we need to counter the additional runs Trout generates because his manager hits him higher in the order. Second, we need to regress defensive stats, a troublesome, if allowable procedure. And lastly, we need to consider the actual replacements who were available instead of some theoretical “replacement level” player who if he’s real might or might not be available to a team in April or May or August of a specific year.
Step 1. Miguel Cabrera has hit 3rd in every game he’s played this year. Mike Trout has hit leadoff in every game that he’s started. Thus, through no fault of his own, Cabrera has fewer chances to help his team.
Before we adjust for that, though, we need to adjust double plays for opportunities. Miguel Cabrera hit into 28, Mike Trout hit into 7. Cabrera came up in 146 situations (in 161 games) where it was possible to hit into a double play. Trout came up in 87 (in 138 games). If he’d had the same rate of opportunity, he would have come up in 125 and would have hit into 10 double plays. On to the next adjustment…
Miguel Cabrera started 161 games and was given 697 plate appearances in them. 4.33 PA/Game.
Mike Trout has started 138 games and had 639 plate appearances (he also pinch ran in a game but didn’t come to the plate). 4.63 PA/Game. He has 42 more plate appearances than he would if he came to the plate at the same rate as Cabrera.
If Trout were hitting third then, he would have approximately the following numbers (with adjusted DPs):
Compared to Cabrera:
Using standard linear weights, we get 139.5 runs created for Trout and 152.5 for Cabrera. According to Baseball Prospectus, Trout has been worth 5 non-SB runs on the basepaths while Cabrera has cost his team 5.5 runs. Adding that up, offensively, Trout has been worth 144.5 runs in 138 games while Cabrera has been worth 147 in 161 games. Clearly an advantage to Trout.
Step 2. All calculated-WAR values use a standard positional adjustment, but we will eschew that for now. Trout defensively has been worth 11.5 runs (Fangraphs) or 21 runs (baseball-reference.com) or 8.5 runs (BP). The average of those 3 gives us about 13.5 runs. Since it takes about 3 times as much playing time to give good defensive values as it does to give good offensive values, we will regress these to average, and we get Trout being worth at least 4.5 runs. Unfair, but we’re trying to make the case for Cabrera (who gets -2 runs).
So, total Trout is worth 149 runs and Cabrera is worth 145.
Step 3. Using any standard value of Replacement Level will obviously make Trout the more valuable player. To make a case for Cabrera, we need to show that he was replacing players who would play at a much lower level than those that Trout was replacing. We’ll have to theorize about who the players actually would have been.
If Cabrera had actually missed the season, he would have been replaced by Brandon Inge. Inge ended up being cut and becoming the regular 3Bmen for the A’s where he put up decent numbers, but also missed a lot of time. He missed two weeks in May and then his season was basically over (aside from some early September heroics) on August 12. Overall, he was unavailable for over eight weeks and played only half a season. Who would have replaced the replacement?
Ramon Santiago and Don Kelly each had a pair of starts at 3B for the Tigers, but they were awful. Audy Ciriaco, the Toledo third baseman was even worse and top prospect Nick Castellanos was clearly not ready. We’re well into guesswork here, but let’s assume Santiago and Kelly would have filled-in in May. By August, the team had added Jeff Baker, not a world beater, but a much better alternative. He likely would have taken over in August/September (and not been traded away instead). Estimates then: Inge – 90 games, Baker – 47 games, Kelly – 12 games, Santiago – 12 games.
Using their seasonal averages and estimated playing time (and a park adjustment for Inge), the four of them would have combined to be worth 104.5 runs on offense. Inge (regressed) is worth about 2 runs on defense and none of the others played any real time at 3B. That gives the replacements a total value of 106.5 runs.
So, if Cabrera has missed the season, and the Tigers had kept Inge and then kept Baker (and Baker had stayed healthy through August and September) they would have lost 38.5 runs.
The Angels, on the other hand, had a plethora of outfielder who would have taken Trout’s time. Peter Bourjos often sat on the bench, Mark Trumbo played games in right, at 1B and at DH allowing Trout (in LF) to functionally sub for not only him, but for Torii Hunter, Kendry Morales and Albert Pujols. Vernon Wells got some time. And Bobby Abreu was released due to overcrowding. It’s hard to breakdown.
When Trout was first called up, he mostly played center and pushed Bourjos (and occasionally Vernon Wells) to the bench. Three weeks later, Vernon Wells got injured, while Torii Hunter was away from the team. Trout moved to left; it’s Kole Calhoun whom he plays instead of for about a week before Hunter returns. At this time, the outfield is Trumbo-Trout-Hunter with Bourjos on the bench. On July 28, Vernon Wells comes back and from that point, Trout plays almost exclusively center field. Peter Bourjos misses two weeks of that time (where we’ll put Wells as the backup CF), but otherwise, Mike is exclusively taking his spot. What we get, in very approximate terms, is Trout taking 5 starts from Kole Calhoun, 10 each from Torii Hunter and Kendry Morales, 20 from Vernon Wells (15 in CF) and the remaining 93 from Peter Bourjos.
Hiding all calculations (and assuming those players got the same PA/game rate as Miguel Cabrera), that’s 87.5 runs on offense. Bourjos is an insanely good fielder (averaged and regressed we still get almost 4 runs in half a season), but the LFers (Trumbo and Wells) are about average, so we’ll add 5 runs to the replacements for defense. That gives them a total of 92.5.
So, Trout added 56.5 runs to his team, or 18 more than Cabrera.
Conclusion. Can we do anymore? Peter Bourjos, starting two games a week and otherwise playing as a defensive replacement, had a horrible season at the plate, putting up a 75 OPS+. To improve Cabrera’s case, we have to allow that he would have hit much better as a regular. His projection for the season has a 96 OPS+ which (for 93 games) would have given him 70.5 runs, or 15 more than our previous calculations gave him. Now we’re almost even.
Should we do this for everyone? Most of our other players played most of the time anyway (Inge, Wells, Hunter, Morales) or were bench players in real life and as replacements (Santiago, Kelly, Calhoun). Jeff Baker is the only one who would rate the treatment, but the difference for him is at most one run either way.
We’re still not quite done. Trout’s home park depressed scoring so each run is worth more there. His hypothetical 41.5 runs added are worth about 45.5 in a neutral park. While Cabrera would be worth about 37.5 runs in a neutral park. So, in the best possible case for Cabrera, Trout is 8 runs better.
That’s a small enough number that it is possible to believe Cabrera had a better season. Maybe Baker would have performed worse with a full time job. Maybe the non-SB baserunning values are well over-estimated and due to other factors like role and batting order spot. Maybe the Tigers have been playing under more pressure since the Angels were mostly written off by May. Or maybe you want to give Miguel a bonus for being willing to move back to a position that he hadn’t played in five years to allow his team to add Prince Fielder.