David Berri, author of the Wages of Wins Journal, asked me today how many wins the Tigers are likely to lose due to the ACL injury keeping Victor Martinez out for the 2012 season. This is not an easy question, but I'll keep it as simple as possible.
According to Baseball-Reference.com and FanGraphs.com, Martinez was worth about 3.0 Wins Above Replacement (WAR) in 2011. We could simply compare that to the WAR of the various free agent and trade options, but there are a couple of factors which make this question a little more interesting than that. First, Martinez was used in 26 games as a catcher last year, something that Carlos Pena or Johnny Damon or whoever they might get won't be doing.
The second factor is situational hitting. Martinez was extraordinary batting with runners on base last year, something he would not have been likely to repeat in 2012. So, instead of calculating his 2011 WAR using Batting Runs, it might be more useful to use RE24. The RE24 statistic considers a players performance in various situations in determining his value. For example, Martinez would get more credit for getting a double with runners on first and third than a double with the bases empty. Inserting RE24 instead of Batting Runs adds about two wins bringing Martinez up to 5.0 WAR in 2011.
Would Martinez have had a WAR of 5.0 again in 2012? Probably not. He'd likely hit about as well overall (lower batting average, more homers). However, he might lose a fraction of a win by not catching. More importantly, we would not expect him to come anywhere close to his 2011 performance in situational hitting. Even if he we think he would have hit a little better in clutch situations than other at bats in 2012, we would estimate that he would have had a WAR of about 3.0.
So, we have two questions: (1) How much will the Tigers lose going from Martinez in 2011 (5.0 WAR) to Player X in 2012? (2) How much would they have lost going from Martinez's expected performance in 2012 (3.0 WAR) to Player X in 2012?
To answer question (1), we can assume that Martinez's 26 catching games would be picked up by Gerald Laird in 2012 and that his 119 DH games would be taken by Player X. Let's assume that Laird is a replacement level player this year as he has been the last couple of years. Now, let's estimate what various replacements might do in 119 games:
Carlos Pena 2.3
Carlos Lee 1.8
Casey Kotchman 1.4
Derrek Lee 1.3
Alfonso Soriano 1.3
Johnny Damon 1.2
So, if they were to get Pena, the Tigers would lose 5.0 - 2.3 = 2.7 games from 2012. If they acquired Damon, it would be 3.8 games. Turning that into round numbers, they'd be losing about three or four games between 2011-2012. That's a lot of games, but remember that they probably would have lost a couple of games even if they kept Martinez as he was not likely to keep up his amazing clutch hitting for another year.
To answer question (2) from above, we just need to replace Martinez with player X for 145 games. These are the new estimates:
C. Lee 2.1
D. Lee 1.5
Based on the above numbers, The Tigers would lose 3.0 - 2.6 = 0.4 games by replacing Martinez with Pena and 1.6 games by replacing Martinez with Damon. In round numbers, that's one or two games.
In conclusion, they may drop as many as four games from 2012 to 2011 with the injury to Martinez, but they were probably going to lose a couple of wins anyway due to his clutch hitting normalizing. In the end, they probably lose two games max in 2012 with the loss of Martinez.
Of course, none of this takes into account the possible benefits of intangibles such as leadership and Martinez's effect on other batters. However, I suspect those factors are overstated and there's no way to measure them anyway.
There's no doubt that losing Martinez hurts the Tigers chances in 2012. Just based on the numbers though, the loss should not be a devastating blow to a team that won the AL Central by 15 games last year. They should still be the favorites to take the division.