So the question is, how much did Albert Pujol's early-season slump cost the Angels. There are two ways to look at this question and thus two sets of answers, both equally important. How much money did Pujols cost the Angels, and how many wins did he cost the team?
The problem with estimating the number of wins a player could have added to a team based on that player's performance are the various calculations available. Rather than try to streamline the calculations, I will give an estimation based on the three most popular Wins Above Replacement calculations: Fangraphs (fWAR), Baseball Reference (bWAR), and Baseball Prospectus (WARP).
Before I estimate how many wins Pujols should have had during his slump, I need to do two things. I need to calculate his deterioration based on age, and I need to calculate what he should have been expected to do this season in terms of WAR. Of course, WAR is not a very good predictive statistic, generally speaking. However, when viewed over the course of a career - and a long one at that - WAR becomes a decent predicted of future performance.
Pujols has been remarkably consistent in his yearly performance for almost all of his career. It wasn't until last year that things really started to drop off. And this season is another drop. But we can't make concrete judgments based a couple of bad seasons. Last year and this year could be anomalies brought on by the conflux of specific circumstances and once those circumstances iron out, we may see the Pujols of old. But for the sake of this article, we don't care about the specifics of one season. We care about the career arc.
Pujols is currently playing in his age 32 season, so using the last data point (2012) on the graph is not exactly fair, so here are the raw numbers for fWAR through 2011 with the average WAR drop per season calculated:
Now, let's move on to bWAR. Again, here are the WAR figures from 2001-2011 with the average yearly drop-off calculated:
Finally, here are the calculations for WARP from Baseball Prospectus:
We can see that bWAR and WARP are pretty similar as their calculations for wins above replacement don't differ too much. fWAR has the highest average drop-off per year. However, if I'm going to estimate where Pujols' wins above replacement should be for 2012 based on past performances, there's still one glaring issue.
In 2011, Pujols went on the disabled list for the longest time in his playing career. He fractured a bone in his wrist and missed about four weeks. He struggled before and after the disabled list stint which may have contributed to a lower than normal WAR year. As such, simply taking his 5.1 or 5.2 WAR depending on which calculation we use and subtracting the appropriate average drop-off doesn't work. A better method would be to average his WAR over his career, then subtract the average drop-off to give us a better projection of Pujols' expectations for 2012.
According to fWAR, Pujols has averaged 7.18 WAR per year. According to bWAR, he has averaged 7.63 wins. Finally, according to WARP, Pujols has averaged 8.46.
I'm clearly going into more detail than I'm sure Angels' GM Jerry Dipoto did, but we can now take the average of the three different WAR calculation over Pujols' career and take the average of each yearly drop-off to calculate just how much the Angels should have expected from Pujols. From a production standpoint, this is a pretty fair way of estimating what Los Angeles hoped to get. It accounts for the differing formulas for WAR, and it accounts for Pujols' normal decline due to age and injuries.
The combined average yearly WAR (fWAR, bWAR, and WARP averaged together) is 7.75. Taking each method's average drop-off in WAR per year and finding an overall average, we get an expected drop off of 0.19 WAR per year. That being said, the Angels could have realistically expected Pujols to be worth 7.56 wins for them this season compared with an average replacement-level player.
The next step is to estimate where Pujols will finish in WAR by the end of the year. Because it is impossible to predict injuries, hot streaks, and how the team performs around him, this is probably the weakest part of the calculation, but it's a necessary one. According to fWAR, Pujols has been worth 2.8 wins this season, bWAR says 3.7, and WARP calculates 2.9. Now, we must extrapolate that through the rest of the season to see where he may finish. Pujols has only missed three games out of the Angels' 112 so far this year, but I can't take into account how often he will play. That's already been figured into the WAR calculations. I must simply look at the remaining games on the Angels schedule verse the current WAR for Pujols to see what's probable.
The Angels have 50 games left, which equals 30.86% of the season remaining. Using the current pace for wins and the remaining games left on the schedule, Pujols could finish anywhere between 3.21 and 4.99 WAR (3.21 fWAR, 4.99 bWAR, and 3.94 WARP). Averaged out, Pujols will finish with about 3.71 wins above replacement - a substantial drop over last season, a continuation of the drop we've seen over his last few seasons, and not even in the same ballpark as his yearly average.
Now, we can finally talk about how much Pujols's early season slump has cost the Angels or will cost the Angels. We can talk in terms of money and wins. Let's start with the assumption that Jerry Dipoto made his contract offer based on detailed statistical analysis (with most players this would probably be true, but with Pujols, I'm sure it was just a strategy of giving as much money as the Angels ownership would allow him to). If Dipoto thought this first season (the lightest of Pujols' overall contract at just $12 million) would see Pujol produce at a level of about 7.56 wins above replacement, and assuming Pujols does in fact finish around 3.71 WAR, the Angels would have overpaid by around $6.1 million.
But in free agent dollars, players are often thought to be worth about $5 million per win. In that sense, the Angels are actually getting a deal by paying Pujols $12 million this season if he finishes with 3.71 WAR. Maybe Dipoto knew Pujols would struggle in adjusting to his move from St. Louis to Los Angeles and purposefully back-loaded the contract so the first season wouldn't be too costly for the Angels. Had we been using the same assumptions for the final year of Pujols' contract ($30 million), the Angels would have overpaid by a lot more. Of course, we can't use the same assumptions. So in truth, Los Angeles probably didn't overpay and Pujols' slump likely didn't cost the Angels anything monetarily this year. But that will change if things continue on this path in the subsequent seasons.
How much did Pujols' slump cost the Angels in the standings? As Pujols slumped early on, so did the Angels. At the beginning of May, the Angels were just 9-15. By the end of May they had finally climbed to .500. So it wasn't until June that Los Angeles started playing winning baseball. Of course, the Angels struggles as a team can't be solely placed on the shoulders of Albert Pujols, but his slump did contribute. But by how much?
Let's take Pujols' average WAR per year of 7.56. At this point in the season (112 games in), if Pujols were having an average season, he would be at 5.18 WAR already. Remember were using a combined average of fWAR, bWAR, and WARP. As it stands, we've already calculated him at 3.23 WAR thus far in the year. For the sake of this argument, I'm going to round that to a full two win difference. We can't have partial wins when talking about a pennant race.
The Angels are currently 59-53. They are seven games behind the Texas Rangers for first place and one and a half games behind Baltimore and Oakland for the second Wild Card spot. If Pujols had ben performing at career-average levels (less the expected yearly depreciation, of course) all season long, it's safe to assume the Angels would have had two more wins and two fewer losses, giving them a record of 61-51. With that record, they would be just five games out of first place in the American League West and they would own the top Wild Card spot.
These calculations and estimates are based on theory. Of course, we have no way of knowing where the Angels would rank in wins and losses had Pujols not slumped early in the year. Maybe with a successful Pujols in the lineup, the Angels would have waited longer to call-up Mike Trout. Maybe, the pitching staff would have been pitching with leads far more often and thus pitching with less pressure. We just don't know. It's clear, though, Pujols' slump had an affect. However, he seems to have figured things out. He now has great numbers - just not the superhuman numbers we are used to.