Ryan Howard won the 2006 NL MVP award. Does this make sabermetric sense? I take a quick look at the issue using two metrics: Win Shares (WS) from Bill James, which takes into account all phases of the game, and the linear weights batting runs (BR) from Pete Palmer.
Here are the leaders in Win Shares in the NL for 2006:
Albert Pujols 37
Carlos Beltrán 34
Miguel Cabrera 33
Lance Berkman 31
David Wright 30
Ryan Howard 29
José Reyes 28
Chase Utley 27
Rafael Furcal 27
Alfonso Soriano 26
According to this, Howard had a fine year but was well short of Pujols. Bill James says it takes 3 WS to get one win. So Pujols is almost 3 wins better than Howard. And as long as whoever replaced Pujols when he was injured did not have negative value (you can't get negative WS or it is very rare), then according to this metric, Pujols was easily the most valuable player in the league (Pujols played in 143 games and Howard 159-so to make a direct comparison between the value of these two means we have to consider who replaced Pujols in those other 16 games).
Part of WS includes what James calles "runs created (RC)." This stat is designed to tell us how many runs a given player would add to a hypothetical team. But one aspect of RC now includes batting average with runners in scoring position (RISP) and home run frequency (HR%) with runners on base (ROB). Howard batted .313 overall but just .256 with RISP. His HR% with ROB was 10.55% while it was 9.98% overall. So Howard's RC would be hurt alot by his poor AVG with RISP and only helped slightly by his HR% with ROB.
Pujols, on the other hand, batted .397 with RISP while it was .331 overall. His HR% with ROB was 11.44% while it was 9.16% overall. So it is quite likely that Pujols gets a big boost from the use of clutch hitting in the RC formula. He hit about 10 more HRs with ROB than non-ROB. He had about 11 more hits than expected with RISP. These two combined could be 20-30 more runs than expected. And Howard had about 11 fewer hits with RISP than expected (while the number of HRs with ROB was maybe just 1 more than expected). So Howard is losing maybe 10 or more runs. The total swing between these two could be more than 30 runs. Since it takes about 10 more runs to add a win over the course of a season, the use of clutch hitting data in RC could be the reason why Pujols beats Howard by so much in WS.
Turning to the linear weights stat called batting runs (BR), a different picture emerges. BR tells us how many more runs a team scores with a given player in the lineup instead of an average player. Here are the run values of of various events:
1B = .47
2B = .78
3B = 1.09
HR = 1.40
BB = .33
SB = .22
CS = -.35
Here are the leaders:
Ryan Howard 83.74
Albert Pujols 81.31
Lance Berkman 70.82
Miguel Cabrera 65.58
Garrett Atkins 61.48
Carlos Beltrán 58.09
Matt Holliday 55.25
Jason Bay 53.64
Nick Johnson 52.5
Alfonso Soriano 49.04
I have not park adjusted BR (as RC is adjusted). In Howard's park, runs scoring was 6% higher than average while it was 5% lower than average in Pujols' park. I estimate that taking this into account puts Pujols about 8 runs ahead of Howard.
Pujols is considered a better fielder, so he probably saved more runs than Howard in that area. That would increase his edge. But he played 16 fewer games than Howard. A "replacement level player" would be below average (meaning negative runs both offensively and defensively). That would make things closer.
Overall, Pujols appears to have the edge. But things are close, so Howard is not a bad choice for MVP, especially if clutch hitting were not included in estimating value. Pujols just barely edged Howard in both OBP (.431-.425) and SLG (.671-.659). They both had great years, and although I would give Pujols the nod, his edge over Howard is probably not so great as to invalidate the actual result.