The Cardinals and the Brewers are in the midst of a drawn-out battle to determine the winner of the NL Central, and with two-thirds of the schedule complete, the Brewers have finally elbowed their way into the lead with a 67.9 percent chance of winning the division, according to our Playoff Odds Report at Baseball Prospectus. Looking at the standings, which show the two teams separated by a mere 3.5 games, one can’t help but wonder—what would the division look like if Albert Pujols had played up to expectations this season?

It’s not as though Pujols has been bad—with 3.6 Wins Above Replacement Player so far this season, he’s already produced more than a typical starter would in a full season, and the fourth-highest figure among all primary first basemen. However, prorated out over a full season of games, that’s only a 5.3 WARP pace, nearly three games short of the 8.1 WARP Pujols was projected to earn by PECOTA before the season began. (And lest we think that PECOTA was a touch optimistic, Pujols’ average WARP over the past three seasons was 9.6.)

Pujols has played less than his pre-season expectation, so we have to account for the performance of his backups as well. The gaggle of Pujols fill-ins employed this season, headlined by Mark Hamilton, have combined to give the Cardinals a grand total of zero wins above replacement. (If one wants be precise, that’d be .002 WARP, so almost perfectly zero.) Thus, for the purposes of this analysis, we can safely ignore the performance of his backups.

If we run the numbers, we find that the Cardinals would have picked up an additional 1.9 WARP had Pujols played up to expectations. Since in the real world we can’t account for fractional wins, let’s call that two additional wins. The Cardinals were only 2.5 games back of the Brewers as of the morning of August 3rd; how big a difference would those two games have made?

Let’s turn back to our Playoff Odds Report, which uses a Monte Carlo simulation to play out the remainder of the season. Let’s spot the Cardinals two more victories, replay the sim again, and see how the needle moves. For the purposes of our sim, it matters slightly which two games we spot the Cardinals; for the time being, let’s assume that the two games the Cardinals pick up would’ve been against non-division foes. If those extra wins had been against NL Central rivals, particularly the Brewers, they would of course have had a larger impact.

After making this adjustment, the Cardinals have a 42.3 percent chance of winning the NL Central, compared to their current 27.8 percent chance. That brings them essentially into a dead heat with the Brewers, who have a 54.8 percent chance in our hypothetical scenario.

Now, it would be unfair to lay all of the Cardinals’ current predicament at Pujols’ feet alone; St. Louis could have come up with two wins elsewhere, perhaps by keeping Brendan Ryan and his 2.4 WARP around rather than getting Ryan Theriot and his -0.2 WARP to play shortstop. Pujols has been the Cardinals’ best player this season, and it’s only because he’s been so superlative over the past several seasons that his performance seems lacking. However, in the playoff hunt, every win matters to a team like the Cardinals, and the difference between what Pujols has been this season and what he’s been previously may end up being the difference in the Central this season.

A version of this story originally appeared on ESPN Insider Insider.

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I agree that it's difficult to allocate half a win in the real world. However, in the Monte Carlo world it should be easy to allocate fractional wins. If you want to implement 0.1 wins, simply have 1/10 of the simulations begin one win above the baseline.
"The Cardinals were only 2.5 games back of the Cardinals as of the morning of August 3rd" Being 2.5 games back of yourself is even harder to allocate.
Since Berkman was shifted to 1B, wouldn't the Pujols "fill in" be mostly attributed to Jay?
As a person who sees every Pujols at bat, every day, it looks like he has lost his ability to judge the strike zone. His walk rate is around 8%, half of what it was at his peak a couple years ago. Which is weird because it doesn't seem like players traditionally decline this way, by losing their batting eye and swinging at everything.
My hunch about the lower walk rate is it's harder to pitch around Pujols now with Holliday and Berkman doing well.
"Pujols has been the Cardinals’ best player this season" Better than Holliday and Berkman?
Trying to place blame on Pujols in this scenario is a bit ridiculous, he hasn't pitched out of the bullpen once this year.