Stathead Sagas: Pujols And Projections

If you used the RotoWire Draft Software, chances are you were pretty bullish on Albert Pujols's season. You may have dropped a top-4 pick on the $250 million dollar man, or you may have paid north of $50 (out of a standard 260) to earn his rights in an auction league.

If that's the case – as it is for me in two of my nine leagues – you're probably not too happy with Pujols's stats so far this year: .272 average, 15 HR, 54 RBI, 46 R, 6 SB in 89 games. Owners would be happy with production of this level from most players, but not Pujols. According to our Actual Dollar Value page, Pujols has only been worth $21 this season, ranking him 32nd among all players. For another perspective, Yahoo's player rank has Pujols all the way down at 53rd overall.

Granted, Pujols had an ADP of 3 in drafts across most formats this season, so users of our software and our projections aren't alone. Still, it's more than fair to wonder where everyone went wrong. We were projecting Pujols as a top-4 pick based on a .309 average, 40 HR, 111 R, 112 RBI and 11 SB.

Stretch Pujols's production this year across 162 games and you get the .272 average, 28 HR, 84 R, 99 RBI and 11 SB. So at least the steals are on the right pace.

But we must consider Pujols's horrific start to the season. He bottomed out at a .505 OPS on May 11, hitting just .192/.228/.277. It's taken a near-heroic effort to get back to where he is right now -- an effort where, he's played at or above his projected levels for large stretches of time.

Observe:

Speaking most generally, this graphic measures Albert Pujols's performance this season against his projected performance. The projected performance is noted by the solid black line, with Pujols's performance noted by the red line. The width of the red line denotes Pujols's effectiveness in that particular game – for average, thicker means more hits; for RBI, thicker means more RBI, etc.

The red line doesn't measure Pujols's season average – he is hitting .272 right now, not .310 as the graph would suggest. Instead, it measures a 30-game moving average. The position of the line at Game 60 measures his average performance from games 31 through 60, and so on.

Pujols was so horrible in his first 40 games that he has very little chance of actually reaching his projected performance over the course of the season no matter how well he plays down the stretch. However, what this analysis shows us is that Pujols has played up to or better than his projections for a good chunk of the season so far.

Pujols has driven his batting average over his projected .309 from the stretch beginning with game 28 onwards. He had multiple 30-game stretches last month where he was hitting for greater than 40-homer power. His RBI production picked up heavily over that period as well, and lately even his run-scoring has hit the 110-per-150 games we've come to expect from a player like Pujols.

Those who pay attention to statistics or statistical analysis in baseball hear so much about regression to the mean. This player who has been killing it will regress because of this indicator; this guy is getting unlucky and will regress to his norms. This here is an actual illustration of this concept in action. Pujols's play has regressed back to his personal mean, or, in plain English, Albert Pujols is Albert Pujols again.

There sometimes is a misconception of regression to the mean that we should expect a player who started with a hot streak to even out with a cold one later, or vice versa. But that isn't regression to the mean – instead, it is a concept known as the gambler's fallacy.

Albert Pujols in April and May was the coin that flipped tails 19 times out of 20. Now he's back to flipping heads every other time, just as we expected back in March. That's the Albert we expected to be a top-4 pick, and that's the Albert we should see for the rest of the season.