This Assertion is Simply Untrue (Or at Least Really Deceiving)

"Albert Pujols has accounted for 33 percent of the Cardinals' runs this year."

Steve Phillips made this claim on Baseball Tonight this morning (go figure), and Bob Brenley made an almost identical remark just now during the Cubs-Cardinals game. Broadcasters often use this "Player X has accounted for Y% of his team's runs" obsevation, particularly in cases such as this one when a star hitter suffers an injury. Now allow me to explain the problem with this claim.

Looking closely at the numbers, I can see that the source of this statistic is just as I suspected. The Cardinals have scored 276 runs coming into today's game. Albert Pujols has driven in 65 runs and scored 52, of which he's scored 25 on home runs.

Of course, every time Pujols crosses the plate on a home run, he registers both an RBI and a run for himself. In order to account for this overlap, Steve Phillips/Bob Brenley/ESPN/The St. Louis Post Dispatch has subtracted 25 runs from the sum of Pujols's RBIs and runs to come up with these "runs he has accounted for," which totals to 92 (in equation form: "RHHAF" = 65 RBI + 52 R - 25 HR = 92).

The 33% arrives by dividing these 92 runs by St. Louis's 276 total runs. Now, it should be fairly obvious why the stat is bogus. It only accounts for the RBI/run scored overlap when the player drives himself in with a home run. What about the overlap created by every other earned run? When looking at a single player's impact on a team-wide scale, this silly formula simply ignores the fact both a run and an RBI are registered on any earned run.

If we apply the Steve Phillips Star Impact Formula (unfair to pin this on Phillips in particular, but I hate him so it's okay) to the entire St. Louis offense, we get the following: [276 R + 265 RBI - 55 HR] / 276 R = 1.76

What this means is the following: If we applied the method to each individual hitter on the Cardinals' roster to obtain what percentage of runs "each player accounts for" and summed all of these percentages, we would get 176%.

Granted, 34% from one player still represents an impressive chunk. (Obviously, we don't need this lengthy excercise to demonstrate that Albert Pujols rules.) But it demonstrates how grossly misleading the original claim is.

The lesson is this: we can manipulate numbers to come up with all sorts of crazy percentages with varying degrees of relevance. The important thing is to understand what they represent and to express them with words in ways that accurately convey their meanings.