Sign in / Join

"Money" and "Ball" and the Cost per Win Fallacy

In his article, "Based on Payrolls, Brewers Faring Quite Well This Season," Tom Haudricourt offers us the following:

"The bottom line of victories and losses is the absolute best way to judge how a major-league team is managing its money. With nearly six weeks of the 2005 season complete, the Milwaukee Brewers have to feel pretty good about how they've fared. With a $41 million payroll, which ranks 27th among the 30 big-league clubs, the Brewers have forged a 17-16 record. Breaking that down further the Brewers have spent $2.41 million per victory, a figure that obviously will decrease dramatically as the season progresses."

This comparative "cost per win" approach is popular with the media. He then goes on to criticize, who else, the Yankees:

"No team has underachieved more, per dollar spent, than the New York Yankees, who have a league-high $208 million payroll - $84 million more than the team with the second-highest payroll, Boston. Despite winning five consecutive games, the Yankees are 16-19, which works out to $13 million per victory."

To his credit, Haudricourt notes the limits of this "snapshot;" things can change during the rest of the season, and the Yankees 1) obviously intended to do better and 2) probably will do much better than their slow start. [Indeed, they have just beat up on my own Mariners to fatten their winning percent.] So let's not get hung up on the particular snapshot. Instead, let's think about the limits of the cost per win concept.

Basic sports economics shows the fallacy of measuring any kind of success across different markets by costs per win. First, fans in New York like winning and apparently are willing to pay more than any other fans in order to see it happen. So, Yankee GMs do their level best to give their fans what they want and collect this truly large amount of money. But there is nothing linear about the spending required to do so! The average cost of a win is far from constant; costs of winning should increase at the margin.

Further, fans in NY may be quite happy to pay even more to watch the very best players (on average) win, regardless of how much winning actually takes place (within limits of course, as witness the Yankees' declining economic fortunes under CBS ownership in the late 1960s). Other consumers in NY appear of similar inclination (I think of opera, for example-- it's just music and singing, eh? But it's doubtful that opera patrons in NY would pay the same amount for the lesser opera offered in, say, Seattle). This suggests that a win in NY is not the same consumption item as a win in Oakland and it's possible that an efficient GM would spend more to achieve a 0.600 winning percent than an efficient GM in Oakland would spend to the same end.

So, cost per win would be useful in comparing two different GMs in the same market; the lower cost per win would be the more efficient GM in that market. But the same measure is invalid when comparing GMs across markets. Cost per win will always show the Yankees to be "under-achievers" as long as the average cost of winning is non-linear and as long as Yankee fans are willing to pay more to watch the game's best win at any reasonable level of winning.

This has relevance for the "money" part of Moneyball. Author Lewis points out that Billy Beane typically shows a lower cost per win than other MLB GMs. And then Lewis goes on to suggest that the rest of the GMs in MLB have something to learn. But this is an invalid comparison. It is valid to compare Beane's success to previous A's GMs, but not to GMs in other cities. Nobody would ever spend like the Yankees if they operate in the Oakland market and care about profits.

Or, the other way around, given that Beane has done as well as any other GM in Oakland has ever done, and given Oakland's revenue potential, we would never expect the same success in Oakland as in NY. The relative level of winning in Oakland and New York bears this out. During Beane's tenure (since 1996 and up to last season, 2004), Oakland's winning percent has only twice been greater than that of the Yankees (2000 and 2001). And Oakland has won its division three times in Beane's 9-year tenure while the Yankees won their division in 8 of those 9 years (1997 being the only exception). The Yankees have also won a few World Series in that time. This is not a knock against Beane, a truly great GM in Oakland. It's just the obvious expected result given the variation in revenue potential in MLB.

Teams are structured to capture the revenue potential in their respective markets. And cost per win is a silly way to judge success at doing so across teams in different markets with different revenue potential.