Money *does* buy wins
In “The Wages of Wins,” the authors determined that the correlation between payroll and wins was about 0.4. I interpreted that to mean that for every dollar a team spends on free agent signings, 40% of that money can be expected to translate into wins. But I was wrong – 40% is way too low.
Suppose 30 boys each have some marbles. They all have different numbers of marbles, collected over a childhood – some they got for their birthday, some were hand-me-downs from their siblings, some they found in the schoolyard. Some of the kids have only 10 marbles, but some have as many as 40.
Now, each boy is given $2, and let loose in the toy store, where he can buy toy store marbles at 10 cents each. Some won’t buy any toy store marbles, while the ones who really like marbles might blow the entire $2 and buy twenty of them.
Suppose that now, economists run a regression, to try to predict the number of marbles the child has based on how much he spent at the toy store. There is some correlation, because the kids who bought marbles will, obviously, tend to have more of them after the purchase. But the relationship isn’t perfect, because the original distribution of marbles was pretty much random. So they might get a correlation coefficient of, say, 0.4.
They conclude that such a small correlation means that “money can’t buy marbles.”
But that’s wrong, or course. Money can, with certainty, buy marbles, at the rate of 10 cents each. While the correlation between the money you spend and the marbles you *have* is 0.4, the correlation between the money you spend and the marbles you *buy* is 1.0.
Because some of the marbles arrived from sources other than money, they act as random noise in the regression. They make it appear, at first, that money only buys marbles at a 40% rate, when, really, the rate is 100%.
You probably see where this is going.
The boys are baseball teams. The marbles are wins. The toy store marbles are wins from signing free agents. And the legacy marbles the boys had are players not yet eligible for free agency.
The new argument goes something like this:
Team payroll is highly correlated with player ability only in the case of free agents. For young players, and non-free-agent players, salary is based more on years of experience than on performance – and besides, those salaries are very small compared to the amount of money spent on free agents. For instance, Albert Pujols made only $700,000 in 2003 not because that’s all he was worth, but because he was only in his second major-league season.
It turns out that the correlation between team payroll and wins is 0.4. But the correlation between non-free-agent payroll and wins is probably close to zero. Therefore, to make the overall correlation between payroll and wins rise to 0.4, the correlation between free-agent payroll and wins must be significantly higher than 0.4. That is:
Non-free-agent correlation .................. 0
Free-agent correlation ...................... x
Overall “average” correlation .............. 0.4
X must be way higher than 0.4 for this to work. (A naive estimate might be 0.8, which is probably too high. But it’s got to be higher than 0.4.)
So, of course money can buy wins. Not with a correlation of 1.0 like for marbles – marbles, of course, don’t get injured or have off years. But, yes, if you spend a bunch of money on free agents, you’re going to improve your team substantially, more substantially than the 0.4 of the simple regression suggests. Money does buy wins.