This post first appeared on Freakonomic.com
If you wish to win in baseball, your team has to spend money. Just look at the New York Yankees. USA Today reports that in 2012 the Yankees led the American League in spending. And the Yankees finished with the best record in the American League.
Of course, one data point doesn't a trend make. What do we see when we look past the Yankees?
Here is a simple plot of winning percentage in baseball in 2012 and team payroll:
As one can see, the regression line -- the positively sloped blue line -- indicates that higher pay leads to more wins. At least, that's what we see when we just stare at the line.
When we look at the actual estimation of the line's equation, though, we note one very important issue. The link between payroll and winning percentage in 2012 is not statistically significant.* In other words -- despite what we see when we stare at the line -- we can't argue that payroll and winning percentage in 2012 are actually related to each other.
When we look at the actual data, it's easy to understand why we get this result.
- The combined payroll of the Washington Nationals (20th in payroll) and Cincinnati Reds (17th in payroll) -- the teams with the best records in baseball this year - did not equal the payroll of the Yankees (third best record this year, first in payroll).
- The Philadelphia Phillies were second in payroll (only $23 million behind the Yankees) but ranked sixteenth in winning percentage.
- The Boston Red Sox were third in payroll but tied for 24th in winning percentage
- The Oakland A's were 29th in payroll but tied for fourth in winning percentage (only one game behind the Yankees).
- Of the top 5 teams in payroll, only two (Yankees and Tigers) made the playoffs. Meanwhile, five playoff teams ranked in the bottom 50 percent of the payroll rankings.
Given these anecdotes, we should not be surprised that payroll and wins were not statistically related in 2012. What may be surprising is that this isn't what we typically see when we look at payroll and wins in baseball.
USA Today reports team payrolls from 1988 to 2012 -- across these 25 years, a team's relative payroll (team payroll in a given year divided by the league average payroll in that season) does have a statistically significant relationship with a team winning percentage. So across all the years for which data exists, payroll and wins are statistically related.
We should note, though, that explanatory power is somewhat low. Only about 17 percent of the variation in team winning percentage (i.e. the R2 from the equation) across the past 25 years is explained by a team's spending on talent. So much of the variation (specifically, more than 80 percent) in winning percentage is not explained by payroll.
That being said, there is a statistical relationship. More spending seems to get you something.
At least, that's the story you tell if you look at all 25 years. When you look at each year individually -- as the following table illustrates -- the power of team spending seems to vary quite a bit. Again, in 2012 we see a relationship that is not significant (NS).
From 1996 to 2011, though, payroll and wins were statistically linked each and every year. However, explanatory power varied. From 1996 to 1999, explanatory power was above 30 percent in three seasons and reached 50 percent in 1999. But after 1999, explanatory power never reached 30 percent again.
If we look at baseball before 1996, we see five seasons where the relationship was again not significant. And when it was significant, the relationship was never that strong (always below 20 percent).
So here's the big question: Why is this relationship not stronger? One would think that as teams spend more they see more wins. But often, that's not what we see in the data.
One issue -- as various academic studies have indicated -- is that a baseball player is only paid what he is worth in the free agent market. And a player can't be a free agent until he has played six years. This means that players with less than six years of experience -- such as Austin Jackson of the Detroit Tigers -- can be far more productive than their salary would suggest. This past year,Jackson was paid $500,000 while producing 3.3 Wins Above Average (WAA). Meanwhile, Prince Fielder produced 2.3 WAA and was paid $23 million. Why was Fielder paid so much more? Fielder just sold his services in a free agent market while Jackson was still working in a labor market where only the Tigers could pay for his services.
Beyond the labor market issues, there's the issue of forecasting performance in baseball.
A player's salary negotiated today is a reflection of what a team thinks that player will do in the future. Unfortunately, baseball performance is difficult to forecast. This is especially true for pitchers, where the interactions between the pitchers' performance and the skills of the defenders around the pitcher are difficult to measure.
Given these two issues, it's not surprising that payroll doesn't explain much of wins in baseball.
But does the result from 2012 indicate that payroll and wins will not be statistically related in the future? Again, one data point doesn't a trend make. So we don't know if the big spenders will struggle again in baseball in 2013. What we do know is that spending doesn't guarantee a team success in the regular season.
As for the post-season? Well, there are right now eight teams left in the playoffs. And the Tigers -- the team I follow -- are one of these teams. Unfortunately, there's a very good chance that I am going to be unhappy in a few days.
Thus is the nature of the playoffs. All but one team walks away sad. And it seems, no amount of spending by your favorite team can change that reality.
* - the p-value on the coefficient for payroll in 2012 is 0.26. Typically we argue a coefficient is statistically significant if the p-value is 0.10 or lower (and some insist on values of 0.05 or lower).