The Bang For the Buck Ratings

We all know about the large money disparities in baseball and how it sometimes leads to having the same teams in the playoffs (especially in the AL) year after year. This year, the Yankees once again lead the majors in team salary at just over $209 million while the Marlins are just under $22 million (less than what A-Rod is making) at the bottom. So in theory, if every team was efficient in their salary paid to performance on the field, the Yankees should have 10 times as many wins as the Marlins, but in reality, only 1 win separates the teams.

The reality is that there is a lot more parity in baseball than we are led to believe, especially since it is a sport where it is a major accomplishment to have a winning percentage over .600 (98 wins). In the NFL, that's the equivalent of 10-6. We've all seen the dollars per wins statistic before, usually to show the Yankees gross overspending versus an overachieving small market team, but those sort of numbers obviously do not reflect anything that could be realistically expected out of 2 baseball teams, because no team ever wins 5-10 times as many games as another team, or even on a smaller scale, spending twice as much never actually promises twice the wins.

So I decided to create the Bang for the Buck ratings, which is set up to compare a team's win total in a season compared to what their expected win total should be based on their salary and the performance of other teams with similar salaries. To do this, I created a linear regression plot of all the teams of their win total versus salary, and used that linear relationship to define the expected win total of a team based on their salary. The farther from the line an individual team is, the greater or smaller "bang for the buck" a team got that season. So yes, an overachieving small market team will always be near the top of the list, but it's also interesting to see where other teams fall, especially the big spending teams, who are expected to win a high number of games. Speaking of those teams, I did the calculation each year from 2004-2008 and I decided that if a team's salary was more or less than 3 standard deviations from the average, they would be considered "outliers" and excluded from the regression calculation, but the regression could still be used to calculate an expected win total. Each year, the Yankees were the only team in this category. Playoffs are not factored into these ratings.

Let's take a look at the results, starting with the top and bottom 5 for 2007:The top 4 teams all share a pretty common trend. They were all pretty young teams that overachieved in 2007, with 3 of them making the playoffs and the 4th losing a 1 game playoff. The Angels are a "big money" team that still manged to get a lot out of their team, gaining 94 wins and the AL West title. The bottom 5 featured the 5th highest salary from 2007, the White Sox, who had a horrible injury plagued season, but also the small market Royals, who were hurt by having a salary higher than 4 of teams in the top 5 but only put up 69 wins. The Astros, Giants, White Sox, and Orioles actually should have put up winning seasons based on their salary and the performance of others but were battling for last in their divisions. The team that came closest to getting what they paid for was the Twins, who had 79 wins and were expected to get 79.5. You may notice that the trendline shows everyone was projected to be around .500, and that was due to a lot of low salary teams doing very well last year, and also opens up another trend I'll discuss later....

Here are the results for 2006:
Once again the top 4 teams were all playoff teams, with top 2 being teams that were expected to have losing records, along with the surprising Tigers, and the big money Mets, who lived up to their potential in a big way. The Marlins, with barely a AAA-level payroll, still managed to pull off 78 wins in one of the most surprising seasons ever. 3 of the bottom 5 were small market teams that had horrible years, the super-inefficient Orioles are in their usual spot, and the Cubs were the most underachieving team, having the 7th highest salary and almost losing 100 games. The team that got the closest to what they paid for was the World Champion Cardinals, who won 83 games and were expected to win 83.3, just enough to make the playoffs and somehow win the World Series.

Now we'll take a look at 2005:
The team with the most bang for the buck in 2005 actually missed the playoffs, falling just short after putting together an amazing run with young players. The World Champion White Sox, who had a much smaller salary in 2005 than in recent years was 2nd, followed by the best record in baseball Cardinals, the always efficient A's, and the Angels, who managed again to outperform their high payroll. In the bottom 5, the above average spenders Giants, Dodgers, and Mariners all had pretty rough losing seasons, but the bottom 2 were probably the most interesting. Despite having the 2nd lowest payroll, the Royals had the worst bang for the buck, winning only 56 games and also being hurt by the over achieving Indians and Brewers, who helped flatten the slope of the regression. Despite winning 95 games and the AL East, the Yankees were 2nd to last because their insane $208 million payroll resulted in an expected win total of almost 112 games. The same thing happened in 2004, when they won 101 games and were expected to win almost 111. The team that came closest to getting what they paid for was the Rangers with 79 wins, expected to get 77.7

And now, the first year I started looking at this, 2004:
The NL Champ Cardinals, with a slightly above average salary and 105 wins got the most bang for their buck, while the seemingly always efficient Twins finished 2nd. The remaining of the top 5 were overachieving low salary teams that just didn't have quite enough to make it to the playoffs. In the bottom 5, the big money Mets had another disappointing season, the Mariners slapped around by 3 89+ win teams in their division all season, and the Diamondbacks had an absolutely terrible season, despite having basically the average payroll. They were a whopping 30.6 games off what was expected. The team that came closest to getting what they paid for was the tiny salaried Pirates, who won 72 games and were expected to win 72.1

Going into today's games, so far in 2008 the Rays are getting the most bang for the buck, 12.5 games better than what would currently be expected of their salary, followed by the Angels, Cubs, Marlins, and Twins. The worst bang for the buck is the Mariners, followed by the Natonals, Padres, Giants, and last year's best bang for the buck team, the Indians.

As I mentioned above, I have noticed a pretty significant trend from 2004-2007 that seems like it could continue in 2008:
The slope of my linear regression is getting smaller and smaller each year, meaning there is more parity in baseball and the "little guys" are able to compete with and defeat the "big guys." You can see it happening again this year with the Rays and Marlins fighting it out in the eastern divisions. We'll probably wind up seeing the smallest slope and expected win span yet, which really can only lead to two conclusions for the future.
1. Big market teams are increasingly (and stupidly) overpaying superstar players, because their salaries keep climbing while the small market teams are catching them in the standings.
2. Being a small market team is no excuse for being a bad team, which has been proven several times in the past 5 years by teams with very low salaries, but a small market team may need to increase its spending to lock up a spot in the playoffs every year.

We'll see how the rest of 2008 goes. I may post an update with some better 2008 numbers as we head into the September stretch run.