One of the things that I have spent quite a bit of time reading about (mainly on the internet) has been the issue of competitive balance in major league baseball.

On one side seem to be the Yankee and Red Sox apologists who seem to like to measure wins or to point out that small market teams do win the World Series or perhaps point out things about how well an organization like the Minnesota Twins does.

On the other side, there are those who seem to be Yankee haters (or perhaps Pittsburgh fans?) who like to point out how often the big market teams win, make the playoffs, grab the top free agents etc...

Here I am going to attempt to address this in a more rigorous, mathematical way. Of course, any rigor that I do offer is colored by the assumptions that I am making, so I will attempt to call out any assumptions that I do make.

**Economic Power**

The first, and perhaps most critical thing, to this entire post is an understanding of how I am measuring the economic power (perhaps buying power?) of a major league team. For the purposes of this study I consider the economic power of a team to be the sum of the salaries that it is paying in any year. I know that this does not consider things like player development costs, management salaries, players who are still under contract but not playing any longer, trades where cash or part of a player salary was involved etc... Nevertheless, it seems to present a fairly reasonable set of numbers to play with without having to delve into the (opaque) world of baseball teams' balance sheets, which are not public record in any case.

I think anyone reading this probably has a fairly good understanding of who in baseball can, or possibly does, spend money and this method seems to pass the sniff-test of the haves vs. have-nots in baseball (data for 2009):

Once I started examining the data I was astounded to see the actual salary growth in Baseball over the past 20 years (which is as far as my data goes). For instance, take the Cleveland Indians, essentially the median from the 2009 salary list, and examine their player salaries for the past 20 years:

They have increased roughly by roughly 10 times! Of course, we have to put that into perspective. Using a lovely tool over at

us inflation calculator we can check what that $9 million in 1989 would be in 2009: The answer I get is ~ $15,734,732. So even adjusting for inflation the salaries have gone up by more than 5x!

All that being said, I needed to find a way of looking at this in year-independent manner. Clearly just adjusting for inflation isn't going to be the answer as the last 20 years of MLB have not been specifically linked to just inflation (nor really are they all that close).

My answer to this has been to look at the teams in MLB essentially in terms of their "Percent of the Pie". This is a pretty simple way of looking at it, but it seems to allow nice calculations, and to give us all the answers we want in a manner that is in no way linked to the revenues of MLB as a whole. The idea is essentially this:

- Sum the salaries of all the teams in MLB in a single year (total-salary)
- Divide a particular teams's salary (team-salary) by the total-salary
- Multiply by 100 (to get a percentage)

Of course, what I end up doing isn't quite this simple. I ended up using a weighted average over the past 5 years (weights unscientifically chosen as 0.333, 0.666, 1, 1, 1) to attempt to smooth the data a bit so a single season of not spending, or a back-end weighted contract does not add unnecessary jitter to the graph. Picking out four teams from each quartile of the salary range, we can see what the trends look like:

Of course, from that chart it isn't at all clear whether the top team (the Yankees) represent a trend in baseball or are merely an out-lier. So, here is a graph of the top 4 teams from 2009:

Here it is clear that over the past 20 years the top four teams had been spending 4-5% of the total amount of salaries until approximately 2000 at which point the Yankees started outspending the next highest teams by 50%!

All this is well documented of course, and this isn't adding too much new to the discussion. The real question is does this affect the competitive landscape of baseball?

**Competitive Advantage**
For the purposes of this post I'm going to discuss success in baseball (or at least competitive success) as making the playoffs. I know that making the playoffs is not the only measure I could choose, so here I will detail a few other metrics that I might have chosen, explain why I think they are not all that great. However before I do that I think it best if I say that making the playoffs is essentially the only goal that GM's in baseball are shooting for as far as I can tell. If this wasn't true, if for example just winning games was the goal each year, we would not see the buyer/seller pattern that we see from GM's around the trading deadline; teams that have a reasonable (or even quasi-reasonable) chance of making the playoffs tend to try and acquire players, while teams that are out of the playoffs become sellers - essentially selling wins this year to attempt playoff runs in future years.

In any event here are some other metrics I could have chosen, but chose not to:

- Wins - wins in baseball are just not as hard to come by as in other sports. The worst team in baseball usually wins around 58 games. So, most metrics just studying wins always conclude that essentially anyone can win in baseball, and they are right! That is due to the nature of the game. It's why they play 162 games, it's why they have 7 game series etc... Studying wins in baseball vs. wins in football or basketball is similar to studying wins in chess vs. wins in poker. They are just not equatable, randomness plays a larger part in baseball than in many other sports.
- World Series wins - for the similar reasons that wins are not very good, World Series wins are not great. The randomness in the 7 game series in the playoffs can dominate in any single year.
- Marginal Wins - Essentially wins over expected (58). I like this statistic, but chose not to use it. I don't have a good reason to use it, and perhaps will come back to it later.

My calculation for playoffs will be to sum the number of times that any particular team made the playoffs, and then divide by the number of years - essentially trying to find the percent chance that any team makes the playoffs in the 20 years of data that I have. When I do this, and then graph it against that teams % of Salary that I presented earlier we get what I think is a pretty telling graph:

What this graph is showing is that money *does* buy trips to the playoffs. Of course, money is not the only factor - it is certainly confounded with management skill and many other factors. These two variables are fairly strongly correlated (r=0.671).

**Conclusion**

As you spend more money your chances of making the playoffs in any particular year (and certainly over in an aggregate of years) goes up. Money is not the only factor, but spending money has a significant effect upon the ability of a team to succeed in major league baseball. Any effort to state that winning and money do not significantly correlate in baseball is incorrect at worst and disingenuous at best.

**Future Work**

What is not clear is whether the money is an effect of winning (essentially winning produces money produces more winning) or winning is an effect of spending money. More work would be needed to try and determine causation.