Math and Baseball

In 2007, when the Indians beat the Yankees and lost in game seven to the Red Sox (I think I might still owe my brother some northeast beer from that series), I remember thinking how much higher both of those teams payrolls were than the Indians. While the Yanks ($195M+) were outspending the universe, the Red Sox ($144M) weren't far behind, and the Indians ($62M) were lower than middle of the pack. When it came down to it, the Sox won 1 more game than the Indians through the ALCS. That means that extra win in game 7 of the ALCS needed to be worth at least $82M for Boston, the organization, to feel satisfied. Now, perhaps the Sox made their money back since they then went out to sweep the Rockies ($54M+) and win the World Series. However, the question remains how much is a win worth and how much does it cost to get a win?

Well, there's an interesting article on The Baseball Analysts about that very topic. The article asks first whether all wins cost the same, but I don't think so and neither does the article. A team of people making just the major league minimum starts of at a salary of $10M (25 men times the 2009 league minimum of $400,000). Even a team of all rookies making minimum will win some games, as the worst teams in the history of the 162 game schedule win at least 50 some games with most teams winning no less than 62, as a 100 loss season is somewhat rare. This means to me that the first 60-some wins and $10 mill of payroll are givens and shouldn't be included in the calculation.

The article goes on to fit a polynomial curve to their information and gets slightly better results in explaining wins (now close to 50% instead of 40% of a win is explained by payroll). I would guess that the results would get better if they started at the base levels suggested above (maybe I'll even calculate this when I'm feeling very bored).

Beyond my concerns in starting point, the numbers tell us something that is relatively well known: money doesn't necessarily buy championships. However, the article doesn't look at several important aspects including:

1) Does money buy playoff appearances?

I'm not sure of the answer of this one, but I'll look it up in the next few days and see what I can find out. My gut feeling is that teams with above average payrolls have a better chance of making the playoffs, but there may or may not be long term trends that prove my gut.

If money buys playoff appearances, then the money is better spent than it might first appear as playoffs mean more games, which means more gate. Not to mention making the playoffs means more excitement about late season games which should lead to yet more revenue.

2) Because of the unbalanced schedule, the money per win is highly affected by the behavior of other teams in your division, league, and, to some extend, immediate geographical location.

I'll answer this if I ever put facts and effort in.

3) Are the teams worried about something else besides winning?

Money, money, money. In the NBA, the Clippers are rather notorius for being more interested in profits than competitiveness. It might not work everywhere, but I am sure there are similar MLB teams.

4) Is there a viscous cycle in spending?

Let's assume that the biggest bump in money comes from making the playoffs and not winning the WS (a big assumption, but I can't imagine the team that wins the WS makes that much more than the team that loses in the same series). So, making the playoffs one year brings in extra revenue. Despite the fact that only one team can win every year, the teams that came close but didn't win it all are more motivated to spend to get over the hump the following year. Those teams' GM's say "hey, look at all this money we could have spent to win" and go out looking to spend money so they can win and make more money. Same thing could happen with teams that almost make the playoffs, since their revenues raise in the playoff race. Teams that win spend more, and need to spend more than the more they already spent to get more competitive.

Of course, the bottom feeders are in the opposite position where they don't make much money because they don't do all that well. The next year, they try to cut their losses on expensive players and, at best, go into rebuilding mode where they rely on inexpensive young players. In most cases, they hit some payroll floor where they can't spend any less and still fill a 25 man roster.

So the trick is how to break the cycle if it does indeed exist. The breaks come in a few ways, such as many players having career/breakout years (2008 Rays) or new management, or a new stadium that shoves new money into the system that needs to be spent.

Wonder what this means for 2009... I'll follow up with at least two of the following: 1) the Yankees still kill competitive balance regardless of luxury tax and revenue sharing, 2) actual facts and figures to back up my thoughts here, 3) predictions for the 2009 season.