Or, alternatively, why the Rangers should be willing to pay Cliff Lee more than the Nationals.
One of the most important things for a front office to decide is how good its own team is. Billy Beane mentions in Moneyball that he tries to spend the first third of the season evaluating his own team to get a good picture of what the strengths and weaknesses were, as well as the overall talent, in order to guide his decisions at the trade deadline. Intuitively, fans know that teams get to a point where the team needs to decide if they are going to go all out to try to win, like the 2010 Rangers, or if the team is just not good enough to warrant the cost of trying to improve the team. This same decision plays out in front offices across the league during the off-season as well.
Fans, in general, want to see their team improve. Most Astros fans are not expecting a 92-win team next year, but they do expect improvement over last year’s team. For the casual fan of baseball, this usually manifests itself as spending their time dreaming of the biggest and best free agents or trade targets, regardless of the quality of their team. The problem with this line of thinking is that these players that every fan wants playing for their team are very, very expensive, either in terms of dollars, total years, or prospects. The financially prudent thing to do may be to play rookies and fill in your team with cheap, aging veterans with little chance of providing an elite performance and save the money. So, the first question that needs to be answered revolves around assessing the talent of the team.
Which brings us to the win curve.
Wins are not evenly distributed in baseball. Most everyone realizes that there are going to be fewer 95-plus win teams than 80-85 win teams because it is quite difficult to have a team that good. However, we can take this a step further by taking a look at the distribution of wins over the last *ten years:
What we see here is a roughly normal, or Gaussian, distribution. As more data gets added to it, it gets closer to a true normal distribution. This distribution is found in an incredibly diverse array of data. Many of you have run into it in various courses as students’ grades in any given course often fit a roughly normal distribution.
This is relevant for a few reasons. First, it shows us the difference in degree of difficulty between going from a 70-win team to an 80-win team and going from a 90-win team to a 100-win team. Hopefully, this helps set realistic expectations for fans and their teams when they talk about wanting improvement. For the second reason, there is something else I need to mention:
Making the playoffs is incredibly important. Seems pretty obvious, right? Let me expand. The financial benefit from making the playoffs is immense. It varies by team due to market size and how long the playoff run lasts. However, the revenue stream comes from a wide array of sources: television, tickets, merchandise, and increased ticket sales the next year.
This brings us back to the second reason that the win curve is important. To make the playoffs, a team generally needs to aim for 92-95 wins. There are exceptions for weak divisions, but this generally holds. While wins are still normally distributed, the reward or payoff for wins is not. There is a very steep jump in payout if you can get over the limit to get into the playoffs.
How does this affect the Rangers and Cliff Lee? Yesterday, Joey talked about the value of a win, in terms of WAR, over the past few years. Different teams will have varying projections for players and this forms the variance we see in any given contract in terms of dollars per WAR. However, the win curve shows us that another part of the variance comes from a team knowing where it is on the win curve.
The Rangers, as presently constructed without Lee, are likely to be an above-average but not elite team. This puts them at the specific point on the win curve where it makes financial sense to give out a contract that overpays in terms of dollars/WAR because the reward for being a playoff team is so great. This applies to more than just Lee; the Rangers can afford to pay more for each win improvement than a 75- or 80-win team because each win added to an 87-win team significantly increases the chances of hitting that playoff payout. There are limits to this, of course. The Rangers should not be paying twice market value.
It has been said that the Rangers should resign Cliff Lee because he is such a good fit for this team. While there are other players about whom this could also be said, what makes this Rangers off-season so interesting is that it actually makes financial sense to pay the extra amount for the elite players. This is no longer a team trying to find ways to add wins cheaply with replacement level or average players.
Update: Josh Garoon brought up the question of whether or not this was really a normal distribution. *I've decided to address this by adding another 5 years worth of data to the original chart. Also, I'm including a second chart here where each data point is replaced the the average y-value (occurence) of that x-value (win total) and the points above and below it. This is a smoothing function that serves to help us spot-check the distribution to make sure it is normal or Gaussian.