The Win Curve
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.
It’s time.
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.
Analysis, Hot Stove Season, The Off-Season
Reader Comments (15)
In a bit of news related to this post, Ignacio Serrano of ESPN Deportes is reporting that the Tigers are on the verge of signing Victor Martinez to a four-year, $50 million deal, pending physical.
Bleh.
So... How would we go about doing a cost/benefit analysis between signing Cliff Lee for ~23 a year for 6 years vs trading a package of prospects for Zack Greinke (assuming he would sign an extension, let's say 6 years at an average of 18 mil a season?) That saves you 30 million over the course of 6 years in salary, and it's reasonable to think they would pitch comparably for the first 3-4 years with Greinke outperforming Lee towards the end of the 6 year period (with the obvious risk of injury for both and maybe a slightly greater risk of Greinke losing his marbles at some point). So then it comes down to 30 million for Perez/Holland/Beltre??. Is that worth it? On second thought, let's just get both.
PF - I think you make great points and I have been thinking these very thoughts. The one problem, and why I find myself getting more pessimistic by the moment that we'll bring Lee back, is that NYY ALSO is on the same place in the curve as the Rangers for a change. Which is scary -- for once, they can reasonably justify spending over market -- which they do anyway. Does that mean they go $27MM/per? $30MM?
Jake - you will deeply regret trading Holland. Look at the Sox -- for all their f/a splashes, it was Lester and Buchholz that carried them this year. Not Lackey and (the traded for) Beckett. Or Dice K. Plus, if you are going to allocate 40% of your payroll to 2 players (Young and Lee), you darned well better have some league minimum guys that have high ceilings. I am all for trading for Greinke, but the bait should be Hunter, not Holland, to throw with Perez.
The sox didn't make the playoffs so that's a weird example for you to use, maybe the Giants would have been a better example of the importance of home grown pitching. Nonetheless I completely agree and it's very risky to sign Lee to a huge deal (Zito) or trade a package for Greinke. My question was just which one seems to be the better deal for the Rangers since the article explained that the point the Rangers find themselves in this offseason makes them a prime canidate to take such a risk versus a team like the Nationals that is further down the win curve. I agree Holland is the guy to hang onto over Hunter, I was just trying to make a realistic package. I would be all for trading Perez/Hunter/Beltre/Sardinas for Greinke, moving Feliz to the rotation and signing a bullpen guy to close/set up for Frankie/ogando. A rotation of Greinke/CJ/Colby/Feliz/Holland is music to my ears.
It should be Holland AND Hunter for Greinke. Keep Perez. 1-2 years down the road, when CJ and/or Colby leaves (hopefully for Type A comp!), Perez moves into that spot in the rotation. Bear in mind that 2012 will be Perez' 21-year-old season. Bumgarner's age this past year.
4 years and over $50M for Victor Martinez is just a tad beyond the curve for me. If Lee gets 7 guaranteed years from the Yankees, that, too is beyond the curve for me.
Oh, and everything Prasanth said about dollars above goes for prospect value in trades, too. A slight "overpay" in prospects is fine if a player will get you those marginal wins. What AZ seems to be asking for Justin Upton is beyond that cost. The Greinke price may or may not be, depending on how you factor in his mental history.
Social Anxiety Disorder is really overrated. Khalil Greene has an incredibly severe case. My wife has a moderate-to-severe SAD diagnosis. She's a highly successful courtroom attorney who frequently makes speaches to large industry groups. A little Paxil goes a long way for all but the most severe cases of SAD. I think Greinke's SAD is actually a plus, in that it represents an opportunity to extend him at slightly below-market money, because he has no interest in playing in NY/BOS/LA/CHI.
Good stuff, keep 'em coming.
I TOTALLY agree! The Rangers are no longer a team that has so many holes that 1 or 2 elite players aren't going to make that big a difference. This team is ready to win... and therefore I feel they need to improve the roster by whatever means possible, even if the inclusion of top prospects is required.
What's better; to have a rotation headlined by Lee or Grienke... or someone that fills the void until a Martin Perez is ready, which is probably a good 2 or 3 years down the road?
What's better, to have a lineup that includes Carl Crawford... or Julio Borbon, who will fill the void until Engel Beltre is ready, which is probably 2 or 3 years down the road?
We're not Kansas City! We're ready to win it all.
Will adding 1 elite player push us over the hump, who knows... but I like that possiblity alot more than relying on prospects that may not pan out.
Time is of the essence... and while I do NOT want to mortgage the future, I am for making significant improvement at the cost of 2 or 3 top prospects.
Would I be happy if we traded a Perez or Beltre or Profar for a guy in his 30's that's on the back end of his prime, no... but going after a 28 yr old #1 strating pitcher, and/or a 23 yr old all star centerfielder, and/or a 27 yr old power hitting first baseman makes all the sense in the world.
JD has a tricky thing on his hands here in striking while the iron is hot while not over-paying and/or mortgaging the future. It has to make sense.
Prashanth, this was very informative. Thanks.
Loved this information Prashanth. Its time indeed. Why can't we just be arrogant enough to want both Lee and Greinke? Our will to win should hold no bounds, and what our team will look like in 5 years should have minimum bearing on any decision making done this hot stove.
I think its reasonable to think the attendance will be top 10 in MLB next year, maybe even toward the top more.
(btw, if having to choose between keeping Holland or Hunter, I definitely prefer keeping Dutchy over BigGame)
I say get both. Pay for Lee, trade for Greinke. I'd hate to see the Dutchman go, but hey, if that's what it takes. What seems to be bothering everyone is the number and quality of prospects that would be given up to trade for Greinke. The thing is, the farm system is better than the 2-3 prospects we'd be letting go. At least, it better be, or it wasn't that great of a farm system to begin with. With a team this young and this talented, the farm system could be incubated for a few more years, allowing the rest of them to mature and be ready for the day when we need, say, a 3B (sorry Mike) or a catcher.
If you get Lee, you can wait a couple of yrs and sign Greinke as a FA, though I do agree this team is young enough to take a hit on the 3-4 prospects it would probably take to get Zack. We don't need any position players really at all, except at catcher. Our rotation could take a hit if we can't get CJ to stay at reasonable numbers after 2011, but its not like 2009 where we had some glaring issues in both the rotation and on defense and needed to resolve those cheaply.
If Cliffly gets 7 yrs on his deal, I think we need to pass. Could we really afford to eat those last 2-3 yrs or so if his performance tapers off badly? THAT would be a lot of extra dollars for somebody who may not be physically able to be our ace past age 35.