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Paying for the Best

by Dave Studeman
January 24, 2005

What a difference a year makes. Last year, Roger Clemens signed a $5 million contract with the Houston Astros, including incentives that increased his total take to $7 million. This year, he'll receive $18 million, the most money ever paid for a major league starter's services. Is there anything that better symbolizes the difference between last offseason and this one?

I'm not going to go on about Clemens, other than to agree that he may now be making a legitimate claim to the Greatest Pitcher of All Time extra-value coupon at White Castle. But I do want to reflect a little bit on the huge contracts superstars get.

I like to use Win Shares to evaluate baseball contracts for a lot of good reasons (at least, I think they're good reasons). Teams make more money when they win more games. Players help teams win, so players should be paid based on how much they contribute to the team's won/loss record. Win Shares supplies the link between salary and performance. Just want to make sure you know where I'm coming from.

I've tweaked the numbers a bit, so that I actually compare Win Shares Above Replacement (WSAR) to salary above the minimum. This may seem like a mishmash built on top of a kludge, but these two little tweaks allow you to make very legitimate comparisons between players and the money they're paid.

For instance, here's a simple graph of the 2004 WSAR that all free agents contributed to their teams, grouped by how much they were paid:

salaries and wsar

In general, better players are paid more money. Told you it was a simple graph. I actually like a couple of things about this graph. First, with one exception, every group of players added two to three WSAR over the previous group. I generally grouped players into salaries of two million dollar increments, so this means that every million dollars invested in a free agent generally bought you a little more than one Win Share. I grouped players who earned more than $10 million dollars differently, however, so we'll look at them in a second.

The second thing is that players who were paid between $8 million and $10 million last year actually performed worse than those in the $6M to $8M bracket. These underachievers included Hideo Nomo, Bret Boone and Preston Wilson -- all of whom were actually worse than replacement-level players (according to my calculations, anyway). I would guess that there is usually a group like this every year.

For players who earned more than $10 million last year, I grouped them into bigger increments because the number of players was small. 21 players made $10 to $14 million last year, and 14 made more than $14 million. You know the names: Bonds, Jeter, ARod, Manny, etc. etc. Overall, their performances didn't disappoint (though there were some obvious clunkers, such as Hidalgo, Ordonez and Morris) and these players fell in line with the general trend of increasing production for higher pay.

However, the fact that I grouped these guys differently creates a misleading straight line on that bar graph. So let me draw a different graph -- this one shows the salary paid for each incremental Win Share that the group contributed over and above the previous group. For example, the $2M to $4M group created 2.3 more WSAR than the $0 to $2M group, and made almost exactly $2 million more. That comes out to a cost of $878 thousand for each additional WSAR. See how that works?

Here's a graph of all free agents again, same salary groups, and the cost of their additional WSAR's (I zeroed out that nasty $8M to $10M group):

I promise this is as complicated as it's going to get, but this is an important graph. It basically says that the salary paid for each additional Win Share last year was between $800,000 and $1,000,000 for all contracts below $8 million. Once you got above $8 million, however, the price for each additional Win Share rose dramatically. In fact, for contracts of more than $14 million, major league teams paid four times as much for each additional Win Share as for those contracts under $2 million.

So those mega-contracts are not only expensive in absolute dollars, they're expensive values, too. Does this mean that highly paid players are taking major league teams to the bank? Not necessarily.

I think there are two possible, rational explanations for this trend:

Twelve WSAR's from one position are more valuable than twelve WSAR's from two positions. This was called "economies of scale" in your Economics class, and I think you can apply the same logic to ballplayers. Odds are that you have a young ballplayer at one position who's making the major league minimum and contributing more than a replacement player. If you have one or more players like that, you may be willing to overpay for the true superstars of the game, because the net effect is the same as filling each position with an average free agent.

The highest-paid players tend to play in the major media markets, for teams who make the most money for each win. For the team, the contract makes business sense because they make more money, even at the inflated salary level. For the league as a whole, however, it looks like the player is being overpaid.

I would estimate that Roger Clemens contributed about fourteen WSAR last year, which certainly qualifies him for the $14 million plus group. Unfortunately, Houston is not a major media market. Roger Clemens might have received Fair Market Value for his services, but I wonder if the Astros can truly afford it.

References and Resources
After publishing this article, I've gotten some great reader reactions:

One reader asked about my assumption that teams in major media market make more money per win. Here is a review of an economic analysis that confirms this assumption.

Another reader mentioned a third reason star players make more per incremental win -- the club's marketing revenue (jerseys, bobbleheaded dolls, etc.) associated with these players is much higher than that for average players. It's a great point. Thanks.

Dave was called a "national treasure" by Rob Neyer. Seriously. Comments about this article can be sent to him through the miracle of e-mail.

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