Win Values Explained: Part Six

Over the first five parts of this series, we’ve discussed all the components of what makes up a Win Value. Today, we tackle the conversion of that win value into a dollar value.

First off, a little background. Since we’ve set replacement level at around a .300 win% (or 48 wins per team), that means that there are about 1,000 marginal wins in a major league season. All 30 teams are fighting over these 1,000 wins, each trying to get more than 45 or so to get them in the playoffs.

Every dime a major league team spends above the major league minimum is theoretically spent in an effort to buy as many of those 1,000 wins as possible. A major league team’s minimum payroll is about $12 million, so MLB as a whole has a floor of $360 million in salary per season. Total payroll for MLB teams in 2008 was reported at $2.67 billion. That means that major league teams spent $2.31 billion to try to buy their share of those 1,000 marginal wins. Basic division tells us that the cost of a win in MLB salary was $2.31 million per win for 2008.

However, a huge share of those wins were created by players whose salaries were not determined by a free market system. Every player with zero to six years of service time had an artificially depressed salary due to not being able to qualify for free agency. As well, most players who signed long term contracts that bought out some of their arbitration and free agent years had salaries below market value as well – they had traded some potential cash for the security of a deal several years ago. The amount of money that teams are paying per win for their cost controlled players is far less than the $2.31 million league average.

So, the market of wins available for purchase doesn’t total 1,000. A significant batch of MLB players simply aren’t available for acquisition at any given time. The Cardinals aren’t trading Albert Pujols. The Mariners aren’t trading Felix Hernandez. The Rays aren’t trading Evan Longoria. The wins that these players generate are not for sale.

Who is available? Obviously, players who qualify for free agency in a given season are available. Also, there are players traded from one club to another, so those players are also available for the right price. But what is the right price?

In general, we can say that the market price of a win is the mean of the dollars per win handed out to free agents in any given year. If you approached CC Sabathia this winter and offered him $12.65 million because he was a 5.5 win pitcher and the league average cost per win is $2.3 million, you wouldn’t have gotten very far. If you want to compete in the market for available wins, you have to know what the going rate for a win is, and the easiest way to calculate that is to look at the free agent market. Let’s look back at 2007, for instance.

90 free agents signed major league contracts last winter, ranging from Alex’s Rodriguez $275 million deal to Josh Towers’ $400,000 contract with the Rockies. The sum of those 90 contracts paid out $396 million in 2008. To figure out what the average cost per win of a 2007 free agent was, though, we need to know how many wins that group was worth.

To calculate this, I did a three year weighted average of their win values, then multiplied that value by .95 to factor in aging and estimate what teams considered considered a player’s true talent win rate for 2008. In total, I came up with 88 wins, or $4.5 million per win. That’s what major league teams were paying for a marginal win last winter, so for 2008, that’s a players dollar per win value as listed on the site. I re-did this for all years going back to 2002, and the dollars per win for each are as follows:

2002 – $2.6m / win
2003 – $2.8m / win
2004 – $3.1m / win
2005 – $3.4m / win
2006 – $3.7m / win
2007 – $4.1m / win
2008 – $4.5m / win

Now, I know there’s some sentiment that teams don’t pay for wins linearly, because a six win player is worth more than three two win players. While I agree with this in theory, major league teams just don’t operate this way. If you just look at the dollar per win costs for the multi-year contracts handed out to hitters last year, the cost per win was $4.3 million for guys with an average win value of 4.4 wins per player. Alex Rodriguez signed for about $3.8 million per win last year. Teams just don’t pay exponentially more for higher win value players than they do for average and below players. You could argue that they should (and I would probably agree), but they don’t. The dollar per win scale is linear.

This afternoon, we’ll look at the opportunities that are presented to teams due the linear nature of dollar per win, and how the smart teams are exploiting this to their advantage.

We hoped you liked reading Win Values Explained: Part Six by Dave Cameron!

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As a long-time lurker on USSM, I’ve read a lot of your analysis into these issues, and something still bugs me about the linear dollar-per-win finding. Isn’t it possible that the high win-value players are signing longer contracts than low win-value players, and thus we can’t correctly identify the dollar-per-win curve without making strong assumptions about how teams and players value long-term contracts?