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July 20, 2009

Ahead in the Count

Get the Doctor, Now!

by Matt Swartz


When sabermetricians try to approximate the dollar value of a player’s performance, we are mostly using recent free-agent values. For instance, if Halladay is worth about six wins above replacement level (which is a good approximation for most teams’ fifth starters), we would say that the value of his replacing a typical fifth starter is about $27 million above the MLB-minimum salary of $400,000. As his current contract pays him $14.25 million in 2009, this would imply that a full 2009 season of Roy Halladay would have been worth the difference ($13.15 million). However, let's say that Halladay gets dealt right now, with about 70 games left to go, instead of around the deadline. Our inclination would be to say that Halladay’s remaining 2009 net value would be this pro-rated, $5.7 million above his contract, but that misses a few essential parts of the analysis.

Free agency is a process by which teams bid for a player’s services in an auction format. The winner is usually the team that offers to pay the most. What that means is that the team who signs the player is probably the team who values the player the most. That may be optimism, but it also may be that the team has more value for his services than other clubs.

Estimating the value of an object at the amount of money the purchaser paid for it is somewhat inaccurate, only because not everyone values things equally. Suppose that I told you that I recently purchased a swimming pool skimmer for $15. You might think that I got a pretty good deal until you found out that I don’t own a pool. Similarly, the Cardinals did not bid on Mark Teixeira this winter, simply because it would not be worth the $22.5 million the Yankees pay him annually to have him sit on the Cardinals’ bench and watch Albert Pujols take his cuts.

Additionally, if I told you that my friends bought a used pool skimmer for $40 at midnight last night, you might think that they were being foolish, but if you found out that their son had a pool party at 11:00 AM and their pool was filled with leaves, you would probably change your mind. The gravity of the situation matters. Similarly, if I told you that instead of letting Tom Glavine pitch the last day of the 2007 baseball season against the Marlins, the Mets were somehow able to pay Johan Santana to join the staff on that fateful Sunday and pitch them to victory instead, you might value that more than 1/162nd of his contract value. That game was definitely going to make or break their season (or at least send them into a one-game playoff), since they were tied with the Phillies on the last day of the season for the division lead, and that game was definitely pivotal.

At the beginning of the season, Roy Halladay may have been worth about $27.4 million to a contender, but a contender might not end up needing those six wins above replacement level; alternatively, they may not even have been enough. We act as though 162 games is a large sample size, but a team that has the talent to win 89 games will finish with 99 wins or more about seven percent of the time, and will finish with 79 wins or less about five percent of the time, just out of sheer luck, good or bad. The odds of even a six-win pitcher like Halladay actually making the difference in a team’s season is pretty low when calculated in April. In fact, the odds of a one-win player actually adding that one crucial game that the team would not have won anyway is about 6.3 percent. However, as the trade deadline approaches, and a team knows that they are in contention but not guaranteed a playoff spot, the odds of a one-win player adding that one crucial game go up to about 9.6 percent. Therefore, even though the number of wins that Halladay adds if he joins a team 92 games late might be only 2.6 wins over the last 70 games (instead of six wins over 162 games), he still will maintain up to 66 percent of his revenue production value while only maintaining 43 percent of his win value.

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