Albert Pujols and Linear Dollars Per Win

Kenny Williams, on whether he would sign Albert Pujols.

“If [Jerry Reinsdorf] gave me $30MM dollars right now, I’m not going to spend it on one guy. Sorry White Sox fans,” the GM said. “But I tell you what, I’m going to take that $30 million and I’m going to distribute it around. My team is going to be better as a whole than it is with one player who might get hurt. Then you’re done. Sorry, that’s just me. And that’s no disrespect to a future Hall of Famer, first ballot, one of the greatest players in history.”

This is an interesting quote, and it sheds light on a subject that comes up quite a bit when we talk about our dollars-to-win salary model. One of the objections that comes up frequently is the linear nature of that model, where we use $5 million per win for a one-win player or for a six-win player, since that is how MLB teams have generally provided contracts. Our model works off of how teams have operated, but to some, this undervalues star players.

After all, a team is theoretically better off with one +6 win player than three +2 win players. While both situations give you +6 wins, having it consolidated into one roster spot gives you the ability to get even more potential WAR from those three spots if you can find better than replacement-value talents at the other two spots. There’s also a scarcity issue, as it is much easier to find +2 win players than +6 win players, so having the superstar gives you an asset that is not easy to re-acquire, while you can stock up on average players without too much difficulty.

These factors lead many people to argue that the dollars-to-win scale should not be linear, but should increase exponentially for higher-end players, reflecting their extra value. In reality, though, Williams’ mindset seems to be the more prevalent one in Major League Baseball. When it comes to big contracts, teams are more interested in minimizing risk than maximizing reward.

Based on his comments and his actions, we can state with some likelihood that Williams believes the White Sox are better off with the combination of Adam Dunn and Alex Rios than Albert Pujols. Dunn and Rios make about $27 million per year combined, so the two of them take up about as much of the payroll as Pujols would. Production wise, Rios and Dunn combined for +7.6 WAR last year, which is right about what you get from an average Pujols season. Williams essentially stated a preference for diversification over consolidation, as he sees the risk of injury to one highly paid superstar as a larger negative than having a higher potential return by having a lot of value tied up in just a single roster spot, and his moves over the last few winters support the idea that this is his roster-building preference.

Is this the right path? You could make arguments either way. I’d rather have Pujols than the Rios/Dunn combination, but Williams is a bigger fan of Dunn than I am, and the length of commitment is much shorter with this pair than with Pujols. While you’re paying for about the same number of player seasons, spreading them out over multiple players does give you the ability to trade older seasons for younger ones. And, as Williams notes, one injury doesn’t immediately remove the performance of both players, insulating his team from the chance that they could lose a large chunk of value in one tragic moment.

Risk or reward – it’s the trade-off we make in nearly every aspect of our lives, and every decision involves balancing the two. MLB teams have decided that the correct balance should result in higher end players receiving approximately the same dollars per win as non-stars, with the risk of injury canceling out the scarcity and potential for overall higher production. Whether it should be or not, this is why the dollars per win scale is linear. Williams just provided the best example possible for why the model works.

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Dave is the Managing Editor of FanGraphs.

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