Teams Continue to Overpay Relievers. Why?

Over the past decade, the decision making of major-league teams has increasingly come to reflect the values of the sabermetric community. There is, however, one prominent area in which the valuations made by major-league teams and those around the blogosphere continue to diverge – and that is the value of relief pitchers, particularly late-inning relievers.

For the last several years, many writers on this site and others have argued that because relievers pitch so few innings, even the best relievers are worth only about 2-3 wins above replacement. However, the industry does not appear to agree, as reliever salaries have not decreased over the past three seasons.

*I restricted my sample to players who signed for over $1 million, and I also removed all long-relievers from the sample. I calculated each reliever’s WAR based on their Marcel projection for the first season of their new contract.

I also broke down the relievers into groups based on whether the player signed a one-year or a multi-year contract, as one-year contracts are typically better values from a team’s perspective.

Over the past three years, teams have paid an average of 4.8 million per win for relievers on one-year deals. That figure increases to 7.0 million per win on multi-year deals. (It’s worth noting that teams likely pay more than 7 million per win on multi-year deals, because the skill of veteran relievers likely diminishes over the course of the contract).

So, although relievers signed to one-year deals appear to be better values than those inked to multi-year contracts, no matter which way you slice it, teams are paying more for each win from relief pitchers than average. But there has been enough written about the relief pitcher market that I’m guessing most of you could have already predicted that relievers are overpaid. The question worth answering is: why, even in the face of all this information, do teams continue to pay a premium for relievers?

While I certainly can’t give a definitive answer, I think there are two particularly plausible explanations.

The first and probably the most obvious explanation is that, psychologically, relievers feel more important than they really are, and research from behavioral economics may help to explain why. In 2002, Daniel Kahneman won the Nobel Prize in economics for his work on Prospect Theory – a system incorporating biases, heuristics, and risk-aversion (among other things) to formulate a more realistic model to explain human behavior. One of the central tenants of Prospect Theory is the power of reference points. Our appraisals of changes aren’t tied to absolutes so much as they are reflections of our current standing. If I go to Vegas and lose $100 the first night and then win $50 the second, I will leave feeling much better than if I win $50 the first night and lose $100 the second, because my reference point has changed after the first night, even though, in an absolute sense, the outcomes are identical.

Our reliance on reference points becomes particularly relevant when trying to accurately value relievers. As any fan can attest, no loss is more painful than the game in which your team blows a save and loses. Consequently, no win is as great as the one that comes in walk-off, come-from-behind fashion. The reason these two games are so emotionally powerful is that our reference point changes during these games. When the team we’re rooting for has a lead, we correctly identify that our team’s probability of winning has increased, and the reference point comes to reflect a high probability of winning. We now expect our team to win. What makes losing late leads so tough to deal with is that we had already begun to mentally bank the win.

Prospect Theory also uses heuristics – psychological shortcuts that ease decision making – to explain behavior, and I think the availability heuristic is particularly relevant in explaining why relievers may be overvalued. The availability heuristic basically says that our estimates of probability are based on the ease with which we can call an example to mind (e.g., the number of shark attacks each year is drastically overestimated because of how memorable they are). Over the past decade, in no small part because of Mariano Rivera, the playoffs have been dominated by shutdown closers. Instances of Rivera, Papelbon, and Wilson dominating in October are fresh in the minds of many front-office members. And because of the recent success of teams with dominant closers, it seems like having a great closer is a prerequisite to getting into and having success in the post-season.

On the other hand, there may be reasons beyond the psychological difficulty of devaluing the contribution of late-inning relievers to account for the sustained demand for relief pitchers. One possibility is that signing relievers offers teams a relatively cheap way to amass a number of compensation picks. Rafael Soriano, Octavio Dotel, J.J. Putz, and Kevin Gregg, were all signed to one-year deals last off-season and will all yield compensatory picks in this year’s draft. Some teams are likely incorporating the chance of getting a compensation pick into the cost of the player. For example, signing Jon Rauch for $3.5 million may make economic sense even if the Blue Jays don’t expect him to post more than .75 wins, as he may bring them a top-50 pick in the 2012 draft.

But determining which relievers will achieve type B status may be more difficult than some teams imagine. Excluding players signed from Japan, only ten relievers signed as free agents since 2006 have yielded compensation picks. Part of the reason predicting the performance of relievers is so difficult is that in 60 innings, there will be a lot of variability in the metrics likely employed by the Elias Sports Bureau to determine free-agent rankings.

All of this analysis is not to say that having a strong bullpen is not an asset, but, given all the information out there, it’s surprising that reliever salaries have not shown signs of decreasing in the past three years.