A couple of days ago, the Oakland A’s signed Nick Punto to a one year contract that will pay him $2.75 million in 2014 and then either pay him $250,000 to go away or an additional $2.75 million in 2015, so the deal is either $3 million for one year or $5.5 million for two. The A’s are not looking at Punto as a regular player, as they already have Jed Lowrie, Eric Sogard, and Alberto Callaspo as middle infield options, but Punto gives them additional depth and reinforces their bench. He’s a good reserve, capable of playing high level defense and getting on base enough to not be a complete zero as a hitter, but the A’s ideal plan for him likely involves him getting roughly 250 plate appearances next year. If he gets more than that, something probably went wrong.

So, $3 million for a quality bench guy seems reasonable. It’s about what you’d expect given how reserve position players have generally been priced in the free agent market. Last year, similar deals were given to Ty Wigginton, Eric Chavez, Raul Ibanez, Jack Hannahan, Placido Polanco, and Geovany Soto. This is, essentially, the market rate for an aging bench guy. Even if teams value their contributions, they don’t play enough to really command much more than a few million dollars on a one year deal.

A Major League can expect to send a hitter to the plate about 6,200 times in a season. A bench player who hits 250 times will comprise about 4% of the team’s total number of plate appearances. $3 million for that kind of marginal role seems perfectly fair.

However, we know that the market for relief pitchers is entirely different than the market for bench players. Last year, Rafael Soriano landed a contract for $28 million over two years, even though the Nationals had to forfeit a first round pick for the right to give him that contract. Jonathan Broxton got $21 million over three years, and Jeremy Affeldt got $18 million for the same three year term. A quality relief pitcher is now valued by the market as somewhere in the range of $5 to $10 million per year, and if they have earned the closer tag, the price can run up to $15 million per season with a multi-year commitment.

Relief pitchers, in general, throw about 60 innings per season. A few workhorses will get up around 70-80, but most of the bullpen guys settle in around 60 innings per year if they stay healthy and pitch the whole season. A Major League team throws about 1,450 innings per year, so again, simple division tells us that a relief pitcher will throw about 4% of a team’s innings in a given year.

Relief pitchers and bench players, on average, carry roughly the same relative workload in terms of a team’s total number of plate appearances and innings pitched. Bench players rarely get more than $3-$4 million per season, because it is widely accepted that they just don’t play enough to make a huge impact on a team’s final record. Relief pitchers get paid two, three, or even four times that amount.

There are a few possible justifications for these different valuations.

1. The runs that good relief pitchers save are more important than the runs created (or saved) by good bench players.

This is almost certainly true, and can be demonstrated through Leverage Index. The average Leverage Index for all relief pitchers in 2013 was 1.18, and for good setup men, it was more regularly in the 1.5 to 1.6 range. Elite closers can have an LI of 1.8 or 1.9 if they pitch in a lot of one run games. This means that the runs they prevent have nearly twice the impact on the outcome of a game as an average run. If you replaced an elite closer with a relief pitcher who gave up 10 additional runs while pitching in the exact same situations, it would likely result in two additional losses, not one.

2. That the spread in talent among relievers is larger than the spread in talent among bench players.

This seems likely to be true as well, as there are really good pitchers who are willing to spend their careers pitching out of the bullpen — either for health reasons or because it just fits their personality and skills the best — but there is not the same supply of really good position players who are content to spend their days as a bench player. Good bench players become acceptable regulars, or are at least given that chance; good relief pitchers do not make that same conversion as often. With the best bench players moving out of bench roles, the population of reserve position players are probably less diverse in talent than the population of relief pitchers.

3. Teams are either undervaluing the contributions of bench players or overvaluing the contributions of relief pitchers.

This would be the market inefficiency argument, and would suggest that teams are allocating too many of their “bench” dollars to pitchers rather than position players. Given the different market prices we’re seeing for guys like Broxton or Affeldt compared to Punto or Chavez, I think you can make a pretty good case that the market pays too much for relief pitchers compared to relief hitters.

That doesn’t necessarily mean that I think they should be paid equally. Relievers can be leveraged to maximize the efficiency of their run prevention, and having good relief pitchers to help preserve one run leads is a way that a team can win more games than you’d expect just based on their runs scored and runs allowed. But even with leverage included, it’s basically impossible to argue that a relievers runs saved are more than twice as valuable as a position player’s runs created (or saved). And those relief pitchers get paid a lot more than twice as much as bench players, despite contributing a similar amount of overall playing time.

I know the world probably didn’t need another article saying that teams are paying too much for free agent relievers. That’s a pretty well established belief around here by now. However, I do think it’s interesting that the market continues to place minimal value on quality reserve position players, even as teams make plans to build golden urinals with their new television money.

Maybe if we stopped calling them “closers” and “setup men”, and referred to them as “backup pitchers”, we’d be reminded that relievers are basically just the pitching equivalent of a backup shortstop. Or maybe we should go the other way and invent fun nicknames for bench guys. Instead of a derisive term like “utility infielder” for Nick Punto, I suggest the A’s start referring to him as their “defensive savior”. Or maybe “infield rescue expert”. Maybe, at the end of the day, bench guys just need better marketing gimmicks and their own intro music.