Sometimes I think that certain baseball writers forget that mathematics is just one scientific discipline out of many, and it's not the only one that applies to the sport. It leads to the conclusion that teams overvalue relief pitchers in general and closers in particular, as Dave Cameron again reiterated on FanGraphs yesterday just before the Huston Street and Rafael Betancourt deals were announced. I think one of the other fields of study that applies here and that isn't given enough credit is behavioral science. Here, see if you can follow this logic:

#1 It sucks to watch your team lose.

#2 It sucks more to watch them lose games that they have a late lead than it does to watch them lose games the opposing team had control of from the start.

#3 It sucks even more if your closer does #2 on you repeatedly.

And yeah, I'm not sure if I wanted to go there on Puritan Purple Row, but I think my point is that even though they count the same in the standings, fans tend to take heart-breaking losses late worse than they do other losses, and I would argue that these losses have a larger impact on the future box office for a team, therefore making high leverage relievers (be they closers or set-up men) more valuable in real terms than the other pitchers in the bullpen. We're programmed like any other animal to shy away from pain, and will avoid going to places we know where pain occurs frequently, even if something we like (in this case wins) can also be obtained there. Winnie the Pooh will be more careful in his pursuit of honey if he knows he's going to get stung and would much rather sneak it from Rabbit than directly from the beehive.

In small doses, we can blot these games out of our memories (for some reason, I only remember the first two games in the NLDS, for instance). In large doses, they drive fans away in droves. I'm going to hypothesize that it's probably not a complete coincidence that none of the 11 teams (a list that includes 2009 contenders such as the Giants, Cardinals and Tigers as well as also-rans) with a negative reliever WPA in 2008 saw an attendance increase in 2009. Of the teams that were in the negatives in this category in 2007, only Tampa Bay, which went on to their first winning season as a franchise, the AL East title and the pennant, saw an increase in attendance in 2008.

Having lived through the Rockies experiment with Shawn Chacon as closer in 2004, I would argue that even for non-contending teams, the box office value of a reliable ninth inning reliever is high enough to put a premium over their expected WAR contribution (at least as far as FanGraphs calculates reliever WAR). I'd imagine that Cameron's counterpoint (and it's a valid one) might be that even if the relative value to a team is high, the cost of replacing a late inning reliever is relatively low, as they actually aren't that much more skilled than other members in the 'pen, so why would a smart team pay more? I think the answer to this is for the same reason that a smart person would take out an insurance policy on a new boat or your house, for that matter.

I used to believe, as many do, that teams pay more for the closer label than the closer skill. I believe now that what teams are actually trying to pay for is risk mitigation in situations where larger amounts of money are on the line than normal. Some teams are more successful at identifying real value in risk management than others. In signing Huston Street and Rafael Betancourt to multi-year deals yesterday, the Rockies got a pair of high leverage insurance policies for at least the next two seasons, seasons when the team very much should be in the thick of competition. 

I do want to add before going on that all my evidence here is pretty anecdotal and much more rigorous study is needed, so Cameron and others who espouse the idea that closers are overvalued by the market could very well still be correct. It's my suspicion, though, given that closers have been paid at this sort of premium for at least three decades now, that they aren't, that there's something other than an overinflated bubble keeping their salaries afloat. I think it's that teams have learned that there's a real monetary payout for successfully identifying solid, consistent, late inning relievers.

Other links/notes after the jump:

• Besides Street and Betancourt, the Rockies also agreed to terms with Jason Hammel. 
• Dexter Fowler got a new agent. 

This sets up an interesting scenario in a few seasons where the Rockies will likely need/want to deal with Scott Boras for a long term contract for either Fowler or Carlos Gonzalez, but will likely have to let the other player walk. What should we do as Rockies fans besides pray that Delta Cleary develops into his potential? For one thing, don't expect Fowler or Gonzalez to sign arbitration buyout deals similar to those signed by Ubaldo Jiminez, Troy Tulowitzki or Chris Iannetta.

That said, I don't know if I'd rule out the Rockies being able to retain one or the other of Fowler or Gonzalez after they hit FA just yet. I'm going to hope that the Rockies are able to keep Tulo long term, and were that the case, at that time he'd have one Heltonesque franchise type of contract with the team. As a team, with careful planning and decent player development (and some contending seasons between now and then to build the fanbase/payroll would help as well) they could probably afford one more, and I'd hope it would go to another up the middle All-Star level player or a staff ace. Internally, that would likely mean one of Ubaldo Jimenez, Fowler or Gonzalez. I don't know, maybe I'm just exercising some wishful thinking here, but there are a few seasons before we have to really worry about it.

******

I've said it here before, and I haven't really seen any disagreement in the comments, so I think most everybody here must be with me on this, but I believe that the Diamondbacks are building their team like they feel they're in a must-win sort of situation for 2010. 

This article does nothing to dissuade me from that opinion. Here are the words from Managing General Partner Ken Kendrick:

"We decided," he said, "that we needed to look at the team in the following way: If we got the right team together at reasonable dollars that the results on the field would hopefully generate better attendance and add to revenues.

"If they don't play well, we absolutely will have a loss. But we're willing to take that risk. We're not about making money. We're about winning and trying to avoid significant losses. That's been our M.O. from the beginning."

Just above I was talking about how behavioral science has applications to the baseball world. There are multiple signs that the D-backs are in some sort of financial bind here beyond what Kendrick is saying on the surface. Start with the end of that first quoted paragraph, that the "results on the field would hopefully generate better attendance and add to revenues."

What this suggests to me is that Kendrick and the Diamondbacks are doing here is little different than what gamblers do when they've exhausted their available capital and approaching the line where they will dip into credit. It's what many struggling companies do in the same situation. It's a hockey team pulling the goalie at the end of a game they're trailing. 

It would be one thing if the D-backs were doing this after a playoff appearance or at least a near playoff appearance in 2009, but this was a team, that though better than their record, won just 70 games last year. I believe a smart FO just wouldn't go into payroll debt after that kind of performance unless they're really thinking that they're at the end of a contending run and are literally going for broke. While I believe they're a bit overrated, I don't believe the D-backs management team to be fools. I think they understand that when Justin Upton and Mark Reynolds get added to their arbitration eligible pile of players starting in 2011, that the cost of maintaining that team will quickly exceed their revenue projections without the kind of boost that the playoffs can provide.

There is no follow-up by the reporter and Kendrick doesn't say what happens if the D-backs again trip and miss the playoffs, or even worse, are far out of contention in 2010. With three other decent teams in the division, that possibility looms for all four with just a bit of bad luck. Let's hope the Snakes again come up drawing blanks in 2010, as that should be enough to knock them out of the Rockies worries for several years to come.