Let's play the old "Pitcher X" game. Below, are the lines for two relief pitchers over the past three seasons, both of whom have spent two of those as major-league closers, and were also inked by their clubs through 2014 in the past 24 hours.
X has more saves, but in terms of how opposing hitters have done, it's virtually identical. Y has better periphs, with a K:BB rate of more than 5:1; X is below three. That's why Y comes out significantly ahead in terms of FIP and xFIP, and thus Fangraphs' WAR. But, really, both are very good: if you had to choose between the two of them, you might almost have to flip a coin. Or, rather, about fourteen and half million of them. Because, courtesy of the contracts they just signed, X (Rafael Soriano, now of the Nationals, in case you hadn't guessed) will be paid $28 million over 2013-2014, while Y (who comes out at Chase to the tune of Thunderstruck), gets $13.5 million for the same time.
There is certainly a case to be made that closers are overpaid, largely because the unwritten rules say that they are only used in the ninth inning. They may be the best reliever on the team, but still won't necessarily be used to get the most important outs. The game can be on the line in an earlier frame - based loaded for the opposition in the seventh, with you clinging to a one-run lead, say - and you'll almost never see any manager in the majors roll out their closer. Jerome Holzman, who created the save as we know it in 1960, has a lot to answer for, his statistic having created the modern closer, almost single-handed.
On the other hand, there's no denying that few things suck the wind out of a team's psychological sails, worse than a late inning blown lead. One of the factors which propelled the Diamondbacks to the division title in 2011, was that we literally didn't have any of those: we went 84-0 when leading after eight innings. Equally impressive, we were 84-6 when ahead or tied after seven. That .933 win percentage compares to .803 across the NL as a whole, or put another way, we won 12 more games in that situation than the average National League team. This season? Our record was 75-17, ten games worse.
Now, we should remember that late losses are attributable, probably equally, to both the defense allowing runs, and the offense failing to score them. However, that drop-off was far more due to Arizona's inability to buy a hit in late and close situations, than any real failings of the bullpen. Our offense's OPS in those situations last year slumped from .810 all the way down to .594; in comparison, our pitchers still held opposing batters to a .682 OPS, largely comparable to the .661 posted in 2011.
Still, let's take a look at the market price being paid for closers, and see if we can figure out what the going rate is for someone like J.J. Here are the ten pitchers, aged 31 or older, who have a total of 50+ saves over the last three seasons. The ranking is by ERA+, and their age is for the 2012 campaign.
Of the seven currently under contract, Putz's value is ahead only of Fernando Rodney in Tampa. I'm pretty sure Valverde will go for more (look at all those saves!); Gregg and Cordero, probably not, but they both pretty much blew chunks last year. Which illustrates a point against overpaying for closers: that ability is a very volatile commodity. You can see that clearly, if you look at all the pitchers who had 20+ saves in 2010: fourteen did so, averaging 31 saves apiece. But those same pitchers in 2012? Only two of the fourteen (Soriano and Valverde) reached twenty again. A couple were no longer in the game, e.g. Billy Wagner, but the other ten averaged only 6.6 saves each.
There's also the question of Putz's age. He is already kinda old for a closer, even though they generally skew a bit more mature than regular relievers, simply because it's a position typically given only to someone with a proven track record. In the past decade, 154 seasons of thirty-plus saves have been recorded, and they're almost evenly-split between those 30 and under (78 cases) and 31 or over (76 cases). Still, there were 22 cases where a pitcher was 37 or older, and reached the mark. Admittedly Mariano Rivera was responsible for five of those, and Trevor Hoffman four, but there was no indication of Putz losing his "stuff" this season, at age 35.
It is a reasonable criticism to say, just because the Nationals made a vast overpay on a poor (and potentially, awful) deal, is no reason we need to follow suit. But it does show one benefit to getting Putz locked up now, from the team's point of view: it avoids them having to bid against such idiocy, when J.J. becomes a free agent at the end of this season. Even in terms of pure WAR, getting three WAR out of Putz in the next couple of seasons is quite plausible, if he can remain healthy, and that would make his contract cost a reasonable return. Add on the closer's premium, and it certainly appears to be well under market price.