Teams that pay steep price tags for “proven closers” often get ridiculed by statistically-inclined baseball writers and readers, often for good reason. This tends to be especially true when these teams already have a viable replacement in their bullpen who is cheaper and maybe even a superior pitcher.

However, as Jeff Sullivan wrote on FanGraphs, when those teams include the Athletics and Rays, we tend to step back and reevaluate our positions since these teams typically know what they’re doing. When the A’s traded for Jim Johnson in early December it was a bit of a head-scratcher, as the team had two young relievers perfectly capable of handling the ninth inning in Ryan Cook and Sean Doolittle. While Sullivan pointed out at the time that the A’s roster was deep and it would be difficult for them to upgrade elsewhere, there was another reason that didn’t receive as much attention: signing a veteran reliever could keep the young relievers out of the closer role, thus reducing their cost.

The Athletics were the most prominent team to make a move like this, but plenty of other situations where teams with excellent young relievers and departing closers opted to sign a veteran to take over the ninth inning. The Rays acquired Heath Bell (and later signed Grant Balfour) instead of giving strikeout machine Jake McGee a chance to close, and the Indians followed suit by signing John Axford (coming off a -0.5 WAR season) to handle the ninth inning despite Cody Allen’s strong 2013 campaign. Most recently, the Mariners committed $14 million so that Fernando Rodney could close out games while Danny Farquhar, with his 34.7 percent strikeout rate and 1.86 FIP in 2013, got bumped to a setup role. Earlier in the offseason, the Rockies signed journeyman LaTroy Hawkins to close despite the presence of Rex Brothers as well.

So what’s really happening here? In three of these cases, the veteran closer had actually performed significantly worse than the young set-up man in 2013, yet the teams went out and committed significant money to these free agents. While these moves may be frustrating for baseball fans, a deeper analysis reveals that these deals might make quite a bit of economic sense for these teams. The idea of saving money on young relievers is occasionally thrown around, but how much money can teams really save?

Let’s try to keep things relatively simple by focusing on the Athletics, given the fact that their in-house closer candidates have amassed multiple excellent seasons but have yet to reach arbitration. You can make a case that the other teams might not have been comfortable with their in-house options, but that argument simply doesn’t hold water for the A’s.

For the purpose of this research, we’ll assume that had the A’s kept their bullpen intact after Balfour’s departure, Ryan Cook would have handled the ninth inning. Cook has a 2.55 ERA over 148 innings in two seasons with the A’s and 7.2 innings with Diamondbacks and has earned 16 saves in that time. So far, Cook looks like an elite set-up man, pitching mostly in the seventh and eighth innings and earning 44 holds with the A’s. Luckily for us, the cost for an elite set-up man in his first year of arbitration is pretty well defined as you can see from the pre-arbitration stats and first-year arbitration salaries in the table below.

Elite Set-Up Men, First Time Through Arbitration Player IP ERA WAR SV Hold Arb 1 ($M) David Robertson 172 2.62 4.0 3 53 1.6 Jonny Venters 171 1.89 2.9 6 59 1.6 Luke Gregerson 209 3.10 3.2 3 83 1.6 Tyler Clippard 239 2.52 3.0 1 64 1.6 Bobby Parnell 163 2.98 2.0 13 38 1.6 Sergio Romo 144 2.38 4.3 3 54 1.6 Average 183 2.58 3.23 5 59 1.6

If we assume Cook maintains his current level of excellence in 2014, he’d project to beat most of this group in innings pitched (222), WAR (4.5) and holds (68). However, even players with lots of innings (Clippard) or holds (Gregerson) received the same $1.6 million figure. Cook also already has more saves than anyone in the group at 16, but once again we see that Parnell’s 13 saves didn’t help him out-earn the others.

I think it’s safe to assume that if Cook remains an elite set-up man in 2014, he should project to earn $1.6 million in arbitration. Now, how much might Cook earn in his first year of arbitration if he were to succeed as the A’s closer in 2014? Luckily, there are a pair of decent comps from this past season for relievers who didn’t become full-time closers until their final pre-arb year.

One-Year Closers, First Time Through Arbitration Player IP ERA WAR SV Hold Arb 1 ($M) Steve Cishek 188 2.54 3.2 52 16 3.8 Ernesto Frieri 198 2.96 1.8 60 13 3.8 Average 193 2.75 2.50 56 15 3.8

You can make a strong case that many of the relievers in the first group had actually pitched better than Cishek and Frieri. No matter, the 50+ saves from each of them pushed their earnings to $3.8 million. You could argue that Cook is better than these guys, but since we’re being conservative let’s just pencil in Ryan Cook the hypothetical closer for the same $3.8 million.

Looks like Billy Beane has already saved $2.2 million from his 2015 payroll, not too shabby. But since we know that arbitration raises are built off of the previous year, saving $2.2 million in year one will also lead to savings in years two and three. This is where the numbers get a bit more difficult. Let’s go back to the first group and look at what a few of the relievers earned in the rest of arbitration.

Elite Set-Up Men, All Times Through Arbitration Player Arb 1 ($M) Arb 2 SV Arb 2 ($M) Arb 3 SV Arb 3 ($M) Arb Total ($M) David Robertson 1.6 5 3.1 8 5.2 9.9 Tyler Clippard 1.6 33 4.0 33 5.9 11.5 Bobby Parnell 1.6 35 3.7 (2015) (2015) ?

Note: The saves (Sv) listed for each arbitration year are the cumulative career figures for each player at that point in his career.

Robertson appears to be the best comp for an elite set-up man who never gets a chance to close, earning just under $10 million over the course of his contract. Clippard and Parnell fit what we might expect if Cook gets a shot to close in 2015 after Johnson’s contract expires, although Clippard went back to being a set-up man in his penultimate year and we won’t know Parnell’s final arbitration contract for another year.

Since Clippard’s ERA (3.72) and Parnell’s low innings total (50 IP) leading into their second arbitration year may have cost them, let’s assume Cook can beat the pair and earn $4.2 million in 2015 in his first year as a full-time closer. To fill in the rest of the blanks, let’s take a look at a few recent relievers who followed similar paths to see how their arbitration costs escalated.

Recent Closers, All Times Through Arbitration Player Super 2 Arb ($M) Arb 1 ($M) Arb 2 ($M) Arb 3 ($M) Chris Perez 2.2 4.5 7.3 Non-Tender Jim Johnson 1.0 2.6 6.5 10.0 Joel Hanrahan N/A 1.4 4.1 7.0 Matt Capps N/A 2.4 3.5 7.2

It’s not easy to find pitchers who didn’t start closing until their third or fourth year of team control, so unfortunately, three of the four recent comps were super-twos, two weren’t all that great, two were non-tendered, and one is Johnson himself. Perez got a $2.8 million raise after a season with 39 saves and a 3.59 ERA, while Hanrahan and Capps both earned $3.7 million raises after eclipsing the 40-save mark with ERAs under 2.5. The key takeaway here is that an effective pitcher who is earning saves as a full-time closer will see raises of $2-4 million in arbitration. While a reliever like Cook is certainly capable of putting up a monster season and earning a $3.5-4 million raise, let’s keep things simple and use $3 million.

Using this knowledge, we can put together a table estimating Ryan Cook’s expected arbitration cost if he had become a full-time closer in 2014 versus waiting until 2015 to close out games.

Ryan Cook, Potential vs. Probable Earnings Player Arb 1 ($M) Arb 2 ($M) Arb 3 ($M) Arb Total ($M) Ryan Cook w/ Johnson 1.6 4.2 7.2 13.0 Ryan Cook, closer 3.8 6.8 9.8 20.4

There you have it. By keeping Cook out of the ninth inning for just one year, the A’s appear to be saving around $7.4 million in arbitration costs. This makes the net cost of having Jim Johnson close for the A’s in 2014 around $3M. You could argue that these numbers are a bit generous, but assuming that Cook continues to be an effective reliever, the A’s appear to be saving at least $5 million with this move. A $10 million Jim Johnson doesn’t look too great, but at $3-5 million he has to be considered a steal.

This analysis also shows us the importance of the first year of arbitration. Since the salaries build on one another, an inflated figure in the first year will have a big impact on the subsequent years. Therefore, the difference in cost between a pitcher who starts closing during his first year of arbitration and one who starts closing during his final pre-arbitration year is much greater than the difference between the former pitcher and one who doesn’t close at all.

We also see the degree to which saves trump skill in the arbitration process. A pitcher like Chris Perez (0.8 career WAR in 333 innings) pitching in the ninth will end up being significantly more expensive than David Robertson (7.6 career WAR in 329 innings).

So where does this leave us? Teams that have effective young relievers in their pre-arbitration years when a vacancy in the ninth inning opens up are put in a tough position. If they hand over the keys to the ninth, they’re almost certain to pay the price in arbitration.

However, if teams sign a veteran closer to keep their young guy from racking up saves until after his first arbitration hearing, they stand to save a lot of money, possibly as much as $7-8 million. At the start of 2011, the Atlanta Braves chose to hand the keys to rookie flamethrower Craig Kimbrel. Now, he’s about to earn more than any other first-time arbitration-eligible reliever and may become so expensive that the Braves have to consider trading him.

Given the amount of money on the line, it’s not surprising that nearly every team that lost its closer to free agency and had a pre-arbitration reliever posed to take over opened up its wallet and signed a veteran. Effectively, these teams have a coupon that gives them a huge rebate on a free-agent closer, but they have to use it this offseason. For a team with deep pockets, it might make sense to simply let the best reliever close. However, smaller-market teams that need to squeeze more value of their cost-controlled players might be more likely to take advantage of this discount. In this context, these types of acquisitions become not only defensible, but actually quite brilliant.

Earlier in the offseason, Eno Sarris explored some of the complexities of the arbitration process on the FanGraphs website and podcast, noting how savvy teams could manipulate the system to save money. Nowhere is there a greater gap between the arbitration process and the open market than in the premium placed on saves.

As front offices get wiser and it becomes more difficult to find values on the free-agent market, teams (especially those with tighter budgets) are always searching for new market inefficiencies to get an edge. Judging by some of these transactions, it appears that teams are realizing the economic advantage that they can get by exploiting the arbitration process to suppress the costs of their own players.