What's a closer worth? Well ... that's complicated

Aroldis Chapman will be the highest paid closer in history. One interesting thing about that sentence is that we even say it.

It's not an observation you'd expect to read about a shortstop, or a center fielder, or a first baseman, because superstar first basemen just get paid as superstars, unqualified. But closers are so weird. They break all the rules.

Every other star player plays as often as possible on a regular schedule. Closers are intentionally held back for moments. It's as if teams benched their fourth-best hitter every day so he could pinch hit.

Most other star players have stable positions. Catchers are catchers from the time they're drafted until, quite often, the day they retire. Center fielders and starting pitchers are center fielders and starting pitchers until somebody decides they can't handle it anymore. But closers hover around the role, sometimes in, sometimes out, defined simultaneously by what they're unable to do (pitch in the first inning) and what they're too good to do (pitch in the eighth).

Meanwhile, other star players fill a non-negotiable need. Every team must have a shortstop, a catcher, and only a handful of people alive can play those positions -- or even fake it. But no team has to have a player who self-identifies as a closer, and scores of nonclosers in bullpens, the minor leagues or on the fringes of starting rotations can fake it. Meanwhile, some teams carry two or three or four players who might pitch as well as the average closer in any given year, while almost no team would ever carry four players capable of starting every day at shortstop. For closers, all notions of positional scarcity and gluts are ever-changing and negotiable.

The way the closer is used changes dramatically in the postseason, both in how often and for how long. This is only a little bit true for starting pitchers, and not true at all for hitters. A team can all but guarantee that in the biggest moment of the postseason, its closer can be on the mound -- that the entire series, the entire season, can rest on the strength of one acquisition. This can't be said of a hitter, no matter how good, because the hitter bats only when the lineup tells him to.

The way the closer as a species is used is also subject to re-evaluation by the sport's decision-makers. There is no promise that the next generation's closers will be used in the same way as the current generation -- or that they'll even be used to close. Shortstops, meanwhile, have pretty much always been shortstops.

For all these reasons, closer salaries have always existed in a different economy than the rest of the league's salaries. And for all these reasons, the decisions GMs make with relievers tell us something about what they value and how they intend to see the game played. Economic indicators might be fuzzy and they might mislead, but they can point us toward some truths about the role. So, then, back to Chapman. A month ago, the highest salary a reliever had ever earned was $15 million per season (Mariano Rivera), and the largest contract ever given to a reliever was for four years and $50 million (to Jonathan Papelbon). Both marks have been surpassed three times in the past month, by Chapman (five years, $17.2 million per) as well as Mark Melancon (four years, $62 million from the Giants) and Kenley Jansen (five years, $80 million from the Dodgers). Records have been broken.

These records reflect choices made by humans in an economic system that is presumably rational. What have we learned?

Hypothesis: GMs are paying more for closers than ever. And I know why.

When they write the book about reliever-ace usage in the 21st century, the chapter on 2016 will probably start with Cleveland's Andrew Miller, the relief ace who redefined (or, at least, re-redefined) the role by entering games in the fifth or sixth innings to get his team out of tight spots. But the chapter should include a lengthy section on another deadline acquisition: the Cubs' trade for Aroldis Chapman.

When Chicago added Chapman, it was seven games in front of its nearest division rival. Its playoff odds at Baseball Prospectus were 99 percent, a reflection not just of that substantial lead but of the strength of the Cubs' roster. Chapman would have practically no effect on the division race, or on the Cubs' chances of reaching the postseason. And yet the Cubs gave up a huge haul for him: A top-50 (at least) prospect in shortstop Gleyber Torres, a recent top-100 prospect in outfielder Billy McKinney and a couple throw-ins. By FanGraphs' prospect projections, the Cubs traded something on the order of 10 future wins for a one-inning reliever whose value to them was going to be concentrated in a single month of pitching: October 2016.

Add to that the fact that the Cubs seemed to already have a great closer. The day the trade was made, the incumbent Hector Rondon had a 1.95 ERA for the year, and in the previous three seasons that ERA was 2.01. Chapman's ERAs in the same time periods: 2.01 and 1.84. The difference between them, over a three-year stretch, had been roughly one earned run every 53 innings. Chapman could be expected to pitch around 10-15 innings if the Cubs went all the way to the World Series. This amounted to an extraordinary valuation for an elite closer.

And now we get three closers signing for a lot of years and a lot of money.

On the most basic level, teams need more relievers than ever. In 2016, a record 15,893 innings were handled by the league's bullpens, compared to 14,665 innings per season from 2010 through 2015. That's 41 more innings per team per season. Unless the world starts producing more good relievers, the demand for good relievers goes up with that new mandate.

The change is even more exaggerated in October, which has become, according to FiveThirtyEight's Rob Arthur, "reliever season." In 2016, starting pitchers averaged 5.11 innings per start in the postseason, down from 5.51 innings just the year before. Lest you think this is due to starters getting knocked out earlier, leaving work that any mop-up man or fifth starter could handle, it's the opposite: Managers are pulling their starters earlier mostly to protect leads. In postseason games that teams won in 2016 -- games where top relievers are more likely to be leaned on -- starters went just 5.52 innings, down from 6.26 innings the year before. To win a game in October takes more relievers than ever.

And increasingly it takes more work from the closer specifically. Last year's two World Series teams got nearly 15 innings apiece from their closers, which is the second-most in the 22 postseasons since wild-card play began. (And this ignores how hard the Indians rode fireman Miller.) Adjusting for the number of games their teams played, it still ranks second, at about 0.88 innings per game played. The 2015 closers were also worked hard, as their 0.81 innings per game were the most since 2004. In the decade before 2015, closers on World Series teams worked just 0.66 innings per postseason game.

That's certainly not a huge difference -- an extra inning or two in the biggest moments of the year -- but it chips away at one of the arguments against paying closers huge contracts, that they don't work often enough to justify a tenth of a team's payroll (or more). And in a league where a third of teams make the postseason, a GM's decisions can skew more than ever toward building a roster for the postseason.

So, sure, they're paying more for relievers than ever before. Why wouldn't they?

Antithesis: GMs are not paying more for relievers than ever before. They're not.

Look, if I tell you that Aroldis Chapman's 2017 salary will break a record set by Mariano Rivera in 2008, the fun fact isn't Chapman. It's Rivera! A 2017 salary should be higher than a 2008 salary, and the only news is that it took a decade for somebody to finally catch Mo.

Consider that in 2008 the average player salary across major league baseball was $2.9 million. By 2015, it was up to $4.0 million, and at that rate of inflation it should be around $4.3 million or so this year. Chapman will get paid as much as four average major leaguers, while Rivera was paid more than five.

In fact, if we chart the top closer contracts signed each winter and the league's average salary, closer inflation has held pretty steady with leaguewide inflation as a whole. ESPN Stats & Information found the top three reliever contracts by average annual value, signed in each offseason since 1990. We narrowed the list to pitchers who signed for three years or longer -- not all of whom were closers, but most of whom were. We charted their annual salaries as a ratio with the league-average salary.

Rivera stands out, as he ought to, as the only reliever to earn five times the average player salary. But otherwise, there's a steady history of players getting paid similarly to Chapman, Jansen and Melancon. You can see eight relievers whose dots form a band across the middle of the chart, above 3.75x but below 4.5x: John Wetteland, Randy Myers, Rafael Soriano, Francisco Rodriguez, Roberto Hernandez, Billy Wagner, Francisco Cordero and Papelbon. All will be paid more, relative to their era, than Jansen will be.

More striking is the paucity of such contracts in the years leading up to this offseason. In the four winters since Papelbon signed his four-year, $50 million contract, only three pitchers have signed contracts guaranteeing more even $30 million -- Darren O'Day, Andrew Miller and David Robertson. It'd be easy to conclude that GMs had mostly moved away from massive closer contracts.

That's also a bit misleading. The best relievers of the past half-decade have been young and under team control, such asCraig Kimbrel, Dellin Betances, Zach Britton, Cody Allen, Wade Davis, Chapman and Jansen, or they have been notably old and limited to shorter deals, such as Koji Uehara and eventually Mariano Rivera were. They didn't hit free agency, which helps explain why Papelbon's "record" wasn't broken. Andrew Miller was probably the best reliever to be a free agent since Papelbon, but his track record of dominance was short, and his career saves total was one.

But David Robertson hit free agency with a resume very similar to Papelbon's. In their three years before free agency:

However, Robertson signed for less money, three years later. Papelbon's annual salary was 3.9 times the league-average salary, while Roberton's was just 2.9 times.

That's notable, and it happened only two years ago. It's still a fresh data point demonstrating how GMs have pulled back from giving massive contracts to relievers, or else demonstrating the limitations of drawing broad economic conclusions based on a tiny number of isolated contracts. Maybe the latter.

Synthesis: Well, what do you know, it's a little bit of both.

If there's anything to draw from the contracts Melancon and Jansen got, it's that the spending trough of 2012-2015 was just a blip, that GMs didn't give up spending big money for closers after Papelbon. The Dodgers are a rich team that needed a closer, so they spent a lot on one. The Giants are a relatively rich team that just lost a division title under an avalanche of blown saves, so they spent a lot on one. Neither team spent that much, considering how good Jansen and Melancon are and considering what comparable closers have always been paid.

(If Jansen getting a fifth year -- something only B.J. Ryanpreviously got as a post-1990 closer -- is interesting, it might easily be explained by his young age or by his unique repertoire or by it being with the Dodgers.)

But there's a lot to take away from Chapman's deal. Not because of the dollars or the years, but because the Yankees already have one of the half-dozen best relievers in baseball. Clubs have always been happy to have two closer-quality relievers in their bullpen, but it's only until very recently that they've been willing to pay for it.

In the past 14 months, we've seen the Dodgers nearly trade for Chapman, despite having Jansen already; the Yankees trade for Chapman, despite having Betances and Miller already; the Red Sox trade for Kimbrel, despite having Uehara already; the Cubs trade for Chapman, despite having Rondon already; the Indians trade for Miller, despite having Allen already; and now the Yankees sign Chapman, for the biggest contract in history (sort of!), despite having Betances already. Chapman's primary value won't be protecting ninth-inning leads -- Betances would have done that -- but freeing Betances up to protect seventh-inning leads, eighth-inning leads, and maybe even copy Andrew Miller by protecting fifth- and sixth-inning leads. It takes two "closers" to try that.

This is probably the most useful thing about big-money closers that we can learn from GMs over the past year: Clubs aren't paying more for their closers, but rich clubs are paying more to have multiple "closers." Closers are not just about the ninth inning anymore, and they might not be for a long time.