Is Papelbon worth $15M a year?

How much is too much when it comes to relief pitchers? With Jonathan Papelbon set to test the free-agent market, that question becomes central to the offseason plans of the Boston Red Sox.

It was easy to envision 2011 as Papelbon's final season in Boston given his apparent regression and Daniel Bard's emergence. However, Papelbon allayed fears of his decline, posting the second-best strikeout-to-walk ratio of his career. He reestablished himself as a dominant late-inning presence, while Bard faltered late in the season.

Now, the Red Sox must decide if they can afford to let Papelbon go -- or how much they can afford to pay him.

On Wednesday, while appearing on WEEI, Peter Gammons speculated that a three-year, $45 million contract would get the job done. At $15 million per year, that would match Mariano Rivera for the highest annual value ever for a closer.

Assuming Papelbon's customary season of about 65 innings, he'd earn $1 million for every 4 1/3 innings pitched. Of course, not all of those innings are high-leverage chances. Only 34 of Papelbon's 63 appearances were save opportunities.

History tells us that giving big contracts to relievers can be dangerous. Contracts for Brad Lidge, Francisco Rodriguez and Joe Nathan, three of the biggest contracts ever given to a reliever, expired after the 2011, and each missed significant time over the course of their deals. The Toronto Blue Jays gave B.J. Ryan $47 million for only 75 saves.

Great relievers are separated from the pack by their ability to repeat excellence. In the six years Papelbon has been Boston's closer, he is one of 49 pitchers to notch 30 or more saves in a season (doing so each year). That list includes the likes of Jeremy Accardo, Chris Ray and David Weathers.

There have been only four longer 30-save streaks in MLB history: Robb Nen (seven), Troy Percival (seven), Trevor Hoffman (eight) and Mariano Rivera (nine). In other words, while a 30-save season isn't hard to come by, consistency at closer is. One of Papelbon's key selling points is his reliability.

The same could have been said for Nathan and Rodriguez when they hit the market. In hindsight, the Twins and Mets surely regret those deals.

Depending on a potential David Ortiz deal, Papelbon would likely be the fifth-highest-paid player on the Red Sox in 2012 (he was seventh in 2011). Of course, even at $15 million, Papelbon would represent just 9 percent of a potential $165 million payroll. That would be the equivalent of a median-payroll team such as the Seattle Mariners spending about $7.8 million on a closer.

Boston's deep pockets allow it to splurge at closer or designated hitter. But would the Red Sox be better off devoting that money to the beleaguered rotation?

Alternatives abound in a deep free-agent market for closers. Papelbon headlines a group that also includes Rodriguez, Heath Bell, Ryan Madson and Francisco Cordero.

Bard has been deemed a closer-in-waiting based on his strong body of work as a setup man. He faltered in September (0-4, 10.64 ERA), but has otherwise been a model of consistency. Over the past two seasons, opponents have a .259 on-base percentage against Bard. Among those to have faced 500 batters, only Mike Adams (.238) has done a better job of keeping opponents off the bases.

Promoting Bard to closer would be the most likely alternative to re-signing Papelbon. Also on the market are several former closers, including Lidge, Nathan, Jonathan Broxton, Matt Capps and Frank Francisco. Each would come at a fraction of Papelbon's cost, while providing insurance in front of Bard.

Given the wealth of alternatives, how much should the Red Sox be willing to invest in Papelbon?

Ultimately, that may come down to how you value relief pitchers.

Papelbon's 3.0 WAR (wins above replacement) was the second highest among relievers behind only Craig Kimbrel (3.2). FanGraphs.com estimates that a 3.0 WAR translates to $13.6 million on the free-agent market. That helps justify a potential Papelbon salary, but it also matches the highest WAR of his career. FanGraphs measures Papelbon's 1.2 WAR in 2010 at just $4.8 million.

In general, WAR makes it tough to justify huge salaries for relievers. Papelbon's 3.0 WAR would have ranked 47th among starters, just ahead of Carl Pavano (9-13, 4.30 ERA). Is it more valuable to have a good pitcher for 180 innings or a very good one for 60? WAR says take the innings.

Yet, there's good reason to discount WAR as a tool for comparing starters and relievers. Consider that John Lackey had the fifth-highest WAR among Red Sox pitchers despite a 6.41 ERA. In 46 fewer innings, Alfredo Aceves had a 2.61 ERA but a WAR of just 1.0. It's nearly impossible to make a case for Lackey being the more valuable of the two.

One of the failings of WAR is that it ignores context. For position players, a large sample size generally evens that out. However, overlooking context shortchanges closers for their ability to pitch in high-pressure situations.

Win probability added (WPA) aims to address the significance of context. It measures a player's impact on win expectancy on a play-by-play basis. In other words, WPA shows how much a player impacted his team's chance to win. Not meant as a predictive statistic, WPA measures what happened rather than what will happen.

WPA argues that Boston's three most valuable pitchers last season were Josh Beckett (3.89), Papelbon (3.53) and Aceves (2.24). By this measure, Papelbon was the seventh most impactful reliever in the majors. Meanwhile, Lackey (minus-2.04) and Tim Wakefield (minus-2.56) had the lowest WPA on the team. That seems to pass the unscientific sniff test.

In his six years as Boston's closer, Papelbon accounted for a 20.7 WPA. Among pitchers in that span, that's topped only by Roy Halladay (22.1) and CC Sabathia (21.2). Not bad company, and an excellent indication of just how important Papelbon has been to the Red Sox. His dominance in high-pressure ninth-inning situations makes up for fewer total innings.

If WAR favors starters, WPA undervalues them because they tend to pitch earlier in games. That's why it's best used to compare relievers with other relievers.

WPA provides far more insight into a reliever's impact than saves or holds. Though one would assume closers would run away with the category, it's interesting to note that Tyler Clippard, Jonny Venters and David Robertson were three of the four most valuable relievers based on WPA. In 2010, those three weren't on the radar when discussing the top relievers in the game. That underscores just how unpredictable relievers can be.

Papelbon and Mariano Rivera are the rare exception to this, as WPA helps confirm. Since 2006, they have accumulated a higher WPA than any other relievers by a wide margin. While both are over 20.0, the next best reliever is Joe Nathan at 15.7.

Saves can easily overrate a reliever, as Lidge proved in 2009. Despite a 7.21 ERA, he picked up 31 saves. According to WPA, that was actually the most detrimental season for a pitcher over the past 30 years.

Saves are clearly an overrated statistic and do not translate to effectiveness. That said, the backlash against saves might actually make Papelbon undervalued.

Since 2006, Papelbon has 219 saves, while Francisco Cordero has 216. In that span, Papelbon has the highest WPA for a reliever, while Cordero ranks 22nd. In other words, Papelbon is as good as his saves indicate. Cordero simply isn't.

Can a relief pitcher really be worth $15 million? Probably not, but sometimes you have to pay extra for elite talent. Among relievers, that's just what Papelbon is.

Jeremy Lundblad is a senior researcher with ESPN Stats & Information. He provides statistical analysis for ESPNBoston.com.