I'm still banging the "bullpen needs a veteran drum" and when looking for experience, the first marker (after age?) is leverage. There's an easy way and hard way of looking into that, and both methods have Tommy Hunter in the mix.
The easy way is to just look at saves or holds. Among the free agent relief pitchers available on the open market, only four are credited with five or more saves to their name in the last two seasons:
Greg Holland - 78
Joe Nathan - 36
Casey Janssen - 25
Tommy Hunter - 12
Hunter as had seven holds credited last season, and 40 holds over the last three years.
The more nuanced approach would be to literally look at the leverage pitched among all remaining free agent relievers, something not very difficult to do if you know where to look.
FanGraphs has a section for "Win Probability" which includes leverage as a measurable statistic, dividing situations into high, medium, and low. And in an even more handy fashion, we can look at relievers who did not finish games, which most of the remaining free agents did not.
Here's how leverage is measured statistically as an "index" (LI): 1.00 is an average leverage situation, 0.85 below average, and 2.00 above average. You can identify how well middle relievers helped the game by comparing their starting average leverage (gmLI) to the leverage when they were lifted by the manager (exLI).
According to that use of leverage index, among free agents, only Joe Beimel, Tommy Hunter, Randy Choate, and Manny Parra were lifted from games by the manager with the leverage in a lower place than when they entered, while also adding to the team's overall win probability (WPA>0).
Among those four players, you get the following stats for 2015:
|Tommy Hunter||- - -||28||60.1||61.7%||96.2||71.0%||.261||4.18||3.83|
As you filter for other aspects, not too much jumps off the page as to say which might be the best choice.
Hunter's mix of pitches seems a bit more valuable over all, but he didn't stand out as having significantly better results last season thank the remaining free agents. It's possible that is related to injury, Hunter needed abdominal surgery this winter, and that has been the primary cause for his free agency.
Overall, Hunter strikes me as a fun pitcher with a lively fastball, and given his experience, that may be enough.
You could get lost on Fangraphs for a while, but the statistics there do not lend them selves well toward identifying experience. Among free agents, Randy Choate has had one of the longest careers, but his Win Probability Added and Leverage Index measures all rank in small doses.
It may be best to abandon the free agent pool and look toward the trade market, and I'll turn to that next, but this at least adds credence to the Tommy Hunter idea.