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In any given era, only a few elite relievers can be counted on to number among the top players at the position with any regularity.Another way of looking at the low reliability of relievers also offers a potential solution to the problem of building a bullpen.At that rate, it can take several seasons to ascertain anything meaningful about a reliever’s performance.Most relievers retire before we can draw any conclusions about their ability to suppress hits on balls in play.However, focusing on strikeout rate is often the best way to identify an effective reliever early on, since an ability to miss bats is both the easiest attribute to discern and the surest route to a pitcher’s success.As is the case with most teams, the most expensive member of the San Diego bullpen was the closer, Heath Bell, who made $4 million.At the time of the exchange, Bell’s sole major league experience was contained within 108 innings distributed over three seasons with the Mets.Louis to complete a prior trade.Lefty specialist Joe Thatcher was another astute trade target, stolen from the Brewers in a trade that sent Scott Linebrink, a formerly elite reliever whose best days were already behind him, to Milwaukee.Tim Stauffer was a 2003 Padres draftee who was taking a temporary break between assignments in the starting rotation, and Ernesto Frieri was signed as an amateur free agent the same year.Once they had excavated these diamonds in the rough, the Padres also showed a willingness to deal them for more dependable properties before they’d passed their expiration dates, rather than become victims of the belief that bullpen performance is eternal.Mujica and Webb were shipped to the Marlins over the winter for former top outfield prospect Cameron Maybin, who had had trouble making contact in Florida but was worth nearly four wins to San Diego in his first season with the team.Stauffer successfully transitioned back to the rotation, and Thatcher lost most of his season to shoulder surgery.The Padres’ pattern wasn’t exclusive to San Diego.The first kiss is magic, the second is intimate, the third is routine.It was a hell of an idea, and I was the lucky recipient, says The Eck.Starting was getting to be difficult.But just pitching one inning, my fastball came back.I was throwing like I was 25 again.One inning suited me very well.I never would have lasted if I had to pitch two or three innings all the time.Plus, I would have had my head knocked off.The results were bewitching.Like a virus, the fever spread, the limited role designed for Eckersley evolving to include other pitchers.Someone might yell at you.Yet, even had the Yankees given up a run in that eighth inning, the game wouldn’t truly have been in jeopardy, it just would have been in jeopardy according to the saves rule, which is a different matter.The manager of the Yankees does not dictate when to use Mariano Rivera, but the arbitrarily defined save situation does.He is powerless before it.Even had he deemed it wiser to skip Rivera that day so that he might be available for some future clash with the Red Sox, he would have had to use him.How did we end up where we are now?And is it truly benefiting the game of baseball?Relief pitchers were so rare in the early days of baseball that it didn’t occur to those keeping the records to track pitchers’ performance both as starters and relievers.We can, however, estimate the split of a pitcher’s playing time in each role, which gives us a useful starting point for analysis.While the historical record is unclear for individual pitchers, it is relatively simple to estimate the number of innings pitched by all starters for a season, as well as the number of relief appearances per game.It is not until about 1908 that we see a decline, settling at 90 percent for a few years and then drifting almost inexorably downward, so that in the modern game less than 70 percent of all innings are thrown by starting pitchers.The arrow of correlation is counterintuitive in that it suggests the more runs scored per game, the more innings thrown by starting pitchers.At the very least this causes us to reconsider the commonly held belief that pitchers don’t throw as deep into games because they have to face tougher lineups than pitchers of old used to.What accounts for the change in pitcher usage?What this suggests is that pitching has gotten harder over the years because more and more of the burden has shifted to the pitcher alone, with less and less reliance on the defense.This has created an increased need for relief pitchers.It took some time, however, for this to lead to the rise of dedicated relief specialists.Using pitchers as relief pitchers seems to start in the 1890s, and by 1910 or so teams relied on pitchers nearly exclusively for relief pitching appearances.This began to change around 1936, when teams began a gradual transition toward pitchers who specialize in relief.And you’re going to try and use your better pitchers in tight games at the expense of your lesser pitchers.This is where we see the first manifestations of what we’d now call a closer, but which at the time were often called firemen, relief pitchers who are supposed to come in with the game on the line and finish it off.If we define a team’s closer as the pitcher with the most saves for his team that year, we can look for historical trends in closer usage.From 1920 through to 1960, the percentage of games where a closer makes an appearance rises dramatically from 8 percent to 33 percent.After, we see a much subtler rise up to an average of 38 percent for the past decade.But right around 1988 we see a dramatic change in how many innings a team’s relief ace pitches each appearance.We see the same late 1980s, early ’90s inflection point for the dramatic change in closer utilization.Pitchers who average at least an inning and a half of work per outing have gone from representing between 40 and 60 percent of innings pitched to representing less than 10 percent.In terms of impact on the game, the creation of the modern closer by La Russa seems as influential as Babe Ruth’s home run prowess ending the primacy of the bunt and stolen base.Having identified where the change began, it falls to us to assess if the change itself has been a positive development.After all, there is no strategy out there that has allowed managers to get their best hitters to face the other team’s closer a disproportionate amount of the time.To find this evidence, let’s focus on situations resembling the archetypal save, with one team leading by one to three runs at the start of the ninth inning or later.There is a slight countervailing impact from increased run scoring, but with a correlation of just –0.28 between runs per game and these win rates, such an effect shouldn’t be expected to significantly alter these conclusions.In an additional bit of irony, the rise of pitchers designed to pitch in these sorts of situations has coincided with a decline in these sorts of chances.The primary driver seems to be the rise in offense, not the change in pitcher usage.That decline in possible save chances, at the least, provides a countervailing effect to the ability of ace relievers to come in and close a game.For the moment, let’s define a close game as one where the fielding team leads by two or less, is tied, or trails by one run.From 1988 through 2011, at the point when the closer first enters the game, he finds himself in a close game only 59 percent of the time.This is because managers have to find work for their team’s supposedly most valuable reliever, and thus must resort to putting him into a game that’s essentially already decided just so he can get his innings in.Would he send chills up our spine when he delivered his first pitch?The cold, raw numbers feel inadequate to explain how it feels to watch a dominant closer.Get your head out of your spreadsheets and watch a ballgame sometime. Yet, as it turns out, spreadsheets are in fact capable of recognizing the heightened excitement that occurs when a closer enters the game.Here’s the basic idea.An average team, at any point in a game, has a certain likelihood of winning the game.For instance, if you’re leading by two runs in the ninth inning, your chances of winning the game are much greater than if you’re leading by three runs in the first inning.With each change in the score, inning, number of outs, base situation or even pitch, there is a change in the average team’s probability of winning the game.Bottom of the ninth, score tied, runner on first, no one out.Let’s say the batter bunts the runner to second.Once again, the concept is simple.Let’s say our batter in the bottom of the ninth hits a single to put runners on first and third with no outs.This increases the Win Probability from 71% to 87%, for a gain of 16%.And the player with the most points will have contributed the most to his team’s win.Related to win expectancy is the concept of leverage, which is simply a measure of the possible change in win expectancy given the context.For our purposes, we will fix the leverage index of each event at one, so that a situation with a leverage index of two would have twice the average change in win expectancy compared to the average plate appearance.Examining all events from 1950 through 2011, we find the average plate appearance in the ninth inning and later has a leverage index of 1.33, compared to .96 for the first eight innings.The Pythagorean model doesn’t care about the order of events.How can we tell if the leverage model of pitcher evaluation is better than our Pythagorean model?What we can do is come up with a prediction based upon the ideas behind the leverage model, and test them at the team level.One thing we find, if we do a little digging, is that relief pitchers tend to pitch in slightly higher leverage spots than starting pitchers.Extra innings have even more leverage.If true, this suggests that we could beat the Pythagorean theorem at estimating team wins by putting a greater emphasis on a team’s pitching performance in the ninth inning.We can use these two variables to predict both a team’s Pythagorean and actual win percentages.We can then compare them to see how close the two models are, and if the Pythagorean method is underweighting a team’s pitching performance in the ninth inning.What the win expectancy model is truly capturing is not how much a play contributes to team wins, but how well an event predicts the outcome of the game itself.There is, of course, going to be some substantial overlap between the two, as things that lead to wins also tend to be good predictors of wins.A blown save is tremendously upsetting emotionally, because it takes what was very nearly a sure win and turns it into a sure loss.But what it does not capture nearly as well is the fact that, indeed, the closer enters the game when it is already very nearly a sure win.In order for his team to win, all he has to do is pitch one scoreless inning.However, in reality all that matters is the final score.Win expectancy may tell a better story than the Pythagorean analysis, but it tells us less about the relative contributions of closers versus starting pitchers to team wins and losses.