We don’t need numbers to know that Mariano Rivera is in a class by himself. We see it every season, every month, every game, every save. We see it as that cutter darts in and out to hitters, as another bat shatters, as another game ends at the hands of the Sandman. But, hey, the numbers look pretty amazing by themselves.

This morning on Twitter, a few baseball analysts found themselves tossing out some Mariano Rivera numbers, and since more people will read this article in the next hour than will see most of those Twitter posts, let’s delve in. Colin Wyers of The Hardball Times started things off with a note on relievers. Over the last 15 seasons, the average pitcher would, he said, “typically convert 70% of 1-run saves, 86% of 2-run saves and 94% of 3-run saves.” Overall, based on the frequency of each type of save, Wyers found that an average pitcher saves 82 percent of all games.

Cork Gains from Rays Index jumped into the fray as well. His number is simply awe-inspiring. Rivera has converted all nine of the save situations in which he enters the game with the tying run on base. The average closer converts in that situation 55 percent; the average reliever escapes with the lead just 22 percent of the time.

On the one hand, these numbers underscore how many overvalue relievers. If an average pitcher can save 94 percent of all three-run games, what is the incremental win value of adding a pitcher who can save 96 percent? 98 percent? Unless that pitcher is the best of the best when it comes to closing, a team will be paying far too much for far too little.

Sky Kalkman, an unabashed Mariano Rivera lover, picked on this thread. Since inheriting the closer role in 1997, Rivera has averaged 40 saves and 4.5 blown saves. The average reliever over that span would have 36.5 saves and eight blown saves. Over the last five seasons, Mo has been even better, averaging 38 saves and just 2.8 blown saves. The average reliever would have 33.5 saves and around seven or eight blown games.

In terms of wins, Kalkman estimates Mariano’s numbers at 3.25 wins above average and around 4.25 wins above replacement over the last half decade. He knocks that down a tad based on the belief that the Yanks would win some of those games blown by the average reliever. At Baseball Projection, Sean Smith offers up a similar take. Mariano Rivera’s career WAR is 49.9, and his average WAR over the last five years is 3.36.

So where does that leave Rivera? On Smith’s all-time pitcher WAR list, Mo is 76th overall with only a bunch of Hall of Fame starters in front of him. Other than Dennis Eckersley, a hybrid starter/reliever, Rivera is the highest ranked relief-only pitcher on the list. He truly is in a class by himself.

In a way, as I said before, we know all of this because we see it. But in another way, it helps underscore why Yankee fans are so obsessed with The Eighth Inning. At some point, Mariano Rivera will retire. He turned 40 a month ago and won’t be able to keep this up forever. Then, the Yankees will began the long process of replacing an all-time great. Maybe that responsibility will fall on the shoulders of Joba Chamberlain or Phil Hughes. Maybe it will fall on some other young stud pitcher asked to don the mantle of Mariano. It will not be easy, and we shouldn’t expect greatness from Rivera’s heir.

In the end, I’m going to do what I always do. I’m going to sit back, watch and love Mariano Rivera for what he brings to the table every day. His greatness as a one-pitch, three-out pitcher who just gets the job done may never be surpassed, and we shouldn’t expect it from the next Yankee closer whoever that might be and whenever he inherits the job.

The following is a guest post by Rebecca Glass of This Purist Bleeds Pinstripes. You can read her (slightly longer) versions on her site, in four parts: Part 1, Part 2, Part 3, and Part 4. We’re republishing it here because a) it took a lot of work and b) it’s really meant to be read as one article, anyway.

Special acknowledgment: This is far and away the most advanced, in depth thing I’ve ever tried. Without question, the best similarity I can come up with is asking someone who’s taken only high school Economics course to run the IMF, that’s basically what’s happened. As with any such endeavor, most of the actual work was done by others. With thanks to Jonathan Mayo, Will Moller, Joe Pawlikowski, Mike Axisa, Jim Johnson, Jamal Granger, Dave Cameron, Brent Nycz, Joshua Rosenberg, Dan Dilworth and Greg Fertel.

In this article, Rob Neyer dares us to come up with a way to measure how many Championships Mariano has been worth. Guess who enjoys masochism?

So, as you may know, there’s a myriad of stats out there, many of which I can only understand in theory, but there’s one measure that’s been created for the regular season that is very useful. You may have heard of it, as it’s called WAR — wins above replacement player.

NOTE: There are two measures we could use here, WAR and WARP, which try to accomplish the same thing (discussed below), but use two different sets of stats/data to do so. I’m going to stick with WAR because I think it sounds cooler. ANYWAY. So to understand WAR, two concepts are crucial: replacement level and leverage. I understand that many of you reading this will already be familiar with both of these, but since my hope is that those that don’t delve into stats very often can follow, and for the sake of my sanity, hope you won’t begrudge me a refresher.

Replacement Level
The idea behind replacement level is that you take any player in any line up on any given day and replace him with someone whose level of performance is what an average team can expect when trying to replace a player at minimal cost. In English, it’s saying that if, say, Andrew McCutchen went down on the Pirates with the flu, what’s the baseline production that the Pirates could expect from John Doe, who’s the cheapest available player to fill the spot? That production is replacement-level production.

Why not just use a league-average performance as a replacement? The answer is that the MLB statistics are largely skewed — MLB “regulars,” the guys putting up the big enough numbers to stay in lineups every day are a minority — while fringe players, those that struggle to stay in the big leagues, are much more common. Simply put, it’s easier to find a player that hits .250 than one that hits .330, but, like that student you wanted to kill because he got an A on that Spanish test while no one else did above a C, the one that hits .330 destroys the curve.

So, instead, you take into consideration what a GM and manager is likely to go for in the event of a player suddenly going down for a game or two–i.e., your utility infielder. Most teams–and the Yankees, of course, are not most teams–will go for whatever option is least costly–dipping into the pool of fringe Major Leaguers, the pool considered “freely available talent.” Of course, if a player is lost for a season, it’s an entirely different thing, but that gets beyond our scope.

What you end up with is on one end, you have your normal team–say the 2009 Yankees, and on the other, replacement-level team you’ve a line up where Wil Nieves is your best hitter, or Sidney Ponson as your best pitcher. What WAR does, then, is like having Nick Swisher go up to Joe Girardi before game six, and say, “Dude, I gave the Yanks, like x number more wins this season than you would have if Jerry Hairston had been your every day right fielder.”

(Note: via fangraphs, Hairston’s 2009 registered a WAR of 1.0, which indicates he performed above replacement level. Actually, this is helpful to give you an idea of how poorly a team with all replacement-level players would perform over the course of a season. Replacement Level is not the bench guys on the Yankees; it’s the bench guys on the Nationals and the Pirates.)

So before we move on, let’s make sure we understand everything that’s been discussed:

1. The concept of Replacement Level enables us to compare performances of MLB “regulars” vs low-cost, “freely-available” replacement players.
2. WAR is designed to measure how many more wins player X will net his team over player Replacement Level (i.e., our Swisher/Hairston faux metaphor).
3. The values set for what a replacement level-performance entails varies by position — i.e., shortstops aren’t supposed to hit like right fielders, etc. Pitchers, too, have WAR. Over here you can see the rankings for pitchers, by WAR, for the 2009 season. To no one’s surprise, Zack Grienke tops the list. The type of season he had will do that to you.

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This is a nerdy subject, so I’ll keep it short and link-heavy. With pitch data freely available, we’re going to start seeing Game Theory used to analyze pitcher-batter matchups. Tommy at Beyond the Box Score touched on this earlier this week, and it’s a good read on pitch type game theory. Today at The Baseball Analysts, Dave Allen looks at Mariano Rivera’s pitch sequences. But, because Marino throws only one pitch, this sequencing deals with location rather than pitch type. An amazing non-game-theory note: Mo is insanely good when throwing to his glove side. Many pitchers have trouble controlling pitches on that side. Allen goes on to show how Mo fares when throwing inside to a lefty after an outside pitch, inside to a righty after an inside pitch, and so on.

As we know, Mo dominates lefties. He’s not quite as good against righties, and he’s particularly bad when going inside after an outside pitch — and is also not quite as good when going inside-outside. Tom Tango runs with that. In most cases with Game Theory, he says, we need to take the batter into consideration, because each batter has different strengths and weaknesses. With the outside-inside sequence, though, the difference is too pronounced to chalk it up to poor choices to certain batters. Mo throws this sequence 37 percent of the time (as in, throws an outside pitch 37 percent of the time after he throws an inside pitch). He would do well to cut down on that. Mo fares best against righties when going with the outside-outside sequence.

Just how long can you continue to throw righties outside cutters? I’m not sure. This is where longer pitch sequences would be helpful. For instance, if Mo goes outside-outside-inside, does he fare well? Or is that the sequence that hurts him the most? After all, he went inside after an outside pitch, which for him produces the worst result. But just prior to that he went outside after an outside. This also raises the issue of whether these sequences cover multiple batters. In other words, if Mo strikes out a righty with an inside cutter and opens the next righty with an outside one, is that counted as an inside-outside combination? Or are the sequences limited to single plate appearances? I would think you’d produce a bit of noise if you overlapped batters. Better to stick to single-batter sequences for these analyses.

This is the type of analysis that gets me excited. Even non-stat-heads can enjoy pitch sequencing and Game Theory. It’s an attempt to break down the most fundamental game in baseball, that between the pitcher and batter. Analysis doesn’t get any better than that.