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Is This Sparta?

We've been hearing about the Mariner bullpen quite a lot this season. For a unit that was entirely comprised of question marks, it's held out particularly well, and is often cited as one of the prime reasons the Mariners have remained above .500 well into September. Perhaps no element of the team has defied expectations so much as the relief corps. With a week left in spring training, there was no closer. Late inning duties this year have been shared by a guy who was traded for a no-name last winter, someone who was a no-name last winter, a guy who's coming back from microfracture surgery in his pitching elbow, someone who isn't Tim Lincecum (he didn't last for very long), and Sean White, who is boring. Complementing the late inning boys was a random crop of AAA arms and Miguel Batista. One can only imagine how bullpen coach John Wetteland must have felt when presented with his men at the start of the year, but eventually he was able to turn them into a functional (albeit more than slightly insane) unit.

How? As the story goes, on an early-season road trip, Mark Lowe downloaded 300, which for those unfamiliar with it, is a ridiculously over-the-top movie about the Spartans at Battle of Thermopylae, which occurred during the second Persian invasion of Greece in late 480 BC (spoiler: they all die). He shared his enthusiasm for the film with Wetteland, and things snowballed from there. Members of the bullpen adopted characters from the movie, Spartan helmets popped up everywhere, and a grand ol' time was had by all. One wonders exactly how badly the relievers expected the team to do if they felt as though they identified best with a bunch of guys who all end up dead, but there's no denying it fueled an us-against-the-whole-damn-world mindset that the bullpen latched onto and used as inspiration to pitch their hearts out. The siege mentality was further reinforced when MLB officials decided to take their helmets away. Small wonder, then, that the bullpen has pitched their collective hearts out this year, keeping games just close enough for the struggling position players to scrape out more wins than losses.

This would be all well and good if the Mariner bullpen was actually as good as traditional numbers suggest. But they're not. They're not even average, despite all the one-run games and saves for David Aardsma. By using tRA-derived valuation statistics, they've been more than a quarter-century of runs below average, which turns out to be the worst mark in the American League. AL West rivals Oakland, on the other hand, are well over the +50 mark, which is a spread of almost seven and a half wins. By the numbers, they have answered the questions surrounding them in spring training, and the answer turns out to have been 'holy crap they're bad'. But this doesn't jive at all with their ability to keep them Mariners in business in close games. The team has won an absurd number of one run games, and generally has the ability to keep games close once the team turns over pitching duties to the bullpen. So what gives? Is the Mariner bullpen an above-average unit with an elite closer as the spearhead, or is David Aarsdma the equivalent of affixing a razor blade to a forty foot tall marshmallow and calling it a weapon? Or is the answer somewhere in between?

I hope it's the last option, because otherwise I've just spent a tonne of time collecting data for no good reason. Let's dig in.

Note: All data current as of 2:39 PM Sept 12th, 2009. Partial innings denoted as .3 for one out, .7 for two.

First, let's look at our cast of intrepid heroes and Denny Stark. Who's been leaned on the most? The quartet of Mark Lowe, Sean White, Miguel Batista, and David Aardsma have accounted for a little over half of the innings thrown by Mariner relievers this season, as shown in the chart below:

Figure 1: Innings pitched by Mariner relievers in 2009

Chris Jakubauskas and Shawn Kelley have also both seen significant time this year as well, and Kelley was thriving in a late-inning role until he suffered a rib injury in mid-May. Five arms have appeared in both the rotation and the bullpen, including Brandon Morrow, who began the season as the closer before a series of meltdowns got him demoted. Now that we have a pretty good idea of who's soaked up how many innings, let's take a look at their numbers in RA and tRA form:

Table 1: RA, tRA, rRAA, and pRAA for Mariner relievers in 2009

rRAA and pRAA are computed by taking the difference between league RA and tRA respectively and multiplying by innings pitched/9 for rRAA and expected innings/9 for pRAA, with Δ denoting the difference between rRAA and pRAA. As the column on the far right shows, Mariners pitchers have, by and large, far exceeded their expected value as far as defence/park-independent statistics are concerned. This is hardly a surprise, as the Mariners have the best defence in the game and play in a pitcher-friendly park. The biggest differences are in Sean White and David Aardsma's numbers, who between them 'should' be worth around 15 runs less than their actual numbers would suggest. Again, this isn't a surprise, as the pitchers likely to have the biggest negative difference between pRAA and rRAA are those who've been highly effective by ERA and associated metrics. The opposite should also hold true: the poor performers are likely to have been negatively impacted by their fielders.

In fact, the only relief pitchers who have a lower tRA than RA are Mark Lowe, Brandon Morrow, and Garrett Olson, and only Lowe has been part of the bullpen all season. The numbers are fairly remarkable - by using traditional numbers, the Mariner bullpen has been worth +6.4 runs total, and with pRAA, they've been at a rather alarming -25.9. Miguel Batista is particularly notable for having cost us almost ten runs over the course of the season, but he's had a couple of competitors for the suckiest bullpen arm award, with Jakubauskas and Stark (in ten innings somehow) pushing him all the way. Some (most) of the numbers in the table above has to have come from the defence, as Safeco Field isn't going to explain away the whole thing. But before we look at defensive contributions explicitly, I'd like to introduce the concept of leverage.

Most of you should be familiar with Jeff's lovely win expectancy charts, which appear after nearly every game. The idea of win expectancy is straightforward. For each game state (outs, score, runners, inning) we can figure out the likelihood of an average team beating another average team. Despite most teams not being completely average and entirely constituted of average players, win probability can be used as a measure of how important a given event was in terms of winning or losing baseball games. A walk-off home run? Worth a lot. A two-out walk with the bases loaded in the second when down by five? Not so much. In fact, for each game state, we know what the possible swings in win probability are. A team cannot possibly make a big impact in one at-bat when they're ten runs down, even if the batter hits a grand slam, but with the tying run at third with one out in the ninth, the situation can become critically important.

Table 2: 2009 AL relief leverage by
                team, descending

Leverage is a measurement of just how important those situations are. Fortunately, the good people at Fangraphs keep track of this number for both teams and individual players. Here we are concerned with the average leverage a pitcher sees, denoted as pLI (the average is 1.00). In general one might expect bullpens to see higher leverage situations than starting pitchers, but as Table 2 to the left shows, this is not the case for most of the American League, which have seven teams below 1.00 and 12 below 1.10. The standout teams are the Boston Red Sox and the Seattle Mariners, with the latter leading the major leagues in bullpen leverage (the Dodgers and Cubs are also both over 1.20 in average bullpen leverage).

There are a number of reasons why we might see such a disparity in the stressfulness of situations seen by a bullpen. One such reason might be that a team is poor enough that they are regularly losing by large enough amounts to make winning improbably: this might apply to the AL's basement teams: Oakland, Kansas City, and Baltimore. Or the opposite could be true and the team could routinely be so far ahead by the time the manager goes to a reliever that their innings simply aren't worth very much, which is the route taken by the New York Yankees and their absurdly powerful offence.

Conversely, a team which finds its bullpen highly stressed will be in contention to win many games, one that relies on excellent run prevention to keep things close. That would be the Mariners. Their bullpen leverage index of 1.23 means that the runs saved or given up by Mariner relievers are worth 132% of those saved or given up by their counterparts in New York.

The same concept applies to individual pitchers on the same team. By multiplying innings pitched by individual pLI, we can see the relative importance of the innings a pitcher has soaked up, as shown below:

Figure 2: IP*pLI for Mariner relievers in 2009

As we can see, David Aardsma springs into the lead once important innings are considered. The top four of Aardsma/Lowe/White/Batista are now responsible for almost two thirds of leveraged relief innings, and the team total has jumped by more than 100 innings (this is insane, by the way). Aardsma and Lowe are entirely responsible for the team's jump in innings total, with the former experiencing the equivalent of 76 extra innings' worth of stress and the latter a robust +38, due to pLIs of 2.21 and 1.55 respectively. Brandon Morrow's adventures in Minnesota and Texas see him grab more innings, and poor Doug Fister, who made his debut at the end of a blowout game, has his contribution marked as wholly irrelevant and thus discarded.

We need to account for leverage when we look at value metrics like pRAA, and again this is a simple case of multiplication. Numbers multiplied by pLI are denoted with an apostrophe:

Table 3: pLI and leveraged rRAA and pRAA for Mariner relievers in 2009

Aardsma's performance is particularly notable, but apart from the fantastic contribution from our closer, what really stands out is how poorly Miguel Batista has been used. His pLI was just a tick below average, and this season he's been running a tRA of almost six. While his contract demanded that he be on the roster somewhere, the damage he's caused could probably have been mitigated by relegating him to mop-up duty rather than deploying him in relatively close games. Denny Stark and Chris Jakubauskas both saw their negative contributions decreased due to their throwing in less stressful situations, which would have left Batista all alone at the bottom if not for the increased impact of The Adventures of Brandon Morrow. The chart does show you why the Mariner pen is held in high regard by those watching, though. The important innings have gone to White, Aardsma, and Lowe, and by and large they just haven't allowed runs, to the tune of 44 runs saved by rRAA. Let's look at an overall comparison between rRAA, pRAA, and the leveraged numbers:

Table 4: rRAA, pRAA, and leveraged values for Mariner relievers in 2009

As shown in the table above, leveraging the numbers results in an increase in both rRAA' and pRAA'. This should go as a feather in the cap of Don Wakamatsu, as it demonstrates his ability use his bullpen arms (sans Batista) effectively - the most important innings have gone to the most able pitchers. It's really no wonder that those watching games and following closely think that the team has a good bullpen. Naturally, we pay more attention when we're in with a shot at winning, and in those situations, the relief corps just doesn't give up runs. It's hard not to be confident in the later innings when your top arms are that good at shutting the opposition's bats. But again, how much of this is the responsibility of the pitcher? pRAA' agrees that the bullpen is generally far better when the game's on the line, but still has the unit as well below average, and almost three wins less valuable than it would appear when simply looking at runs, which is a similar result to what we saw earlier when looking at unleveraged values.

The defence, then, has to have some responsibility for the perception of the bullpen as an elite unit. How much defensive support has each pitcher received? Is defence clutch in any way (the most likely explanation for this would be sensible use of defensive replacements)? Although you could probably figure things out from the numbers above, we like our graphs around here - the chart below shows the defensive support given to each pitcher per tRA's xRR, which is simply expected runs minus actual runs with park effects accounted for. Both plain xRR and xRR multiplied by pLI are shown.

Figure 3: Defensive support (standard and leveraged) for Mariner relievers in 2009 (click image for full size).

Aardsma and White have been the primary beneficiaries of the defence this season, but it's hard to argue in favour of defensive clutchness: Morrow didn't get much support, and Lowe has been a little better than his traditional line too. In fact, summing leveraged xRR and subtracting plain xRR leaves you with one extra run, which is a little surprising considering the average pLI of 1.23. Overall, the defence hasn't cared who's pitching or what the score is - it's just gone out and made plays no matter the situation. Despite some of it being explained away with leveraged numbers, I have to conclude that the greater part of the difference between 'common knowledge' and a quick statistical peek at our pen's numbers is due to Franklin Gutierrez and company.

All in all, I think it's pretty clear that although the bullpen isn't as good as commonly believed, it hasn't been as bad as simply looking at unleveraged pRAA would suggest, simply because the guys relied on when the games are on the line have been much better than those in mopup duty (surprise!). However, the bullpen has still been below average, and without the safety blanket of the best defence in the game to make them look good, we'd hear less about resilience and esprit de corps and more about fatigue and the need for mechanical tweaks.

If this is Sparta, it's been more Sellasia than Thermopylae.