Dialing back the Leverage Index

We're living in an age of baseball analysis where new measures and ways of looking at the numbers of the game seem to reveal fresh insights as to how the game should be played. In some cases, though, we should really take a closer look at how we're interpreting that new knowledge, because it's not always as impressive as we think it is

Case in point, the 'leverage index'.

The 'leverage index' is a way to calculate the value of innings pitched based on the likelihood of victory resulting from success in those innings. It's largely been used as a way of justifying the large salaries that closers get, because closers pitch in the highest leverage situations of all -- late innings, small leads. If the club gives up the lead in that situation, they'll have little to no opportunity to get it back, and thus having a solid closer is seen as a requirement for any team that wants to compete, let alone contend.

By itself, I have no problem with that conclusion. The problem I have comes when people move from that conclusion to others, without putting enough thought into the implications of what their new conclusions are. Case in point (and it pains me to call out the Geek on this one) was a Twitter sent out by John Bonnes about a week ago:

"Awesome. I've said it before, I'll say it again - we're wrong about the value of IPs. Dominant late-inning RPs are as valuable as most SPs."

I understand the motivation behind the comment -- he'd just finished watching a game in which the Twins, trailing the Orioles heading into the bottom of the 6th, rallied to tie, then held on until they pushed across the game-winner in the bottom of the ninth. Obvious, right? The guys who pitched the 7th through the 9th were the MVPs of the game.

Sure. I'll give you that one. Sadly, though, that's just one game, and it takes far more than one game to win a pennant. If you're going to talk 'value', then you have to be talking about the ability to win more than just one game.

Let's take a gander at some example of what I'm talking about, using a tool that we should all know about, but probably don't -- the team scoring summary at

The KC Royals in 2003 put together an impressive spring and tenacious summer, had a share of the division lead as late as August 29, and hung in the pennant race until mid-September. Here's some numbers for you to consider:

When leading after 1: 32-14 (.696)
When leading after 6: 72-12 (.857)
When leading after 8: 75-6 (.926)

Of the 83 games the Royals won in 2003, 72 of them were games in which the Royals were leading after 6. Now the Royals had solid if unspectacular seasons from closer Mike McDougal and setup-man Jeremy Affeldt in 2003, but the rest of their bullpen could hardly be described as 'dominant'; D.J. Carrasco, Jason Grimsley, Kris Wilson, and Sean Lowe were all guys with average-to-below average ERAs and sub-par WHIP values. The best relievers in the pen, Curt Leskanic and Alan Levine, were both mid-season pickups, and worked while the Royals as a club fell from leading the division to struggling to stay in it, to finally falling out of it; in other words, Leskanic and Levine don't get credit for the Royals's good start, and oddly, despite supposedly replacing inferior relievers, didn't seem to have much of an impact during the disappointing finish. Is that value?

Now let's compare that Royal club to another, less successful Royal club:

When leading after 1: 17-18 (.486)
When leading after 6: 48-17 (.738)
When leading after 8: 52-7 (.881)

This is the 2006 Royal club that lost 100 games, with no appreciable strength anywhere in the pitching staff. The club was over 200 points worse in winning percentage when leading after 1, largely because they had just about nobody on the club who could help hold a lead. But when leading after 6, they were less than 120 points worse than the '03 club, and when leading after 8, were a mere 45 points worse. And 'less than 120 points' and '45 points' overstates the case, because the '06 Royals lost only one more game when leading after 8 than the '03 Royals did, and just five more when leading after 6, despite losing more than thirty more overall.

Could five games make a difference in a pennant chase? Sure, for a team that isn't on track to lose 100 games already. But can a team even in the fringes of a pennant race lose that many more (or fewer) games in that situation to make a difference? Let's shift gears and look at a team with the same overall record as the '03 Royals -- the 2005 Twins:

When leading after 1: 22-7 (.759)
When leading after 6: 55-8 (.873)
When leading after 8: 62-1 (.984)

The 2005 Twins clearly had a far superior bullpen to the 2003 Royals; Joe Nathan was among the top closers in the league, and the only other relievers on the entire staff with above league-average ERAs were guys who pitched less than 10 innings, plus Francisco Liriano. And you can see the difference in the record after eight -- the Twins lost just one game where they went into the ninth with a lead all year, five better than the 2003 Royals.

But take another look at that record after six: at first glance, you might think that the Twins were four games better than the Royals in this mark as well, but you'd be missing an important point -- if the Twins lost eight games when leading after 6, then they have to have given up that lead in the 7th, 8th, or 9th. We've established that the Twins gave up only one lead that cost them a win in the 9th all season, which leaves 7 games that the Twins lost in some other late inning. Compare that to the 2003 Royals -- which by that reckoning only had 6 games in which they lost a top-of-7th lead in some inning other than the 9th. The Twins may have had a better bullpen statistically, but you wouldn't have been able to tell from the won-lost record.

Last but not least, the baseball-reference report lets you aggregate all teams in baseball into a single massive set of numbers, which shows something interesting: if you believe in Win Probability Added, then it's clear which inning of the game is the most important to have a lead in:

When leading after 1: (2008) 815-376 (.684); (2007) 859-395 (.685); (2006) 837-401 (.676)
When leading after 6: (2008) 1827-306 (.857); (2007) 1865-300 (.861); (2006) 1840-308 (.857)
When leading after 8: (2008) 2087-91 (.958); (2007) 2108-102 (.954); (2006) 2100-118 (.947)

In fact, if you look at a number of seasons and aggregate them, looking for the relative points where they line up, you can see that the following progression of winning percentage holds remarkably steady for about as far back as you care to look:

Start of game: .500
Leading after 1: +.180 (total .680)
Leading after 2: +.035
Leading after 3: +.035
Leading after 4: +.035
Leading after 5: +.035
Leading after 6: +.040 (total .860)
Leading after 7: +.040
Leading after 8: +.050
Leading after 9: +.050 (total 1.000)

The first inning is clearly the most important inning to have a lead after, by far. After that, the 8th and 9th innings are slightly more important than the rest, and there's no real difference between the 7th and the 2nd as far as value toward winning a game is concerned.

So if you're asking the question, 'is it better to have a starter or reliever on in the 7th', I'd argue that, if each pitcher is likely to be equally effective, there's no difference -- there's likely a small advantage toward leaving in the starter in this case, since you're not turning to arguably your 8th best pitcher to get to your setup man.

If on the other hand, you're asking 'is it better to have a gassed starter or a fresh reliever in the 7th', then clearly it's better to have the reliever in the game, but that has nothing to do with the relative value of a starter's innings versus a 'dominant' reliever's innings, and everything to do with having an effective pitcher in the game when he's needed.

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