Average Leverage Index of events

A few days ago I began looking at league average Win Probability Added and Leverage Index values on home runs with the intention of using that information for an upcoming article. After running those numbers for all event types, however, I found the the results interesting and thought I might instead share them with you this morning.

For those not familiar with these metrics, our Hardball Times glossary defines Win Probability Added (or WPA) as “the impact each specific play has on the team’s probability of winning” and Leverage Index (LI) as “a measure of how critical a specific batting situation is.”

In other words, the average WPA on singles of “0.04” tells us that a single moves the batter’s team four percent closer to victory– say from 52 to 56 percent. A home run moves that needle a whopping 13 percent on average, while a triple play puts the fielding team 16 percent closer to the win column.

For Leverage Index, the average scenario is scaled to equal 1.0 for our convenience. A figure greater than one implies that the situation was more critical than average, while a figure of 0.8 or 0.7 means the situation was not nearly as dire. Naturally then, early innings and blowouts are more prone to less critical situations, while late and close situations drive Leverage Index upwards.

In an effort to generate values as relevant as possible, the following (sortable) table uses data from this second “pitcher’s era” beginning in 2010 to a few months into the 2013 season. I’ve also limited the results to some of the more frequent outcomes. (WPA values are from the batter’s perspective.)

LI and WPA by event

Homestretch: The 1967 AL Pennant Race, Part 3
A tight race shows no signs of letting up.

Event PA Start LI
Ground out 121845 0.86 -0.02 0.74
ROE 4848 0.92 0.04 1.34
Fly out 121504 0.95 -0.02 0.79
K (looking) 29106 0.95 -0.02 0.79
2B 26794 0.96 0.07 1.17
HR 16021 0.96 0.13 0.51
1B 96152 0.99 0.04 1.36
Line out 10372 0.99 -0.03 0.79
3B 3001 0.99 0.10 1.12
BB 47468 1.00 0.03 1.59
K (swinging) 87380 1.01 -0.03 0.85
Fly out (foul) 11917 1.01 -0.03 0.85
HBP 5226 1.06 0.03 1.64
PKF/CS 3867 1.21 -0.04 0.77
SB 9746 1.23 0.02 1.37
Balk 574 1.34 0.03 1.23
Adv on WP 5259 1.36 0.03 1.31
FC 15145 1.45 -0.03 1.12
GiDP 12119 1.50 -0.07 0.74
Sac fly 4288 1.72 0.01 0.86
IBB 3892 1.75 0.01 2.37
Sac bunt 4938 1.79 -0.01 1.70
double steal 367 1.81 0.04 1.72
triple play 11 2.06 -0.16 1.23

Many of the event descriptions in the database are separated in ways one otherwise might not expect. For instance, inside-the-park-home runs are differentiated from regular home runs, while ground rule doubles are classified separately from standard two-baggers. For this reason some of the values above may appear slightly off. I’ve uploaded a google doc with all 51 event types here. (A few events with smaller samples may require a better description.)

One of the most obvious takeaways from this table is that events that require baserunners (GIDP, Sac Flys, stolen bases, etc.) naturally occur in higher leverage situations. While other events are clearly more leverage-nuetral. It is these discrepancies between the more leverage-neutral situations that are most interesting.

For instance, neither a single or a home run requires any base runners, but home runs more often occur in less critical situations, with a .96 average LI compared to those of singles at .99. That may seem like a small difference, but when you consider the size of the sample it is clear that the effect is real.

We know home run rates drop with runners on base, and that there are also slight trends that show both later innings and closer scores favor higher home run rates as well.

I imagine part of this is due to a bias—better pitchers are called on to pitch more often in high leverage scenarios. Hard-throwing lights-out closers and set-up men are brought in to replace the fatiguing starters in the eight and ninth innings, when the leverage is usually higher. Similarly, we see that there is a tendency for hitters to hit home runs more often in situations often considered “mop-up” duty, while the long ball is harder to come by in tie games and close contests.

One might suspect that part of this is because pitchers may be less likely to pitch in the zone in high leverage situations, which might explain why the effect holds true for doubles as well. Next to batted balls that clear the fence, batted balls that nearly clear the fence are typically hit with the most authority. Not all doubles meet this criteria, of course, as some speedsters may leg out a grounder into the gap or down the lines, but generally they are just as well-hit as home runs and as a consequence have a similar low average LI.

Batted ball types

Any theory of this sort of relationship between quality of contact and leverage may appear to fall flat when we look at the average LI on ground ball outs, fly ball outs, and line drive outs. We see that Line drive outs typically occur in the more critical situations (.99 LI), while we see remarkably more ground ball outs in far less critical situations (.86 LI). Of course, the database separates ‘generic’ ground outs from other events like ‘GIDP’ which require base runners and consequently a higher average LI.

So in order to get a more accurate idea of how leverage may impact batted balls, we need to look at all batted ball types, regardless of wheather they led to hits or outs. Then we see the relationship between quality of contact and leverage does not appear very strong:

LI and WPA by batted ball type

Fliner (Liner) 51124 0.971 0.03 1.13
Fliner (Fly) 53757 0.976 0.02 0.88
Fly ball 104605 0.977 0.00 0.79
Ground ball 197897 0.978 -0.01 0.93
Line drive 36033 0.980 0.02 1.16
Non-BIP 200672 1.044 -0.01 1.11
Bunt ground ball 9161 1.535 0.00 1.54
Bunt Fly 1124 1.568 -0.03 1.45

We see here that the “fliner-liner” has a higher average WPA than any other batted ball type, and it also boasts the lowest average LI. But not by very much. Not to mention that we also see “regular” line drives with a higher average LI than ground balls, which have the lowest WPA (for the batter) of any batted ball type other than a bunt.

I also found it interesting that we observe a lower leverage for hits on batted balls of all types than for non-hits with the exception of ground balls. That is, what stringers define as a “line drive” is more likely to result in an out in higher leverage situations. Is this the effect of better quality of contact in lower leverage situations? The line drive out is after all more often a weaker brand of line drive than the line drive hit. Or is it simply a matter of quality-of-pitcher bias?

For ground balls, however, we see the opposite is true. Presumably this is because higher leverage situations (at-bats with runners on base) tend to have infielders in less than optimal position while holding the runners. As a result, more ground balls sneak through into the outfield.

LI of batted balls, hits and non-hits

Batted ball PA hits LI hits PA non-hits LI non-hits Diff
Bunt grounder 1831 1.15 7330 1.63 -0.48
Bunt fly 127 1.16 997 1.62 -0.46
Fly ball 14020 0.96 90585 0.98 -0.02
Line drive 25168 0.97 10865 0.99 -0.02
Fliner (fly) 20032 0.97 33725 0.98 -0.01
Fliner (liner) 35230 0.97 15894 0.97 0.00
Ground ball 45947 0.99 151950 0.97 0.02


Another curiosity from the table that I was drawn to is the difference between strikeouts looking versus strikeouts swinging. Batters are much more likely to watch strike three with the bat on their shoulders when the situation is not so critical (.95). Conversely, it seems that hitters may be more willing to go down swinging when the situation is a bit more important (1.01 on average).

This agrees with some earlier investigation of batter’s swing rates outside the zone, where we found significantly more reckless swinging in bases loaded situations than in bases empty situations.

Unless of course we are seeing the effect of a bias here as well, one that I may not be immediately recognizing. Strikeout pitchers with higher whiff rates are certainly more likely to pitch in high leverage situations like late and close games, but I am not quite sure how much of that plays into this. (This difference in average LI holds true as we expand the sample back to 2000-2013 as well.)

Sacrifice bunts

It should be no surprise that bunting is used in some of the most critical game situations possible with an astounding average LI of 1.79 since 2010. But what I found really entertaining is that the sac bunt still has an average WPA of -.01, suggesting that the sac bunt (still) leads to a loss more often. Even in a post-Moneyball, post-Brad Pitt world, the sacrifice bunt is losing ball games.

I’ll admit I did expect to see an improvement over time in the usage of the sac bunt in terms of Win Probability, but even when you break it down by decade the results have been just about the same since 1974:

Sac bunts by decade

Decade PA Start LI WPA End LI
2010s 4960 1.79 -0.01 1.70
2000s 15174 1.72 -0.02 1.64
1990s 14691 1.78 -0.01 1.69
1980s 14400 1.83 -0.01 1.73
1970s* 10097 1.80 -0.01 1.68

Reached on error

This one really amuses me. The average Leverage Index for a plate appearance in which a batter reaches base on error is remarkably low (.92) compared to legitimate hits, including regluar old singles (.99). Is there any reason why errors should occur more often when the game state isn’t all that important? The natural inclination is to suggest that fielders become lackadaisical and less alert in blowouts and other non-critical scenarios, but is that the whole story?

Hit by Pitch

And one final point of intrigue deals with average leverage on hit by pitch. We see that both a walk and a hit by pitch are just as damaging to a teams Win Probability at -.03, but for some reason we see hit by pitches in much higher leverage situations. Bases on Balls are distributed throughout a game with a perfectly random 1.00 average LI, but the HBP jumps to 1.06 (the LI drops to 1.05 in the 2000-2012 sample, but still very noteworthy).

It may be tempting to suggest that nerves play a factor in a pitcher’s wildness, and therefore we see a slight increase in HBP in more critical situations. And I imagine it’s tempting to suggest nerves play a part in any of these events. But it’s premature to say so.

This really raises a number of questions for me that all deal with the general question of how does the game change when it matters more? And it is likely that this is just the first of several articles related to that inquiry. But I am very curious what you think of all this. Is there anything I may have missed? Or any oversights I may have made? As always, I appreciate your feedback.

*excludes 1970-1973

References & Resources
Thanks to Fangraphs, Retrosheet, Dave Studes, and Matt Hunter.

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Craig Tyle
Craig Tyle

I wonder if the ROE/single difference could be partially explained by official scorer tendencies – e.g., the scorer may be more likely to “reward” a batter who reaches base in a key situation.

James Gentile
James Gentile

Great point!

One thing I want to look into before we jump to conclusions on the ROE mystery. After re-examining the google doc this morning with the 51 event types, I noticed that one is labeled “FC w/ error.” Those events would require baserunners and a higher LI therefore, and is kept separate from the other ROE event. This may be causing some bias.

I’ll need to combine the fields and find the new average LI to be sure.

James Gentile
James Gentile

So while the field marked “FC w/Error” consists of only 985 PA, the average LI was a very significant 1.5.

When I added these 985 events (along with a 250 events marked ‘sacrifice w/ Errors’) to the “ROE” field, the combined average LI jumps to 1.05. This means that on average errors actually occur in slightly more important situations, not in less important situations as reported in the article.

I’ll most likely be following up on this correction with a post in a few days.

AJ Christopher
AJ Christopher
RE: more frequent HBP in high leverage situations?  My intuition points to a few factors that might explain the phenomenon. 1) pitchers with dominant stuff but poor control are more often used in relief than starting; 2) pitchers effective in high leverage situations take control of the inside corner (or try to) to keep hitters off balance; 3)some hitters in high leverage situations are looking to drive the outside pitch, but are crossed-up when the pitcher comes inside by surprise; and 4) some hitters know the value of a HBP in a high leverage situation and don’t avoid it.  I… Read more »
James Gentile
James Gentile

Interesting. Your theory has some potential:

From 2010-2012 relievers as a whole have hit 0.92% of batters they’ve faced, slightly more than starters at 0.79% (including post-season). I’ll definitely be following up on that.

As an aside, I’ve also broken down some of the reasons ROE have such a high LI in this article: