THE BOOK--Playing The Percentages In Baseball

You can even expand this to include the event.  For example, let’s look at the HR and walk:

boLI hrLI bbLI 1B 2B 3B Outs
0.87 0.72 1.27 __ __ __ 0
0.58 0.72 0.90 __ __ __ 1
0.39 0.72 0.43 __ __ __ 2
1.52 1.14 1.98 1B __ __ 0
1.20 1.22 1.27 1B __ __ 1
0.84 1.33 0.71 1B __ __ 2
1.28 0.97 1.27 __ 2B __ 0
1.21 1.12 0.84 __ 2B __ 1
1.13 1.27 0.40 __ 2B __ 2
1.33 0.76 1.36 __ __ 3B 0
1.09 0.95 0.93 __ __ 3B 1
1.25 1.24 0.56 __ __ 3B 2
2.09 1.40 2.91 1B 2B __ 0
1.86 1.65 2.23 1B 2B __ 1
1.55 1.88 1.11 1B 2B __ 2
1.91 1.15 1.86 1B __ 3B 0
1.77 1.45 1.36 1B __ 3B 1
1.81 1.83 0.90 1B __ 3B 2
1.34 1.08 1.58 __ 2B 3B 0
1.73 1.29 0.68 __ 2B 3B 1
2.14 1.76 0.59 __ 2B 3B 2
2.46 1.44 3.10 1B 2B 3B 0
2.44 1.85 3.10 1B 2B 3B 1
2.74 2.34 3.10 1B 2B 3B 2

If you look at the first line, it says that with bases empty and no outs, that a HR in this situation is 72% as impactful as in a random situation.  But a walk is 127% as impactful as normal.  That is, a walk is worth +.41 runs here, where normally it would be +.32 runs, while a HR is worth +1.00 runs, where normally it would be +1.40 runs.

You can see here how a hitter would shift his approach.  Compare with men on 1b and 0 and 2 outs.  Here we can see how the walk is very powerful, being twice as impactful as it normally would be (worth +.64 runs), while a HR is worth around what it randomly would be (+1.59 runs).  But with two outs, the impact of the walk takes a beating, while the impact of the HR is elevated.

The fascinating thing for a hitter/pithcer approach is to calculate their LWTS by the 24 base/out state based on their expected approach.  You can plug in different approaches, and you can see how a batter/pitcher would do. 

If you look at Table 50 in The Book, and with runner on 3b and 1 out, you can see how a guy who Ks alot must change his approach drastically, because the K is extremely costly.  But, if he does that, he might reduce his number of HR. 

That Table 50 is central to the hitter/pitcher approach, and every player should be plugging in the “approach” in that table to see how he should approach the situation optimally to maximize their skills.

Let me introduce another way to look at it, this time focusing on strikeouts:

boLI kLI k/bo 1B 2B 3B Outs
0.87 0.87 1.0 __ __ __ 0
0.58 0.58 1.0 __ __ __ 1
0.39 0.39 1.0 __ __ __ 2
1.52 1.33 0.9 1B __ __ 0
1.20 1.10 0.9 1B __ __ 1
0.84 0.84 1.0 1B __ __ 2
1.28 1.52 1.2 __ 2B __ 0
1.21 1.23 1.0 __ 2B __ 1
1.13 1.13 1.0 __ 2B __ 2
1.33 1.75 1.3 __ __ 3B 0
1.09 1.88 1.7 __ __ 3B 1
1.25 1.23 1.0 __ __ 3B 2
2.09 2.04 1.0 1B 2B __ 0
1.86 1.72 0.9 1B 2B __ 1
1.55 1.55 1.0 1B 2B __ 2
1.91 2.20 1.2 1B __ 3B 0
1.77 2.36 1.3 1B __ 3B 1
1.81 1.81 1.0 1B __ 3B 2
1.34 1.78 1.3 __ 2B 3B 0
1.73 2.69 1.6 __ 2B 3B 1
2.14 2.14 1.0 __ 2B 3B 2
2.46 2.75 1.1 1B 2B 3B 0
2.44 2.78 1.1 1B 2B 3B 1
2.74 2.72 1.0 1B 2B 3B 2

With bases empty and 0 outs, the boLI is 0.87, and the kLI here is also 0.87.  While the LI for the strikeout is 87% as impactful as random, it’s also in a situation where the average event is also 87% as impactful as random.  Therefore, the strikeout is no more or less impactful than expected, and a hitter/pitcher approach to the strikeout should not change.

We see that it’s the runner on 3B and less than 2 outs situation where the strikeout’s impact changes, and it’s in those base/out states where the batter/pitcher has to think about changing their approach to affect a strikeout.

(The batter is thinking of reducing the K, while the pitcher is thinking of increasing the K.)

One thing I find interesting about the first table is the relationship between outs and LI.  I think when most fans think about a high-leverage situation, it’s close and late, men on, and 2 outs (and that is high LI, of course).  The only base state in which 2 outs means a much higher LI than 0 outs is _ 2B 3B.  In all the other states, 2 outs means an LI that’s about the same or much less than with 0 outs.

In general, it appears that outs tend to reduce leverage. Or perhaps it’s more accurate to say that outs reduce the impact of new baserunners, while increasing the impact of run advancement.  I wonder if you could expand the idea of table 2 (BBs and HRs) to show how different out/base states effects the LI for OBP vs. SLG, or something similar?

Actually, the formula is pretty straightforward.  Take the values in Table 50, and divide by the simple average values in Table 52 (which is the same as the weighted average values of Table 51).

I think the most interesting line you’ll find is the runner on 3B and 1 out.

It is fascinating to look at how batters and pitchers should change their approach depending on how the leverage is impacted by each event (or vice versa).  I am willing to bet that batters and pitchers do not make near optimal use of this kind of analysis other than the obvious ones (e.g., don’t K with a runner on 3rd and less than 2 outs).

I don’t know how many times I have seen a pitcher (closer usually) walk a man in the 9th when he does not represent the tying or winning/go ahead run.  Of course you sometimes can’t help but walk a batter, but that should rarely happen.

I remember watching a game around 10 years ago.  Greg Maddux walked the pitcher and after a while the commentator remarked that that was the first pitcher Maddux ever walked in his ML career and he had been pitching for almost 10 years in the bigs.  I thought that was incredible.

It looks like it’s time for managers to develop the KOOGY!

It’s pretty interesting to see that a pitcher should always be aggressive early in an inning and more cautious later in an inning (looking at BB/HR). Too bad there don’t seem to be any splits based strictly on the number of outs to see if pitchers change their approach to reflect this.

One of the problems you run into in trying to see whether pitchers or batters as a whole properly change their approach is that since batters are trying to do the opposite of the pitchers, they often cancel one another out.  For example, with a runner on third and less than 2 outs, the data indicate that batters are not “able” to hit more flyballs than they usually do.  However, since pitchers are generally trying to keep the ball down and strike out the batter in that situation, the batters may in fact be trying to hit more fly balls, but that effort is cancelled out by the pitchers.

“One of the problems you run into in trying to see whether pitchers or batters as a whole properly change their approach is that since batters are trying to do the opposite of the pitchers, they often cancel one another out.  For example, with a runner on third and less than 2 outs, the data indicate that batters are not “able” to hit more flyballs than they usually do.  However, since pitchers are generally trying to keep the ball down and strike out the batter in that situation, the batters may in fact be trying to hit more fly balls, but that effort is cancelled out by the pitchers.”

That is one example. What does the data say about the K? For example in a situation where getting a K is relatively a much worse an outcome (man on 3rd, 1 out) does the data show that batters modify their approach?

If not all batters what about a certain subset? Perhaps hitters with better plate discipline are more able to modify their behavior, while those who hack away continue to strike out?

Yes, I think it would be interesting to see which batters and pitchers modify their approaches at the plate to leverage their PA.  Of course, it is inevitable that you would find differences among batters and pitchers.  The trick is to first determine whether these differences are likely due to chance only, or whether there is skill element as well (are they “true” differences?). Then the next step is to figure out the regression coefficient (there can be a skill component, but it could be small as compared to the noise).  Then the final step is to identify the players and estimate their skill using the regression coefficient.

With the K and a runner on third, I don’t know what the data say, but whatever it does say, all we know is that it is based on the sum of the bater’s and pitcher’s approach combined.

"With the K and a runner on third, I don’t know what the data say, but whatever it does say, all we know is that it is based on the sum of the bater’s and pitcher’s approach combined.”

True, but by looking at a batter’s approach across a wide range of pitching, vs another batter’s approach against the same pitching (ie 2 batters in the same league) we should be able to differente between hitters—as we are effectively controlling for the pitcher, sample size issues aside. Although your point does stand: the data are based on the sum of the batter’s approach and the approach of the entire univers of pitchers that he has faced.

The way I would approach it is:

Using the LWTS values in Table 50 for man on 3B and 1 out, apply those figures to the player’s overall batting record.

This will give you the guys best suited to perform well with man on 3b and 1 out, if a batter/pitcher could not take extra advantage of the situation.

Split those guys up into various buckets by quality, and compare how they did with man on 3b and 1 out. 

You can also try to break up the players by K rate, or FB rate, since that’s what changes in value the most.  Are the high K guys the ones who can most change their K rate when they are too damaging?

Tango:  Have you ever presented the average LI by inning, weighted by actual game situations?  I think this would be interesting to see.  (For the 9th, would probably be important to separate the half innings.) We often tend to think of leverage as increasing as the game proceeds, but of course the reverse is true in blowouts.  How does it all net out?

I have not, but my guess is that it would be close to 1.0 all-around.  Maybe starting at 0.90 to 0.95, and reaching to 1.05 to 1.10 in the 9th, on average.  Extra innings would be at 2.0.

Pizzacutter attempts a sort of Leverage by base/out state.

http://mvn.com/mlb-stats/2007/05/12/whats-the-most-important-at-bat-in-an-inning/

But it looks like he’s following the Woolner approach, which I’ve explained is wrong.

The top of this page shows the right way to do it.

Bumping for the newcomers.

I draw your attention to the main entry and the first two posts.  And if those interest you, read the rest of the thread.