THE BOOK--Playing The Percentages In Baseball

Nice illustration of the limitations of K:BB ratio.  In the normal range, K/BB ratio values a reduction in BBs about three times as highly as an extra K:
6K/3BB = 2.00
7K/3BB = 2.33 (+0.33)
6K/2BB = 3.00 (+1.00)
The denominator in a ratio has far more “leverage.”  However, each extra K is actually worth very nearly the same in runs prevented as each BB prevented.

I think the problem with K:BB ratio is magnified when used as a tool for evaluating young pitchers.  A hi-K/hi-BB pitcher has a lot of potential to improve, if they can bring down their BB rate (for which there’s ample historical precedent).  But pitchers rarely improve their K rate as they age.  So a young pitcher who post 5 Ks and 2BBs per nine has a nice-looking 2.5 K/BB ratio, but has less upside than a 7.5K/3BB pitcher with the same ratio.

Doesn’t the strikeout minus walk ratio breakdown pretty heavily at the extremes?

Let’s take two pitchers, Pitcher A and Pitcher B

Pitcher A has
SO: 200
BB: 160
Ratio: 1.25
Differential: +40
FIP Component: +80

Pitcher B has
SO: 80
BB: 40
Ratio: 2.0
Differential: +40
FIP Component: -40

Taking the raw stats (not doing any regression) Pitcher B has done much better than Pitcher A, but their differential is the same.

Why not instead…

Calculate the league average SO/BB ratio.  I have no idea what it is, but let’s call it LaSBr.  Then let’s use the LaSBr along with the SO and BB for each pitcher and convert to a counting stat that shows how many BB above or below league average the pitcher is (same can be done for SO too).

BB+ = (SO / LaSBr) - BB

Using the stats from the two pitchers above we get.  I will use LaSBr = 2.0, only because I have no idea what the number actually is.  But the following is for demonstration purposes only.

Pitcher A
BB+ = (200 / 2.0) - 160
BB+ = -60 (Below average by 60 walks)

Pitcher B
BB+ = (80 / 2.0) - 40
BB+ = 0 (Average)

Guy #1 took the words out of my mouth. If the lg K/BB was 1.0 instead of 2.0, the ratio and differential should work about the same, right.

But by the same logic, it should work the opposite way for hitters—that the ratio is better than the differential. But I don’t think this holds, because of the strong association of high BB and K with HR for batters.

As we know in FIP, the correct weights is 3:2…. if we ALSO have HR as a parameter.

As we know in Batted Ball FIP, the correct weights is 1:1… if we EXCLUDE HR as a parameter.

So, there is extra information linked to SO and BB that makes the differential work as well as it does.  For pitchers anyway.

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Btw, I submitted this as an ESPN blog post.  It didn’t make the cut, which makes me think that some of what I do might be a bit too niche for their tastes.

Tango, I think with ESPN we have to remember that their audience is still years behind the curve regarding stats.  At least looking at their “fantasy” coverage (where most of their “analysis” has been happening in years past) it is only this year that they have been really using things like BABIP, HR/FB etc to look at players.

So I think they might have shot down your post more because their audience knows so little about how advance stats have been looking at pitchers that talking about the relative value of differential over ratio will sound meaningless because the audience didn’t even know that everyone has been using ratio.

You might have been better served just writing about how differential has such and such predictive powers and not even mentioning ratio.

I wonder if the ratio construct is so problematic that you could actually better predict future performance using K rate alone, while completely ignoring BBs.  If so, that would be a cool way to illustrate the limitations of K:BB. 

*

To sell differential as a stat, I think you need a better presentation than you use here.  Probably the easiest for people to understand is (K-BB)/9.  I understand this is less accurate than using per PA metrics, but that may be the sacrifice required to get sites to include this in their stats pages.  I also like (K-BB)/game, meaning (K-BB)*38/BF.

Guy: the day I dumb down a stat to appeal to a broader audience is the day I retire.

If K minus BB per IP was better than per BFP, I would use that.  It’s not, so I won’t.

—-“As we know in FIP, the correct weights are 3/2, if HR are incuded as a parameter.”

Just to be clear, are refering to the correlation with the same years ERA or the next years? If it’s for the future, then I wouldn’t be surprised if the best weighting is 1/1, even with HR included. And the denominators are different—IP for FIP, and PA for the K-BB differential, right.

For same year.

And yes, the other reason the coefficients are 3/2/13 is because IP is in the denominator.

The point I was trying to make was to Xei that you can’t treat the 3:2 as some inviolate thing.  It’s predicated on HR and IP being parameters in the equation.

#9. Ok, feel free to strike my FIP component from my post.  I was just trying to provide more info and it wasn’t even important to my post.  I’m sorry that it distracted away from the point I was trying to make.  I should’ve just left it out.
But point taken. 😊
vr, Xei

“the day I dumb down a stat to appeal to a broader audience is the day I retire.”

Fair enough.  But in some cases there is a gray area, where a slightly-simplified stat tells the story nearly as well as a “perfect” version of the stat, but much more accessibly.  That’s essentially the decision you made with FIP, using integers for all the coefficients.  Perhaps in this case the use of innings as the denominator introduces an unacceptable amount of error.  But I don’t think you should take an absolutist position that accuracy always trumps all else.

And if you’re going to use per PA, I do think (K-BB)/G makes for a better presentation.  Then AJ Burnett is +4.6 per game, compared to a league average of about +3, meaning he retires 4.6 batters a game more than he gives a free pass to.  I just think that’s more intuitive than figuring out if .122 is a good or bad rate.

Guy, I agree with your basic sentiment.  Yes, I will lean toward less precision if it makes it easier.  “1” as the coefficient for K and BB is just something that happened to work out.  It’s really close to 1, so I settle for “1”.

But the IP and PA as denominators goes to the idea of IP including K.  Once you do that, this will change the coefficient of K and BB.  This is why the 3/2 works so nicely with FIP, because I use IP.  The IP includes K information, and so, the 3/2 balance works out nicely.

I could present it as “per game” and just add a note that a “game” is 38 PA, rather than 9 IP.  This is what MGL does with UZR, as he doesn’t use IP, but “expected outs”.

So, I am in favor of what you are suggesting, which still leaves me with the core construction intact.

I took a quick look at qualifying starters the past two seasons.  In both years, SO rate correlates with same-year ERA as well as or better than K/BB ratio.  So the K/BB ratio, because of its poor construction, actually manages to subtract information compared to looking at Ks alone. K-BB, as you’d expect, has the highest correlation.

2009:
K/BB .45
K/BF .48
K-BB .52

2008:
K/BB .54
K/BF .54
K-BB .62

Interesting stuff.  Try BB/K.  This goes to the asymmetry I talk about in using ratios.

Correlation of BB/K and same-year ERA:
2009: .47
2008 .58

That’s interesting:  it has a stronger relationship, presumably because it “weights” Ks more heavily by putting them in the denominator.

Guy, any way you can do the same thing for batters?

#15. Ks should be weighted more heavily, right?  How about leaving BB in the denominator and instead of using K/BB, use (K * 1.5) / BB.
See if that evens things out.
vr, Xei

Xei: in a correlation, it automatically figures the coefficient, so you can put 1.5 or 15 million, and it won’t change anything.

Guy/15: good stuff.  It’s so obvious with a ratio that a 3:1 ratio should be as far from 1:1 as 1:3 is.  But, in one case it’s 3.00 and the other is 0.33.  So, there is no symmetry and the 3.00 is going to carry more weight around.  It’s “distance” is farther.  This was the run-in I had with JC when he was using GB/FB ratio, and I told him he should use rates, not ratios.  That’s actually what started his anti-Tango view.  (And I was right of all things.  I wouldn’t mind at all if he was anti-Tango because I was wrong.)

So, to you kids at home, any time you have a choice to use ratios or rates, use rates.  Don’t do AB/HR.  Do HR/AB.  Don’t do IP/ER (i.e., ERA+).  Do ER/IP.  etc, etc, etc

Tango: I guess I haven’t mastered the Excel “correlation” feature then.  When I use K*1.5 instead of K, I get a higher correlation.  I don’t have nearly the data set that Guy has though.
vr, Xei

The ratio v. rates is a good point.  The way I try to get around this when analyzing ratio data is to log(2) transform the data.  This eliminates the “distance” issue.

As I’ve said in the past, the log issue doesn’t always work.

In this case, it works perfectly fine, as this is the right place to use a log.

The bad place to use a log is in things like salaries, where the use of the log is used to force the linearity, even though no linearity exists.  Indeed, what you are doing is trying to minimize the error of the log of the term, rather than the error of the term.

So: logs on odds = good idea
logs on everything else = usually bad idea

Don’t just do logs for the sake of doing logs.

Dave/16:
It’s not easy for me to provide similar #s on hitters.  And as you say, it’s a vastly more complicated analysis for hitters because K rate is correlated with power.  On the surface, I imagine BB rate is much more correlated with wOBA than K-rate.  But of course that doesn’t really mean the ability to avoide Ks “doesn’t matter.”

I’ve using a K-BB-HR*4 to eval SP for years.  It works well for roto.

Ghost: that’s close to FIP.  Compare the two:

FIP Ghost
13 4 HR
3 1 BB
2 1 SO

If you multiply Ghost by 3 you get:
FIP Ghost
13 12 HR
3 3 BB
2 3 SO

So, pretty close.  The overweighting on SO for Ghost might work out swell for foreacsting purposes.

‘The focus therefore should be on strikeout minus walk differential, and not ratio.  There were 137 pitchers who faced at least 800 batters in 2008-2009.  The top 27% of those pitchers had a strikeout to walk ratio of 2.5 or higher.’

So what are the Strikeout minus Walk Differential for the following pitchers;
A. Harang (CIN)
T. Cahill (OAK)
H. Bailey (CIN)
C. Tillman (BAL)
B. Penny (STL)
B. Norris (HOU)
J. Masterson (CLE)
B. Zito (SF)
A. Sanchez (FLA)
J. Niese (NYM)
I. Kennedy (ARI)
C. Richard (SD)
J. Chamberlain (NYY)
B. Bergesen (BAL)

What is the exact formula so that I might calculate it myself?

Jamaal:  It’s just (K-BB)/TBF.  Or to scale it to a per game stat, multiply that by 38.

An article today at Fangraphs on this topic. I responded in comment #12.

http://www.fangraphs.com/blogs/index.php/clayton-kershaw-like-a-boss-of-the-strike-zone/

Actually my response is #13 (dcs)

I don’t think the term “more representative of a pitcher’s ownership of the strike zone� is the proper way to describe Tango’s finding–he simply found that the ‘difference’ correlates with overall effectiveness better than the ‘ratio’. I would argue that the ‘difference’ represents some combination of control of the strike zone plus stuff, and that is why it correlates better.

This is, IMO, not just a semantic thing. The spread of BB among pitchers is about half that of K, per PA. So, it is twice as ‘difficult’ to get one fewer walk allowed than to get an extra K. But weighting them the same as in the ‘difference’ formula ignores that reality, while using the ratio captures it.

I see what you’re getting at: K-BB doesn’t reward pitchers who manage a very low BB rate as much as K:BB does.  But I’m not sure how we could distinguish “control of the strikezone” from “stuff,” since Ks clearly reflect stuff.  The fact is that an additional K is roughly as valuable as one less BB.  But a 6K/3BB pitcher who adds one K only improves to 2.33 K:BB, while one less BB yields a 3.0 K:BB—and that’s quite misleading.  Why do we care if the latter is “more difficult?”

David:  If you wanted a “balanced” metric, you could start by creating K+ (K%/lgK%) and BB+ (2-BB%/lgBB%) metrics.  Then take the average of these two to measure “strikezone control.”  That way a pitcher’s relative strength in each dimension has equal weight.  I think that would be superior to K:BB, in which the “leverage” given to BB in the denominator skews things.

But I would think of this as a toy stat, like power-speed scores, with no pretense that it corresponds directly to run prevention.

Why do we care if the latter is “more difficult?�
***************

I’m not saying we should. But these are really just fun stats, meant to answer a different question than simply which pitcher is better. If the question is which pitcher is best in the categories of Ks and BBs, it’s not unreasonable to look at it from a frequency approach instead of a run value approach, and convert into Z scores or whatever.

This is the kind of analysis that drives me crazy—you’re cherry-picking groups of 20 pitchers (out of literally thousands over a 17-year period) who happen to fall into specific categories, and purporting to reach grand conclusions about which statistical measure is better???

Bill:

How about 2513 pitchers?

http://www.insidethebook.com/ee/index.php/site/comments/k_minus_bb_differential_or_ratio/

Grp    IPouts    diff/PA    R/27    6-14*diff/PA
4    206352     0.169      3.66      3.63 
3    436797     0.116      4.33      4.37 
2    866050     0.079      4.80      4.90 
1    530103     0.047      5.26      5.34 
0    208194     0.009      5.94      5.88

“diff” above is K minus BB.

This current thread was written as a short illustrative article, to highlight the more robust findings (such as the link in this post).

***

I can see if you walked into the middle of this conversation how it would look insane that I would reach such a strong conclusion based on flimsy evidence. 

Unfortunately for you and many drive-by readers, my blog is not really setup for people to walk into the middle of a conversation. 

Stay a while, ask questions, and I’ll point you to more evidence.  If after all that, you are still not convinced, then consider driving yourself crazy.

Ok thanks. In the future I will try to remember to search for related material first rather than treat each thread in isolation (just learning!)

—-“I think that would be superior to K:BB, in which the “leverageâ€? given to BB in the denominator skews things.”
**************

I haven’t worked thru your proposed stat, but it looks good. But K/BB also has the advantage of super simplicity. And I’m not sure what you mean by the leverage of BB in the denominator….

The current K/BB ratio is about 2 to 1. So if an avg pitcher has 75 BB and 150 K in 200 IP, the ‘plus 1’ method will give twice the weight to an extra BB prevented than an extra K in the K/BB ratio. And since it’s twice as ‘difficult’ (given the spread of BB and K) to do so, that seems fair to me. No?

K minus BB per PA (first proposed by Guy several years back) directly correlates to runs allowed.

K per BB directly correlates to x.  What is it that we want to test it against?  Called strikes to called balls?  Called+swingAndMiss Strikes to called balls? Called+swingAndMissOrFoul Strikes to called balls?

Those are all legitimate “x” things to look for.  So, if you want to propose a metric that uses only K and BB, what is it that we are going to test it against?

The current K/BB ratio is about 2 to 1. So if an avg pitcher has 75 BB and 150 K in 200 IP, the ‘plus 1’ method will give twice the weight to an extra BB prevented than an extra K in the K/BB ratio. And since it’s twice as ‘difficult’ (given the spread of BB and K) to do so, that seems fair to me.

Not really.  A 7K/3BB (per game) pitcher has a ratio of 2.33.  A 6K/2BB pitcher is 3.0.  So the marginal BB reduction has 3x the payoff of an extra K.  And among the elite pitchers we care about most, the disparity grows:  9/2.5 = 3.6, but an equal pitcher who is 8/1.5 gets a ratio of 5.33.  That makes the marginal BB appear to be 5x as impactful.  (That’s what I meant about changes in the denominator having a lot of ‘leverage’ in the rating.)  And of course the fact that very low BB rates are scarce don’t make them any more valuable—but I think we agree on that. 

I actually wonder if driving down BB rate really low is necessarily the right move, for pitchers who have that ability.  I’m hesitant to second guess a Cliff Lee or Curt Schilling about their pitching strategies.  But I do wonder if a little bit more wildness might have paid off in a lower BABIP for these guys.

Guy, your ‘plus 1’ method is different than the way I have always done it. Using very small numbers like 6/3 or 7/4 or 6/4 will of course show a more major change. I have always used very large numbers to get the ‘instantaneous’ change (I guess you could use calculus to be more precise?). So instead of adding 1 to 3 or 6, I would add 1 to 30,000 or 60,000. That gets the 2 to 1 change that also reflects the spread of BB vs K.

David:  You are right that the implied valuation of BBs to Ks in the K:BB ratio is 2:1, if the question is the marginal impact of adding 1 K or 1 BB over a full season.  But that ratio will not remain 2:1 if we look at pitchers who are not approximately league-average in these metrics, which of course is the whole point of this exercise—we’re trying to decide whether or not Kershaw should outrank Lee, and by how much.  And when we compare these kind of pitchers, the K:BB ratio becomes extremely misleading. 

Indeed, the fact that the marginal value of Ks and BBs varies so greatly, depending on your choice of starting point, is itself a good sign that the method is flawed.  The marginal value of avoiding a walk is the same regardless of whether you start out walking 3 batters a game or 2—but K:BB ratio implies the gain is much larger for the second pitcher (whose K:BB ratio doubles).  That’s the advantage of the metric I suggested:  in comparing any two pitchers—or measuring a change in one pitcher’s performance—it will always value a BB at about twice the value of a K.

Guy, you could take your stat and do a couple extra things:
1)Instead of taking the avg of the 2 results, you could multiply them together and then take the sq rt. This would reward pitchers who are ‘balanced’ between the categories
2) The ‘2’ multiplier in the BB formula could be customized to the lg K/BB ratio. Now it would be 2.1 or so, while in the 1980s it was 1.8 or some such, and so on back in time.

As you said, it’s mainly a toy stat, but I like it.

Actually, I’m not sure you would use the straight lg K/BB for the multiplier, but it would be simple to figure out how to base it on that.