Baseball Beat February 21, 2006
Strikeout Proficiency (Part Two)

In A New Way to Measure Strikeout Proficiency yesterday, I introduced the concept of strikeouts per pitch (or 100 pitches) and proclaimed that "this stat just might be the best way to measure pitcher dominance, if not overall performance."

Well, as it turns out, strikeouts per pitch (K/P) explains runs allowed better than strikeouts per inning or strikeouts per batter faced. The stat measures dominance and efficiency, and I strongly believe that it is "the single greatest Defense Independent Pitching Stat out there."

Today's article is focused on the technical aspects of this argument. I refrained from getting overly technical yesterday because I wanted to share the idea without overburdening the reader with statistical terms such as correlation coefficients.

Among pitchers with 162 or more innings, I compared the correlations of three strikeout measures (by inning, batters faced, and pitches) against Earned Run Average (ERA), Runs Per Game (R/G), Component ERA (ERC), Fielding Independent Pitching (FIP), and Defense Independent Pitching Stats (DIPS).

ERC, FIP, and DIPS are metrics that estimate what a pitcher's ERA should have been, based on variables within his control (such as K, BB, HBP, and HR).

In addition to ERA, R/G, ERC, FIP, and DIPS, I am also going to use K/IP for strikeouts per inning, K/BF for strikeouts per batter faced, and K/P for strikeouts per pitch.

The correlation coefficient measures the strength of a linear relationship between two variables. The correlation coefficient is always between -1 and +1. The closer the correlation is to +/-1, the closer to a perfect linear relationship.

All of the correlations in the tables below are negative. A negative correlation is evidence of a general tendency that large values of "X" are associated with small values of "Y" and small values of "X" are associated with large values of "Y". Think of "X" as strikeouts and "Y" as runs.

Correlation Coefficients Matrix For 2005

```            ERA       R/G       ERC       FIP      DIPS
K/IP     -0.414    -0.436    -0.516    -0.615    -0.659
K/BF     -0.503    -0.528    -0.614    -0.681    -0.720
K/P      -0.534    -0.557    -0.656    -0.717    -0.755
```

As detailed above, K/P has the highest correlation in each of the five run measures. K/BF has the second-highest correlation and K/IP has the lowest correlation. In any other words, K/P > K/BF > K/IP.

Conversely, DIPS has the highest correlation to each of the three strikeout measures. FIP has the second highest, ERC the third highest, R/G fourth highest, and ERA the lowest correlation. That is, DIPS > FIP > ERC > R/G > ERA.

Correlation Coefficients Matrix For 2004

```            ERA       R/G       FIP       ERC      DIPS
K/IP     -0.520    -0.527    -0.621    -0.637    -0.655
K/BF     -0.581    -0.587    -0.673    -0.701    -0.704
K/P      -0.592    -0.595    -0.703    -0.718    -0.736
```
Once again, K/P has the highest correlation in each of the five run measures. K/BF has the second-highest correlation and K/IP has the lowest correlation. Just like in 2005, K/P > K/BF > K/IP. Conversely, DIPS has the highest correlation to each of the three strikeout measures. ERC and FIP switch spots with the former having the second-strongest correlation and the latter the third. R/G ranks fourth and ERA has the lowest correlation. That is, DIPS > ERC > FIP > R/G > ERA.

Despite claims to the contrary by some readers around the baseball blogosphere (including our site), the evidence is indisputable. K/P is not only a better measure of strikeout proficiency than K/IP and K/BF, but it has a stronger correlation to runs allowed than these other measures.

For whatever reason, many people are slow to accept new ideas. No matter how much proof one provides, there will always be naysayers who don't want to embrace the truth. But that is OK with me. You see, I'm not a member of the Flat Earth Society.

Wow. Sometimes things sound too intuitive, too rational, too simplistic and too good to be true, especially in baseball. But in this case, simplicity is beautiful.

Yes, but K/BF is almost as good and the data is a lot easier to find. Why didn't you include K/BB in your survey?

So let me see if I understand this: if you have a pitcher who is capable of K's but prefers to pitch to contact, the K/P stat will incorporate their skill better than the K/9. K/9 rewards pitchers who always try to strike batters out (and build up high pitch counts), while K/P rewards pitchers who strike batters out when the opportunity presents itself (lower pitch counts), because a first-pitch groundout isn't as much of a drag on the denominator with a single pitch as with a single out. Is that right?

Seems to me that you're probably picking up vestiges of K/BB. Pitchers who don't walk many batters will have higher K/P ratios.

The really key comparisons are ERA and R/G. The correlations will naturally be higher with FIP and DIPS because those stats are focused on strikeout and walk rates.

Another test might be to compare K/P and BB/P against K/BFP and BB/BFP to see which pair of variables better correlates with ERA and RA.

I have found that K/27BF often comes close to K/100P. Most pitchers would have K/100P K/27BF, implying he was quite efficient at getting strikeouts and put him in the same company with Santana, Pedro, and Carpenter. On the other hand, young strikeout pitchers like Prior, Peavy and Beckett are all on the other side, which makes me wonder whether efficiency can be learned as pitchers age.

whoops. I meant to say "Most pitchers would have K/100P less than K/27BF, because power pitchers use more pitches. But sometimes, pitchers can have K/100P greater than K/27BF, like Loiaza last year..."

The signs for Greater Than and Less Than cut off part of my post, damn you html!

What is the comparison between strikeout per pitch and strike per pitch? Are we moving towards a simpler percent stat here?

One other thing:

"For whatever reason, many people are slow to accept new ideas. No matter how much proof one provides, there will always be naysayers who don't want to embrace the truth. But that is OK with me. You see, I'm not a member of the Flat Earth Society."

This is a complete crock. You posted the hypothesis on your blog one day ago, February 20th. You had damn well better expect to spend a significant amount of time defending it. Right or wrong, you're going to have to shoot down every single person who questions it. Look at what McCracken had to go through to get DIPS accepted, then what real scientists have to do to defend 150-year old theories with mountains of evidence behind them.

You've got to expect to have to take some time defending this, and if you respect your own work, you'll be a little less flip about it while you're still trying to get others to rely on it for their work.

geez powers, two scoops of crabby in your coffee this morning or what?

It's a great thing if he's found a way to advance the predictive value of pitcher performance, it's a terrible thing if he thinks saying it's so is enough to make him right. There are people around with some decent questions about this that might lead to a refinement of it or other components of DIPS, and one regression analysis isn't going to inoculate him from answering those questions if he wants people to take it seriously.

For example, the groundball questions (aka the Greg Maddux Argument) over at Baseball Musings might lead one to wonder if GB/FB pitchers' value might be better estimated by Outs Per Pitch than Strikeouts Per Pitch. We all accept at this point that strikeouts are the best, but what if we could find more accurate predictors for other kinds of pitchers?

Dealing with science all day, I often find myself poking at people not to feed ignorant trolls, but that's a matter of limiting yourself to "one link responses" until said troll demonstrates he'll do his own homework. There's a difference between limiting yourself to one measured response and brushing off all questions with "take this on faith or you're a Flat Earther." After all, he's not posting each equation and the exact source data he used so others can repeat the test, as a real scientist would have to, and he didn't have anyone verify his work before he took it public. It's natural for people to question a one-day-in-the-wild idea.

I've got a question. I'd like Rich to address the issue of "strikeout as process" versus "strikeout as result" that Pinto and XeiFrank brought up. In other words, I also question if this stat is telling us something that K/BF isn't already telling us. Might it be a problem that K/P assumes every pitch is equal?

Jason,
i understand your idea as far as the Maddux example, but Out per pitch doesnt work for me, as it cant take into consideration the defensive prowress behind the pitcher and doesnt account for things like a long out in pittsburgh, a home run in Cincinatti, and countless other factors. He clearly stated he was going for "the single greatest Defense Independent Pitching Stat out there."

Studes makes the important point here. This is just a poor man's K/BB ratio, with perhaps a pinch of BABIP thrown in. If you have two pitchers who both have a K/BF of .20, but one has a lower K/P ratio, that will usually mean he allows more BBs and/or hits on BIP (and thus faces more batters). If you want a measure of dominance, K/BB is clearly better; if you want the best metric for strikeout proficiency, K/BF is the right choice. It's not clear what one would use K/P for, if anything.

So J. Santana with 5.29 K/BB is a worse pitcher than Carlos Silva with 7.89K/BB? Give me a break.

If you want a measure of dominance, K/BB is clearly better

Is that so? Let's take a look at the correlations among pitchers who pitched 162 or more innings last year...

```        ERA     R/G     ERC     FIP    DIPS
K/P  -0.534  -0.557  -0.656  -0.717  -0.755
K/BB -0.434  -0.450  -0.530  -0.548  -0.565
```

Here are the results for all pitchers with 38 or more innings (which, for these purposes, is essentially all of 'em)...

```        ERA     R/G     ERC     FIP    DIPS
K/P  -0.496  -0.506  -0.540  -0.661  -0.705
K/BB -0.454  -0.459  -0.559  -0.626  -0.635
```

The facts win out over unsubstantiated opinion again.

Re Ken's question (in comment #3 above), my answer would be "not exactly."

K/P is an indicator. It doesn't reward or say anything about pitching to contact. If anything, pitchers with low K/P are more apt to be those considered to pitch to contact than pitchers with high K/P.

However, as it relates to K/P vis-a-vis K/IP, pitchers who rank higher in K/P than K/IP will almost always be those who walk fewer batters and, therefore, throw fewer pitches than pitchers who rank higher in K/IP than K/P. Therefore, the pitchers in the former group are more efficient than those in the latter.

Re comments by Robert and Studes re K/BB, K/P is a better measure of run prevention than K/BB. Check the correlation matrices two comments above for the details.

Another test might be to compare K/P and BB/P against K/BFP and BB/BFP to see which pair of variables better correlates with ERA and RA.

Negative outcomes, such as BB, don't work particularly well with respect to number of pitches. But, in any event, here is the correlation matrix for walks per pitch (or BB/P) among the latter sample size (which includes 360 pitchers with 38 or more IP):

```
ERA    R/G    ERC    FIP   DIPS
BB/P    .232   .236   .374   .358   .336
```

What is the comparison between strikeout per pitch and strike per pitch? Are we moving towards a simpler percent stat here?

I have the number of pitches per pitcher but not the number of balls and strikes. However, that information is available so I will see if I can come up with it. Thank you for the idea.

Rich, I know your shorts are in a bundle about people who don't like your idea, but you haven't shown anything yet that refutes my point.

My point is that K/P has a higher correlation with ERA simply because it's K/BFP with a dollop of BB/BFP thrown in. It's not a better measure of "strikeout dominance", but it is a measure that correlates better with ERA because it's capturing something other than strikeout dominance.

As Guy says, it's probably also capturing BABIP luck. Pitchers who get more outs on batted balls will pitch fewer pitches, regardless of their strikeout dominance.

Of course, I could be wrong, but your additional analyses haven't shown that yet.

Rich, you make a valid point on K/BB ratio. I was thinking about distinguishing among high-K pitchers, which is the main point of K/P. If two pitchers have the same K rate, the one who gives up fewer BB will be, on average, more effective. But some low-K/low-BB pitchers post good K/BB ratios, mixing apples with the organges.

However, Studes' point remains valid: the only reason K/P correlates better than K/BF is because it's not only an indicator of strikeout proficiency -- you're including a little bit of BB and H-BIP info as well. Any measure that included Ks and BBs in their right proportions (essentially FIP w/o the HRs) would show an even better correlation. I'd guess that something as simple as (K-BB)/BF would do the trick.

I still think K/P suffers from being neither fish nor fowl -- it's not a true measure of strikeout proficiency, and if you want a broader measure of pitcher effectiveness, there are many better (more comprehensive) metrics available.

It isn't a bad idea at all, really. Though Dave S. over at the baseball musings comment you linked had a composite formula that seemed to provide a better correlation.

Let's see if it holds up in different situations. I don't fully understand why correlation with ERA is critical, since ERA is based on judgement calls (hit or error?), so at this point I'd be looking at correlation with Runs Allowed and also (for a laugh) at the correlation between this year's K/P and next year's RA, to see if it has predictive value. Or I'd plug it into the existing predictive models like PECOTA and see if the projections are improved or harmed.

"This is just a poor man's K/BB ratio, with perhaps a pinch of BABIP thrown in. If you have two pitchers who both have a K/BF of .20, but one has a lower K/P ratio, that will usually mean he allows more BBs and/or hits on BIP (and thus faces more batters). If you want a measure of dominance, K/BB is clearly better; if you want the best metric for strikeout proficiency, K/BF is the right choice. It's not clear what one would use K/P for, if anything."

If that is indeed what it is, then it could be very useful in determining long-term efficiency, with an easier calculation than adding together several other indicia. If it works out as a way to tell whether someone has a long-term consistently low BABIP and high K/BB ratio, you've just managed to combine two of the most useful statistics in determining a pitcher's long-term prospects, not to mention that it also incorporates outs per pitch on a more primevial level. Someone does well with this statistic for two years, or makes a jump in this statistic, then it bodes pretty well for the future and may have a higher correlation for future success than the other statistics because (a) by incorporating BABIP, you catch the rare 10% of major league pitchers who have the ability to force a lower BABIP than normally would be expected based on luck, (b) by incorporating K/BB, you get a measure of overall dominance versus efficiency and (c) by incorporating pitches per out, you get an idea of who may be able to have a higher 'workload' without having as much risk of long-term injury. Sure, to get a better idea of the overall picture, you'll still want to look at the component ratios, but to the casual fan or fantasy baseball player (or Jim Bowden and certain other GMs who can't stand to look at numbers for more than 20 seconds at a time), it could be a very useful indicator regarding who to dig deeper on.

I suspect that this stat would be even more useful at the minor league level (for figuring out pitchers who could be useful major league players without the tools to immediately jump out at you, simply because it probably means that they're getting into all the right habits), but unfortunately, you'd need MiLB to put out better numbers before one could make that determination.

"This is just a poor man's K/BB ratio, with perhaps a pinch of BABIP thrown in."

I would call it a "rich man's" version - not because the information is necessarily better but because it costs more (pitch counts) to come up with the metric.

First of all, thank you everyone for the feedback. I will try to answer most, if not all, of the questions, as well as to respond to as many comments as humanly possible. However, I will need your patience. Baseball Analysts is a hobby and not my occupation so my time is limited.

I would disagree, though, with the apparent conclusion that striking out batters on three pitches represents the ideal for pitching effectiveness - if that is what Rich is saying.

No, that was not my conclusion. The one statment that Pinto focused unfortunately is being misconstrued as the basis for my argument. I apologize if I misled anyone and would be happy to retract that paragraph if it means reducing or eliminating the confusion inherent in it.

The point of K/IP is as follows (which is excerpted out of my original article):

"We have known for some time that strikeouts are the out of choice. The more Ks, the better. We also know that the fewer pitches, the better. Combining high strikeout and low pitch totals is a recipe for success. The best way to measure such effectiveness is via K/100 pitches...I believe this stat just might be the best way to measure pitcher dominance, if not overall performance."

The bottom line is that if you believe in the power of strikeouts, you should believe in the power of K/100P as an indicator of pitching success. K/100P does a better job of identifying run prevention than K/9 or K/BF.

I would call it a "rich man's" version - not because the information is necessarily better but because it costs more (pitch counts) to come up with the metric.

All of the information I used for my study is both readily and publicly available at no cost. I just happened to access it at ESPN.com in the stats section on the baseball portion of the site.

There are some high fallutin' stats out there that cost money to access but not this one. One of the beauties of this stat is that it is for the common man and not the so-called rich.

That's true at the major league level for recent seasons. But I can't test the value of K/100 for pitchers playing in the majors twenty years ago. I also can't test it out for minor leaguers playing one year ago.

... and not to sound like a "flat earth" guy, but if we are really looking for the "single greatest Defensive Independent Stat out there", why not use DIPS or something more simple like (SO - (1.5*BB))/BF ?

This information is widely available, would reflect strikeout "dominance", and would do a more complete job of capturing control/efficiency than the K/100 does. (SO - (1.5*BB))/BF would also do a better job of predicting runs allowed.

I don't think this is "the single greatest Defense Independent Pitching Stat out there." While it is apparently the best at measuring strikeout proficiency, as was the aim of your study, I don't believe it would hold up FIP and other DIPS of the same sort--when correlated with runs allowed or runs allowed/game.

So, my real question is, are you implying that K/P is the best DIPS, or the best indicator of pitching dominance? My thoughts are a little jumbled on this--gotta pull out a notebook and good ol' Excel!

Despite these uncertainties, nice study and interesting findings...

I looked at (K-BB)/9, and as I suspected it correlates much better with R/G than does K/BB. It's the differential btwn Ks and BBs that matters, not the ratio. And K-BB/9 correlates with R/G better than K/BF or K/P as well, at least in 2005. (K-BB)/BF is even more powerful -- very high correlations.

K-BB/9 (or K-BB/BF) is simple, and a better measure of pitcher effectiveness than either K/BB or K/P.

I was wondering why, as Rich pointed out, K/pitch correlates better with ERA than does K?BB, so I broke it down.

K/BB can be written as (K/IP) times (IP/BB).

K/pitch can be written as (K/IP) times (BFP/pitch) times (IP/BFP).

The 1st terms are the same. The second, (BFP/pitch), is pretty neutral--good pitchers and bad pitchers, as a group, are about average. The 3rd term, (IP/BFP), is essentially a form of OBA allowed.

So the reason K/pitch has a better correlation with ERA is that the hidden information it includes (OBA allowed) is important. It has nothing to do with being a better measure of "strikeout proficiency".

Also, K/pitch is not really "defense-independent", since the fielding certainly has an influence on OBA allowed.

david smyth wrote:
So the reason K/pitch has a better correlation with ERA is that the hidden information it includes (OBA allowed) is important. It has nothing to do with being a better measure of "strikeout proficiency".

Wouldn't the solution be to run a multiple regression including the other factors that correlate with K/P? I think this is what studes was suggesting earlier when he wrote "Another test might be to compare K/P and BB/P against K/BFP and BB/BFP to see which pair of variables better correlates with ERA and RA."? (studes-Sorry if I'm attributing a statistically incorrect idea to you).

Here is an effort to respond to a number of readers who have presented overlapping comments and questions.

***

First of all, using # of Pitches in the denominator has "hidden" information in it but using # of Batters Faced doesn't?

Yes, pitchers who don't walk many batters will have higher K/P ratios. I'm not disputing that. In fact, that is one of the beauties of this stat. However, the same thing can be said about K/BF. That is, pitchers who don't walk many batters will also have higher K/BF ratios.

As it relates to K-BB, yes, that correlates better with run measures than K/BB. It also has a stronger fit than K/P. I realized that going into my study. But I wasn't looking for a derivative stat. The numerator is obtained by altering the number of strikeouts by subtracting walks.

Strikeouts divided by total pitches uses two variables only. The numerator isn't being altered in any way. It is a pure stat or what I termed a "single" stat in my article.

One can always improve a correlation by placing more variables into the equation and multiplying or dividing this by that and/or adding or subtracting this to that.

What I believe I have found is the highest correlation to run measures using two variables only. In hindsight, I wish I had been more explicit in stating that point in my articles.

I will have more on this subject in the future as I continue to believe that K/P is a simple and extremely valuable metric. To say that Johan Santana led the majors last year by striking out 7.14 batters per 100 pitches is a lot more comprehensible (and, therefore, useful) to me than stating that he led the majors in (SO - (1.5*BB))/BF with .187 or that he led the majors in (K-BB)/BF with 5.72.

Thanks for the comments, Rich. I don't consider myself to know as much about stats as many of the other posters here, so take the following for what it's worth, and hopefully some others will chime in.

If we are just looking at correlations, then I think what you showed is complete. But if we want to infer something about the correlations, mainly, what effect does K/P have an ERA (i.e., examine causation), I do not think what you did is sufficient. And I also think that while showing some sort of relationship via correlations is useful, especially when we have the intuition that the two variables might some sort of causal relationship (i.e., we aren't correlation ERA with attendence), I think it's good to try and go further, and see to what extent we can use K/P to predict ERA/etc.

That said, I think there is an inherent problem in using regressions of y (ERA/etc.) on x (K/P) where there is some other factor z (e.g., K/BB), that influences y, and correlates with x. The OLS model makes the following assumptions, among others:

(1) y[i] = a + b*x[i] + e[i]

where e[i] are "other factors"

(2) corr(x[i],e[i])=0 --> other factors are uncorrelated with the regressors

Now, if k/bb is among the "other factors" and K/BB correlates with x (K/P), then assumption (2) is violated. This leads to the conclusion that OLS estimate for b is no longer consistent. That means that there is an omitted variable bias, that is, if our sample size -> infinity, our value for b will not approach the "true" value, but will be off by a factor that includes the covariance of K/P and K/BB (covariance basically can be thought of as measuring the correlation). The larger the covariance of K/P and K/P, the larger the omitted variable bias.

Perhaps I'm just anxious to apply some of the statistics I've learned and am doing so incorrectly. Again, I'm less experienced than many here.

Rich,

Can you run your correlations on this measure:

K/(K+BB).

The problem with "ratios", like K/BB and GB/FB, is that they are not symetrical when you take their inverse. If the league average GB/FB was 1.0, then 2 GB and 1 FB or 2 FB and 1 GB should be equidistant from the league mean, and they are not when using ratios, but they are when using rates.

I cringe everytime anyone does a regression on ratios. They are bound to break because of its inherent nonlinearity.

Clearly a regression of K/BB to ERA or BB/K to ERA should give you the exact same result (or you'd want the exact same result), and we're not going to get it. K/(K+BB) or BB/(K+BB) *will* give you the exact same correlation to ERA.

That said, this has been a fun look, though as others have said, making pronouncements is a little early. Then again, without pronouncements, where's the fun?

Tom

Great idea, Tango. It meets Rich's criteria of using only two variables, but may well have an even higher correlation with ERA or RA. Should be close, anyway.

Rich, thanks for clarifying what you were trying to do. I was thrown off when you called K/P the "best measure of strikeout dominance" (or words to that effect). I agree that, from that perspective, K/P is more useful than K/BFP.

"What I believe I have found is the highest correlation to run measures using two variables only."

I'm pretty sure you'll find that K/HR has a better correlation than K/P. So if the award is for "Best 2-variable Stat without Use of Subtraction," I'll nominate K/HR. But I'll confess I'm not clear on the rationale for this particular Oscar category.

"To say that Johan Santana led the majors last year by striking out 7.14 batters per 100 pitches is a lot more comprehensible...[than] stating that he led the majors in...(K-BB)/BF with 5.72."

I'd agree that K/P is simple to describe, and simplicity can be a genuine virtue. But the problem is that most fans, told this stat is a good measure of pitching prowess, would conclude it shows that the fewer pitches a pitcher uses the better. And indeed, you say this in making your case. But it isn't true: there is no correlation at all btwn P/BF and R/G. K/P really 'says' that pitchers should try not to allow BBs and hits (true), but seems to say it's important to be "efficient" in the number of pitches made (false). So yes, K/P has a certain clarity of message, but but one that would lead many to incorrect conclusions.

Also, I personally find (K-BB)/9 to be quite intuitive and easy to explain. It's just "strikeouts minus walks per game" -- how many batters you erase by yourself minus those you give a free pass. If fans can understand K/BB ratio, and they do, this is at least as easy to understand. And it's more predictive than K/BB, K/BF, or K/P.

But the real test for a stat is whether the larger community finds it helpful and starts to use it. Maybe K/P will catch on. Time will tell.

In any case, as a new visitor here I just want to add that -- my knocks against K/P notwithstanding -- you've got a great site here. Congrats on reaching your first anniversary....

That makes a lot of sense, Tom. Thanks for teaching me something new :-)

Tom,

That formula doesn't have any correlations whatsoever with runs allowed...

```
ERA     R/G     ERC     FIP    DIPS
K/(K+BB)  -0.038  -0.042  -0.039  -0.024  -0.009
```

K/(K-BB) feels like it would make more sense to me. Plus, they both would need to be turned into a rate stat to compare to the above run measures.

That said, this has been a fun look, though as others have said, making pronouncements is a little early. Then again, without pronouncements, where's the fun?

Yeah, I've got the writer devil on one shoulder and the analyst devil on the other competing with each other all the time. Analysis without the writing can be boring. So leave it to me to be a bit "edgy."

Rich, you probably have a sample size issue. I ran several regressions, with the results you can find here:

http://mb3.scout.com/fbaseballfrm8.showMessage?topicID=1166.topic&index=23

Rich, you probably have a sample size issue.

I think my sample size is fine. I'm using 360 pitchers from last year. The difference in your results and mine isn't related to sample size; it's due to the fact that the equations are different.

You used a different formula [BB/(BB+SO)] in your regressions than the one [K/(K+BB)] you asked me run.

In any event, if BB/(BB+SO) to ERA is .62 and SO/P is .62 "when P is estimated as BFP*3.3+SO*1.5+BB*2.2 (Actual pitches may result in a better correrlation)," I don't understand how BB/(BB+SO) and BB/IP can have more influence than SO/P, which you say "has almost no influence."

"You used a different formula [BB/(BB+SO)] in your regressions than the one [K/(K+BB)] you asked me run."

Actually, they are directly related.

BB/(BB+SO) + SO/(SO+BB) = 1

So, regardless of which of the two terms you use, you will get identical correlations (just different coefficients).

***

The sample size doesn't simply relate to the number of samples, but to how relevant each sample is. In my case, every single pitcher had at least 1000 BFP. In your case, maybe 1 or 2 did.

***

Three posts later in that thread, I retracted my statement about running the regression with all the variables, because they are clearly not independent. The rest of the post stands however, and all these "two or three variable" metrics have a .6x correlation. FIP stands tall at .84.

It should be retold that I used an estimate for pitches, and it is possible, though highly unlikely, that using actual pitch counts would have yielded a better correlation. The reason I say "highly unlikely" is that this simple pitch count estimator has a high .9x correlation to actual pitch counts. It doesn't seem reasonable to think that using actual pitch counts will change the correlation that much, if at all.