# Cubs Den

## EconoBall: The Value of Strikeouts to a Pitcher

I've recently uncovered a source of data that will allow me to write a series of articles I've been thinking about for a long time.  What I plan to do is look at sabermetrics through an economists eyes.  Sabermetrics is a term everyone here is familiar with.  In short, it seeks to better understand baseball performance through advanced statistical analysis.  FIP replaces ERA.  OPS take the place of batting average.  Economics you may be less familiar with.  Modern economics has developed a comprehensive set of tools for analyzing large sets of data.  Economists who write for large audiences, such as Paul Krugman or Steven Landsburg, tend to speak in broader terms so that they're more interesting to more people.  However, detailed statistical analysis underlies all (well, most) of their claims.

In the simplest terms, then, I plan to use economic tools to answer Sabermetric questions.  This marriage has been tried before, in the now defunct Sabernormics blog.  I plan to expand upon this and build the work in slightly new directions hence the new name "Econoball."

The first question I'd like to explore is something that's come up in the comments section of late: old school pitching stats like ERA and WHIP vs. sabermetric stats like strikeouts.  The argument goes that ERA and WHIP give a better indicator than Sabermetric stats because, at the end of the day, the goal of the game is to keep runners off base and limit the runs the opponent scores.  Sabermetricians respond that strikeouts, walks, and home runs are the only things a pitcher has direct control over and, moreover, give a better picture of what the pitcher has done independent of poor luck such as fielding.

The key to the debate is really whether or not there is direct relationship between strikeouts and ERA and WHIP.  If there is an absolute distinction between pitchers and "brain-dead heavers," as Maddux put it, we should see no connection between strikeouts and ERA or WHIP.  That is, some pitchers with high strikeouts will have a low ERA and WHIP and others will have a high ERA and WHIP, and the same holds true for low strikeout pitchers.  However, if power pitchers are systematically more likely to have success, they should systematically give up fewer hits and runs and, as such, have lower ERAs and WHIPs.

The tool I'll use to investigate this is a linear regression.  (The workhorse in economics.)  A linear regression tries to fit data points into the following equation:

Y=α+βX+ γZ+ ε

Here, Y is our variable of interest (the dependent variable).  We're trying to understand what impact one or more X variables (the independent variables) have on Y.  (That impact is β.)  Often, control variables will also be employed (Z in the equation above), these are factors that might impact the dependent variable that we want to control for when we look at the impact of X on Y.  For example, if we were interested in the impact of father's height on child's height, we'd want to control for mother's height and the child's diet.  ε is an error term which represents statistical noise or omitted variables.  In the example of the child's height, for example, we know there are differences in height between siblings, even though they have the same parents and diets.  The error term catches this.  Mechanically, the error term is the difference between the prediction for Y and the actual value of Y.  The goal of regression is to minimize errors.

To test the hypothesis that strikeouts, walks, and home runs impact ERA and WHIP, I started by pulling data on every pitcher who threw more than 10 innings last season.  I collected data from the 2013 season on a pitcher's K/9, BB/9, HR/9, ERA, WHIP, starting status (started more than 90% of the games he appeared in), and his team.  I then regressed both the ERA and the WHIP on K/9, BB/9, and HR/9, controlling for starter and team.  The team variable should absorb the impact of two different things, team defense and home stadium effects.  For simplicity, I dropped the 42 pitchers who pitched for more than 1 team.  (Including them as a 31st team does not impact the results.)  This leaves me 524 players.

The results for ERA are as follows:

• ERA decreases by .18 points per 1 point increase in K/9.
• ERA increases by .34 points per 1 point increase in BB/9.
• ERA increases by 1.56 points per 1 point increase in HR/9.

All three of these effects are highly significant.  I can say with 99% certainty that they have an impact different than zero on ERA.  Interpreting this, a one point increase in HR/9 having an impact of more than 1 on ERA (ER/9 ip) makes sense as the home run automatically leads to one run, usually earned.  Walks emerge as killers.  Going from 4.86 BB/9 ip (the average of the bottom quartile) to 1.95 BB/9 ip (the average of the top quartile) would be associated with .99 point decrease in ERA.  The same exercise with K/9 IP (5.46 to 10.18) results in a .85 point decrease in ERA.  Simply: high strikeout pitchers tend to give up fewer runs, all else equal.

The results for WHIP are

• WHIP decreases by .046 points per 1 point increase in K/9.
• WHIP increases by .12 points per 1 point increase in BB/9.
• WHIP increases by .14 points per 1 point increase in HR/9.

Again, all three are different than zero with 99% certainty.  Just looking at calculations, a 1 point increase in BB/9 should increase WHIP by .11.  Interestingly, the .12 I find in the regression is not statistically different from .11.  A HR is just one hit, so it should also increase WHIP by .11, a one point increase in HR increases WHIP by more than .11.  It's possible that this reflects the fact that pitchers who give up more home runs are more likely to make mistakes that are hit for singles than pitchers who give up fewer home runs.  Alternatively, these pitchers may have more control issues and, hence, walk more batters.  Most likely, it's a combination of the two.

However, strikeouts is interesting here.  What explains the connection between strikeouts and WHIP?  Pitchers who pitch to contact open themselves up to bad luck.  A "ground ball with eyes," a "texas league single," these can't happen to a hitter who strikes out.  The number above suggests that about 4.6% of the time, when a ball is put in play, it finds a way through the defense.  So, a strikeout removes that chance.  (The 4.6% is very rough -- a much better experiment would be required to find the exact percentage.)

So, we see here that the Sabermetricians do have solid ground in using strikeouts, walks, and home runs in their analysis.  The next question, which I hope to address next week, is whether power pitchers are more likely to repeat strong performances year over year.

Filed under: Uncategorized

• Excuse me... my Brain is full, may be I excused?

One of my favorite Far Side cartoons.

I'm sure it was a wonderful article, but I'm not bright enough to fight my eyes glazing over. That is on ME, though.

• Good stuff Mike.

I think that the issue with the strikeout pitcher is that they are generally hard throwers that walk a lot guys, throw a lot of pitches and have shorter outings putting more stress on a bullpen.

It seems like it is difficult finding a pitcher out there that has good control with a high K/9 rate - there certainly are some but again, not as prevelant as we would like.

I think this is a good starting point. Mike can probably go a lot of directions from here, so whatever ideas you all can give are welcome.

John beat me to it, but this is an excellent point. I'll have to find a way to test that -- it could definitely change things some.

• In reply to Mike Moody:

So many good things here. As someone with a psychology and economics degree (undergrad though, not grad), I'm loving it. I'd also love to see the meathead fan responses. BUT...TWTW!!!

You could run some similar tests with innings pitched as the Y variable, no? Perhaps with starters only, or maybe separating starters and relievers?

You better be careful, Mike -- if you keep throwing articles like this out here, I'll be shooting ideas out the wazoo like an excited school nerd.

• In reply to Mike Moody:

Is there a good site to get info on pitches a pitcher has thrown for swing and misses? Was going to look into the whiff rates of different breaking balls but didn't know if there was a good site that you used? Looked at fangraphs but didn't really find anything thanks

• In reply to T dizzle:

Try BrooksBaseball.net

Here's a link to Kershaw's whiff rates with each pitch as an example.

Give you lots of options on how to view. Caution: You can waste many hours looking through that site :)

• In reply to John Arguello:

Thanks. Oh I know spent like 3 hours last night looking thru stuff and it felt like 15 minutes lol

• This is really interesting, Mike. I enjoyed the objective analysis.

The data certainly seems to show strikeouts have a positive impact on performance. Maybe a good follow-up would be how velocity ties in with strikeout rates. From there I suppose we can assume that as a rule, velocity positively affects strikeout rates which in turn positively affects ERA.

• In reply to John Arguello:

How would you do an objective analysis on velocity?

I mean for example, every pitcher (Shark is still learning this) needs more than max gas in his repertoire. So it doesn't matter if your FB is 98 and CU is 88, it's the difference in velocity that disrupted the hitters timing and thus caused the swing and miss. That is the same scenario if the pitchers FB is 91 and his CU is 83.... Then you've got breaking balls some are hard like sliders and others not so hard... What am I missing?

You guys are actually a step ahead of me here. I'm definitely working on analyses using velocity.

Both posts are good points on things to consider. Keep it coming!

• In reply to Mike Moody:

I would be curious to see the difference in average ball break on different breaking balls and the comparison between that an speeds, i.e. is it more efficient to throw a hard curve or a looping 12-6. It would seem difficult to draw that up, however.

The other things that immediately popped into my head were wild pitch count and pitches thrown. Both would be easier to quantify, and may have some curious, Dock Ellisian, results.

The former is cool but, as you say, it would take access to Theo's personal database to really get at that one. The data would be very difficult to find.

The latter is interesting. I'll look and see if information for that is available.

I believe you are missing more than Shark. He gets more of his strikeouts from his changeup/split than from his fastball, a fact of which he is aware and commented on numerous times. The big problem for Jeff is that he has a lot more problems controlling his split than most pitchers do a changeup which is easier to control. Perhaps if he added a circle change which breaks less sharply than the split he would fool more hitters and have less pitches taken for balls, thus increasing his average innings per start and cutting down on his pitches per game.

• Great stuff. Strikeouts and HR's are the new stats! lol.

Thanks. The new-fangled stat is FIP, which just blends HR, K, and BB into one number. :)

• So it takes 2 ks to negate one BB and 5 walks are as bad as one HR.

Yes, this analysis suggests that walks are very bad, indeed. Knowledge of this may well be why pitchers with high walk totals fare much worse in MLB than pitchers with low strikeout totals. (Though high strikeouts and low walks is obviously ideal.)

• Intuitively this makes sense too. As you alluded to, the more bats you miss, the less balls in play, the less balls in play, the less that fall in for a hit.

• For anybody who does not understand this, it can literally be explained by any entry level statistics class. Nice job Mike. This is actually a type of thing that, if I were not busy with college, I would be interested in assisting with.

I've actually taught such a class. :-)

• In reply to Mike Moody:

I actually passed such a class, barely!

• In reply to Mike Moody:

Many moons ago I passed a couple such classes. Actually could set up and do the SAS programming language to run ANOVAs and Multiple Regression analyses,....

Rarely use anything more complex than a T-test or Pearson's correlation at this stage of my life.

My wife (if she had any interest in baseball,.... she doesn't btw) could probably do some interesting things with these sorts of data. She's a 'messy data' demographic modeler now doing freelance stuff with medical testing data. She starts talking about that stuff I just do a lot of nodding and smiling,.....

Let us know if you have time in the summer.

• In reply to John Arguello:

Will do John

I certainly want to give elusivekarp first dibs, as he mentioned it first, but I'd also be happy to help. My day job isn't that stat-heavy per se but it involves taking numbers and making stories out of them. WIth the numbers at your disposal I bet you could do a ton of cool things with this stuff.

• The number above suggests that about 4.6% of the time, when a ball is put in play, it finds a way through the defense.

I thought BABIP was the stat that shows batting average of balls put into play, and the average is a helluva lot higher than .046

Either you didn't splain yourself perfectly or you gots some missing maths somewhere

• In reply to Rob Letterly:

Not quite the same thing.

BABIP gives the batting average on balls in play. Some of those are screaming line drives, for example, and are likely to be hits anyway.

However, notice that a strikeout shouldn't, by itself, reduce the walks and hits in an inning. One out is as good as another. Yet, for some reason, WHIP shrinks when the pitcher throws a strikeout. So, if the batter doesn't strike out -- that is, puts a bat on the ball -- WHIP goes up. One explanation for that is that balls in play that *should* be outs find their way through the defense. And the data suggests that happens about 4.6% of the time.

• In reply to Rob Letterly:

Another explanation is that, because of the pitches they throw, strikeout pitchers are systematically more difficult to hit, so the relationship between high K/9 and lower WHIP is attributable to that. Definitely worth testing -- however that, also, works against the idea that strikeout pitchers are not more valuable than pitch-to-contact pitchers.

• My amature conclusion is that if one is not a strikeout pitcher, he better keep the ball in the park and not give up any walks, if he wants to play with the big boys.

Definitely one way to read it.

• In reply to Mike Moody:

Basically the reason Travis Wood had success last year. Hopefully Samardzija can lower lower his HR/FB rate and fulfill the potential of his great K/9.

• Great read. I enjoyed the data. Of course it's a little dense, but you explained it very well.
Mike, you stated that you're a PH D student in economics. Are you able to integrate your baseball fandom/love for statistics into your academic program?
I had interest in economics as a high schooler, but went a very different direction. However, I'm fascinated in seeing the academic backgrounds of all the FO types.

There is a fairly large branch of economics called sports economics, so I theoretically could integrate my love of baseball into my program. However, I've decided to focus on economic history (My dissertation looks at the impact of high school quality on economic development; the second I finished working on this, I started looking at census data -- which is fun for me, too!), so this is kind of a hobby using stuff I love.

• In reply to Mike Moody:

Cool stuff Mike. I enjoy reading your work and it's cool to know a little more of the lens it comes from. My favorite times in grad school was when I was able to integrate multiple areas of my life.
Actually, my reward for myself for finishing grad school was my first trip to Wrigley (lived in Oregon at the time).

I've actually fallen in love with minor league baseball since starting grad school. I was the opposite of you, lived in Chicago pre-grad school and moved south for grad school.

I should have a web page going up within the next six months or so. With John's permission, I'll post a link on the site for anyone whose interested in my non-baseball work. (One way or another, there will be a link on my Twitter page.)

• Nice piece Mike, I've taken my share of data analysis and regression classes so I know all about statistical significance, beta coefficients, and t-values :)

Count me in, if you guys happen to need a hand for this in the future. I'm pretty good with R.

Awesome, this is pretty much a work in progress, so I'm still figuring out what resources I'm going to need. (I use STATA, though I probably should learn R because the world is going non-parametric and R is so far ahead in non-parametric regressions that isn't even funny.)

• Very interesting article Mike. It's a good starting point, as others have mentioned, and I would like to see the difference in impact between strikeouts & other types of outs at the plate (lineouts, flyouts, & groundouts). Because to me, strikeouts should affect ERA & WHIP, as should all outs, and as should all non outs. Unless this was covered already in the equation -- it's been quite a while since I took statistics ;)

• Have you looked at the interaction compontents between BB/9 and K/9 relationships?

For example - is there more, or less a correlation seen when you look at BB/K rates for individual pitchers (or rather for their collective) to ERA or WHIP?

It would seem to me that the real statistic to look at - although there might be some plateau or critical value below which a correlation appears or disappears?

So the quick response is that the correlation between BB/9 and K/9 is pretty low (.0768). However, looking deeper at interactions might lead to some interesting results.

• In reply to Mike Moody:

Lower correlation than I might have initially expected,... but hey,... that's why you do the analyses.

It'll be interesting to see what some of that deeper digging might find. My guess (also) is a lot of success/failure especially for the pitch to contact guys (regardless of their absolute K/9) is dependent on the defense behind them.

• Nice analysis, but please excuse my random questions:

So where does this analysis leave a pitcher like Rick Reuschel who nearly always pitched to contact? As a better pitcher or worse?

How does this affect strikeout pitchers who as a result of consistently high strikeout numbers, have higher than usual pitch counts? Does it increase or decrease their value to a ball club, long term?

How does this affect fielders as far as keeping them alert and mentally in the game?

How do strikeout pitchers ultimately affect the game itself by reducing the amount of action on the field by turning the game into more of a pitch and catch game?

"How does this affect fielders as far as keeping them alert and mentally in the game?"

Ooo, That would be some awesome analysis.

Reuschel is an odd guy -- he fits in with the analysis above, but he survives lower K/9 with low BB/9 and very low HR/9. Also, his WHIPs are relatively high, which fits with this. That seems likely connected to very low HR totals.

The others are good questions. Long term is going to require looking at multiple years of data and finding pitch counts. It's an interesting place to go.

The latter two questions are worth looking at further however, on the surface, it seems that any benefits the pitch-to-contact pitcher gets from keeping his infield in the game are outweighed by the strikeout pitcher's ability to keep guys off base. If I can show that those two factors are working here, it would suggest that strikeout pitchers actually save more runs than I found, because the defense "goes to sleep" behind them.

• In reply to Mike Moody:

I'm sure you are correct in your last statement, but I think you meant "despite the defense going to sleep". I do think the difference in runs allowed would be closer than the numbers would suggest.

Looking at long pitch counts long term might not help, especially when if you consider what went on in the 60's, with complete games numbering above 25 or even 30 for pitchers like Gibson and Jenkins and the thought that starters were supposed to pitch 300 or more innings a season. Those guys rarely had arm problems despite all the pitches thrown.

• Great Job Mike, Bill James and Ludwig Von Mises would be proud, but it wouldn't matter how hard you tried to break it down for mass consumption, the Jim Hendry and John Mayanrd Keynes fans wouldn't have gotten it. Somewhere, as I type this response, a Keynesian is trying to determine how many windows a 95 mph fastball can break so that they can create jobs replacing them.

• In reply to Michael Caldwell:

Keynes is such a politicized figure now that bringing him into a baseball discussion probably isn't a good idea. Let's leave Democrat or Republican out of this, agreed?

You essentially called people who think that demand drives an economy dolts. Is that really necessary?

Oh boy, a Krugman and Bernyankme fan. For the record, I never brought up D's and R's, as if there's a difference, you did. The joke was for Moody, who I knew would appreciate it. Sorry if you were offended, but while we're at. The Austrian school is not Republican. It's libertarian.

• In reply to Michael Caldwell:

I never said who I agree with or don't. You're making assumptions about me, but I'm not offended so no apology needed.

What I did say is you're bringing politicized economics into a baseball blog and smearing one side. There's no call for that. Just keep it out of here, okay? Let's keep it to baseball.

Agreed. Wwasn't around last night so I missed the comments, but I think yours sums up my my thoughts on the matter well. Let's keep this about baseball.

• In reply to John Arguello:

John, I know there has been little talk of it. But I think
the Cubs should go after one of the top pitchers this
year (santana,jiminez or burnett) and maybe they're
waiting for the price to hit rock bottom. Some of these
guys can be picked up for 2 or 3 year deals and they
can be flipped at any time. If you are going to flip assets
wouldnt you want the best assets to flip?

I don't agree with that one, bleachercreature I've been on a stance against signing those kind of large multi-year deals for 30 year old pitchers. The high 2nd round pick is a big factor, so you'd have to subtract that value (picks in that range have included top 10 guy Johnson and a couple of top 15 prospects in Zastryzny and Blackburn). You'd also have to pay a chunk of those guys salaries if you want good prospects as I don't think they'll sign for 2 years. You wind up buying a guy for \$40-60M to get another win or two, then hope he stays healthy and effective enough for him to trade for value higher than that of a top 10-15 prospect.

I think it can work out, but a lot of things than can go wrong. It's a risky, roundabout way to get an extra prospect. Too many factors outside the Cubs control and they try to avoid those situations. We haven't seen any team really employ this strategy except for the Marlins and their prospect haul for Reyes, Buehrle, et al wasn't all that special.

• In reply to John Arguello:

John, thats right the 2nd round pick and eating a chunk
of the salary are a negative. But 2 or 3 year deals I wouldnt
consider long term deals. If you get a top 10 pick back then
you have traded a 2nd round pick (lost in the signing) for a
1st round type pick (received in the deal) for \$10million or
so and maybe a lot more if a team is desperate. I read
Santana can be had for 3yr/\$11mil per, but ya if you get stuck
with even half that salary then that is pretty expensive.

It is one strategy and I understand the argument for it, but it's too much risk for too little reward for my tastes.

• Here is another one.

What is the liklihood that a pitcher will have favorable ratios for all 3 categories?

i.e. we can see many cases where a high K rate can lead to a high BB rate. But what about a high HR rate as compared to a high K rate or BB rate?

I looked at Fergie, Maddux and Schilling real quick as I know those are three of a handful of pitchers that have over 3000K's and less than 1000 BB's and took a look at what their HR rate was. Sadly, I don't know what a good HR rate is, so couldn't draw any conclusions, but hoped these examples kind of explained my question a bit better.

They are actually 75% of an exclusive quartet that also included Pedro Martinez.

• Good piece Mike, great research.

I may see this a little different than others, but I can just see how all of these stats are related...

For example, take an old school stats like whip... Which is walks + hit per inning pitched... I bet that the lower the whip, the lower the opponent obp and we know how important obp is whether you're pitching or hitting.

A pitcher with a low whip and low obp, but a high era, even with a high hr rate can be considered as having bad luck, because the peripherals more often than not, will look good... Even hr's are related to park factor.

In the other hand, a pitcher with a high whip, but low era could be considered lucky for the same reasons explained but reversed.

To expand on your K/9 point... We know that BABIP in MLB is roughly around .300 and that's standard, so, looking for a low BABIP pitcher is not going to be efficient since that number will likely just jump back up to the standard .300... So what you can control is to look for a pitcher that reduces the rate in which opposing hitters put the ball in play, in other words, a pitcher that can miss bats.

So, I pretty much agree with the fact that low walk, high K pitchers capable of keeping the ball in the park are the 3 main attributes to look for, as long as these pitchers have a track record for doing this and not just a fluke season.

The WHIP, IMO is a stat that serves as a bridge for you to look into other stats.

• Well done Mike. Where do I send my tuition check for Econoball 101?

Just keep tuning in :)

• Future suggestions:

Pitches / out -- how long does it take a pitcher to record an out? Thinking of strikeouts, every pitcher would obviously prefer a 3-pitch strikeout to one that has a bunch of fouled-off pitches.

Percentage of pitches thrown for strikes -- similar idea, but could show general control and efficiency.

Salaries -- this could get into an easy way to show market inefficiencies with pitchers.

Similar stuff with RISP -- this could get into how well a pitcher can "dig down"... or could largely be a component of luck.

Comparing pitching measures to BABIP -- who can induce weak contact vs. throwing meatballs out there? Could also be simply a measure of luck.

• In reply to Matt Mosconi:

Your thinking on this is *almost* as nerdy as mine.

:D

• In reply to Matt Mosconi:

Salaries is fascinating stuff. That actually goes into the realm of "real" economics -- athlete pay is usually the most interesting subject, by far, to undergrads in a labor economics class. But the idea of what forms an athlete's "worth" could use some better definition. A good example of this is John talking about how Tanaka was a marketable commodity for the Cubs. In that sense, he would have provided value to the team above and beyond his performance on the field. Anthony Rizzo's community involvement is another example of this.

• This is good stuff. Looking forward to more of it.

• Nice article, as long as the pitcher stays healthy! My HS Baseball Coach told me once as I was trying to show him the stats I had compiled for the opposing pitchers for our upcoming Regional game. He said "Stats are for Losers!" and walked away. The next day, we got shelled, and lost the Regional due to one of those pitchers striking out 8 and only giving up 2 hits.Maybe he should've listened to me. That was back in 1975!

• I'm much more of a "saber-fanboy" than a sabermetrician, so I'm glad you're here to explain how these better statistics are built and why they are better than the old school numbers we all grew up with.

• Thanks for a great article, Mike. It was a piece this mathematics major could sink his teeth into and really enjoy.

I haven't read all of the comments, so maybe this was addressed, but every time the sabermetric state that pitchers can only control strikeouts, walks, and homeruns I think of pitchers like Mariano Rivera.

In 2009 Rivera threw his cutter 92.9% at an average of 91.3 MPH. Batters knew what was coming and it wasn't like he was rushing it up there like Aroldis Chapman, yet his K/9 was 9.77 and his BABIP was .248. Both, pretty decent numbers for a one pitch pitcher.

Movement and location are key. To steal one of John's words: pitchability. I would not put Rivera in the power pitcher category, and his K/9 may resemble that of a lot of the "brain dead heavers", but he could spot a nasty pitch that was good at chewing up bats.

Find a way to measure pitchability through a linear regression model and you'll find yourself working for Theo. Just my two cents.

• Carlos Rodriquez?

I was skimming through a 2014 baseball prospect book last night from Joseph Werner (The 2014 Prospect Digest Annual). He has a list of the top 300 baseball prospects. In at # 238 (which would have been the Cubs #13 prospect - just behind Arodys and just before Vitters and Candelario) - was an 18 year-old LHP named Carlos Rodriquez.

Anybody heard of him? I went back and checked all of the prospect list on this site and didn't see any mention of him. I am aware (and excited) to watch the progress of the Conway's and McNeil's of the Cubs' world, but never have seen mention of him.

Looks like Az. Phil has him listed as likely to be in the bullpen at Kane County this year.

Oh yeah, John has talked about him here... Not a lot of upside, but not a lot of risk either... He pitched for AZUCAR last year at the age of 17, he's very advanced for his age, has good command but doesn't have a plus pitch that I know of just yet.

• So brooks baseball website has everything. I was wondering if there was a related site for minor league players? Probly not since minor league parks are not equipped with the same technology but just wondering???
Thanks

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