Strikeouts and the Anna Karenina Principle, or: Why K’s Don’t Hurt MLB Batters

By David Roher

“Happy families are all alike; every unhappy family is unhappy in its own way.”
Leo Tolstoy’s beard, seen here giving Bruce Sutter’s beard a run for its money.

So begins Leo Tolstoy’s 1878 masterpiece, Anna Karenina, an engrossing novel about late 19th century statistical analysis in baseball. Or about Russian aristocratic society. I’m not sure; I read it pretty quickly.

I only had to pay attention for the first sentence, since it’s only the above quote that’s pertinent. Its meaning is essentially that in order for a family to be happy, a lot of different things need to work out, while only one of those things needs to fail in order for a family to be unhappy. Scholars and authors like Jared Diamond have extended this idea beyond families: the “Anna Karenina principle” is that any one factor can cause the failure of its system. An important corollary is that if the system does indeed work, then it inherently possesses all of those factors.

After the jump, I’ll try to use this principle to answer a perplexing question: why do Major League hitters who strike out more perform better?

One of the main points espoused by sabermetricians in the early days was that high strikeout hitters could still be very valuable, and that the ability to avoid striking out was highly overrated. But it is nevertheless bizarre to me that, every single year, strikeout rate never inversely correlates with offensive production.

Maybe this isn’t as weird to you as it is to me. Think about it this way: strikeout rate is simply a subset of overall out rate, which is another way to express on-base percentage (it’s 1 minus OBP). OBP is extremely highly correlated to production: in 2009, 82% of the difference among qualified players in wOBA, a great measure of overall hitting production, could be explained by OBP. Furthermore, strikeouts are integral in evaluating pitching production: 46% of the change among qualified pitchers in FIP, a great measure of overall pitching skill, can be explained by strikeout rate.

So given all that, wouldn’t you expect strikeout rate to be at least a little predictive for hitters? Well, it is – in the wrong direction. In 2009, strikeout rate among qualified hitters explained 5% of the change in wOBA – a small but statistically significant figure (P = .001), and the coefficient was positive. In other words, the more a qualified hitter struck out in 2009, the better he probably was.

I’ve thought for a while about how this could be. When I learned about the Anna Karenina principle last semester, it hit me. Here’s how that quote applies to baseball and athletics in general: I believe that in order for an athlete to reach an elite level, there are some skills and attributes that he or she must possess. If they don’t possess a certain trait, then they can’t make it. I see this on a daily basis on our rowing team: different rowers have different strengths and weaknesses, but because of the selection bias it takes to assemble an elite team, they all have a lot in common: every rower in our first varsity lightweight boat last year was between 5’10” and 6’2″, for instance. That’s an example of the Anna Karenina principle at work: a rower could have the technique, strength, commitment, bizarre willingness to wake up early in the morning as a college student, etc. necessary to row well, but if he were my height, he’d have too much trouble getting the necessary length through the water on each stroke, and couldn’t compete on an elite level. And if he were too tall, he would not be able to make the weight limit with a body type conducive to rowing well. (Great lightweight rowers can be out of that specific height range, but likely not by more than a couple inches on either end.)

Even in baseball, where there are different positions and different approaches to hitting that enable a wider possible skill set than that of crew, this is still the case. Case in point: every single qualified pitcher in 2009, no matter what type of pitcher he was, threw a fastball that averaged at least 84.7 miles per hour with some semblance of control. All but 5 pitchers averaged over 88 miles per hour. Think about what percent of pitchers in the world can do that – it’s far from 100%.

Here’s my hypothesis for strikeout rate: in order for a hitter to be good enough to get at least 3.1 plate appearances per game in Major League Baseball, he has to possess some skill that prevents him from being unduly penalized by strikeouts. The way to test this hypothesis is to look at the relationship between production and strikeout rate in minor league ball. If we start to see a change from a positive correlation to no correlation to, finally, negative correlation as we move down the ranks, there’s strong evidence that the Karenina principle is at work: hitters who are too vulnerable to the strikeout will get weeded out and thus won’t move up any further than that level (or, they’ll acquire the skill).


R^2 is a measure of how well strikeout rate predicts wOBA. P-value is a measure of significance; if it is below .05, then the results are statistically significant. Coeff. (+/-) is the nature of the relationship: if more strikeouts means more production, then it’s positive. If it means less, then it’s negative.

Level R^2 P-Value Coefficient +/-
ML 0.0598 0.0013 +
AAA 0.0261 0.0215 +
AA 0.0048 0.3758 Neither
A+ 0.0013 0.6457 Neither
A 0.0098 0.1078 Neither
A- 0.0481 0.0063
R 0.0651 <.0001

As you can see, strikeouts are positively correlated with offensive production in the Majors and AAA ball. In the middle three levels, there is no significant relationship. But in Short-Season A ball and Rookie ball, there is a negative correlation.


My findings support the existence of the Anna Karenina principle in this case. Players who strike out more are less likely to succeed in the lowest levels, and there is a smooth transition from the Majors to Rookie ball. If I were to examine college and high school ball, I think we’d see the R^2 values continue to increase.

I think it’s a compelling explanation for why players who strike out a lot are still able to succeed. It might also lend a view into how hitting and pitching change as players move up the ladder: it looks like the “weeding out” is mostly happening between A- and AA ball. I’d be curious to see if we could find the same thing through scouting.

Can anyone else think of a case in sports where the Anna Karenina principle (or just simple selection/survivor bias) explains something similar?

(All data from (where else?) Fangraphs.)

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  • Excellent post. I’ve argued in the past that strikeouts don’t matter to hitters because players who really strike out a lot never make it to the majors. That’s why there is probably an upper limit on the major league strikeout record of around 200. A player who struck out 300 times in a season can’t put the ball in play enough to make up for the high K rate.

    • That’s a very interesting hypothesis. I wonder if it’s affected by the quality of the record-setters. Reynolds, Dunn, and Howard, the guys who have been rewriting the strikeout record books over the past few years, generally have great seasons when they K that much. Reynolds obliterated the record with 233 this year, and was still one of the top 30 or so hitters in the league. Does that mean he could stand to strike out even more?

      It would be interesting to empirically find that breaking point of K rate where a player wouldn’t be allowed to get at bats anymore. Obviously it would depend on the quality of the team as well as the quality of the player. I’d also like to find how strikeouts eat into other results – are they taking bites out of GB totals, FBs, the 4 different hit types, etc. Perhaps a future blog post.

    • Actually, David, I think you have the story precisely backwards. Strikeouts “don’t matter” in the majors because the only high-K hitters who make it in the majors have other offsetting skills (power and/or BBs). This is a survivor bias we’re seeing. Players who strike out a lot do make it to the majors, but only if they have other skills.

      Speed is similar. The correlation between speed and wOBA is either zero or negative. Is that because all the slow players were weeded out in the minors? Not at all. It’s because the only slow guys who survive are those who can do other things well. Speed and avoiding Ks are both good things, all else equal — but all other things are not in fact equal.

      A good example of what you’re talking about is pitchers’ BABIP. There pitchers have to exceed a basic threshold to advance — below about .315 — or they get screened out (and even at .315 you must be excellent on Ks, BBs, and/or HRs). The result is that at the MLB level the spread in pitcher BABIP is rather narrow.

      • You’re absolutely right in that strikeouts alone aren’t a good example of this, but the skill I’m talking about is not really avoiding Ks alone. It’s about preventing Ks from unduly interfering with production. The way I see it, a player who strikes out less than Adam Dunn could still have more of a problem with strikeouts than him. Take Brandon Inge, who strikes out 30% of the time and was below average. A pitcher can neutralize his production through striking him out, while he can’t do that with Dunn.

        Now, I realize that this *alone* is still what you’re saying – that it’s the other skills that allow Dunn to succeed, to overcome his K rate, and therefore it’s not the Anna Karenina principle. But here’s why I think it’s still there: Inge is good enough when he doesn’t strike out to be an above average player. If he reduced his K rate while holding all other at bat results proportionally constant (and even if they all got a little worse), he’d be a better player. That is NOT true for guys like Vernon Wells, who had production similar to Inge’s. If they struck out less often, they’d still suck. I realize all of these guys are still good enough to be in the majors, but if you just switch “average” with “replacement level” and find players in the minors who are similar, it’s the same thing. Inge wouldn’t be able to make MLB because he would strike out too much. It’s still a strikeout problem, just not one of raw K rate.

        I realize from the discussion over at Baseball Think Factory that I didn’t make this clear enough, and perhaps I’m still way off base in terms of the way I applied the principle. If you think that’s the case, I hope the data analysis alone still holds up.

        • I’m not sure it’s a helpful distinction to say one hitter’s strikeouts “interfere with his production” while another’s do not. A K is a K, with the same consequence for offense. What matters is what the two hitters accomplish on their other, non-K plate appearances — which is entirely a function of his other skills (BBs, BABIP, HRs).

          The AK principle seems to apply in cases where any weakness undercuts the entire performance. Maybe an offensive line in NFL is like that, since offense can target your weakest man. Probably applies pretty well in tennis: a player can’t reach the highest levels with a weak serve, forehand, or backhand, because any one of those can be exploited. But strikeouts for baseball hitters doesn’t seem like a good example, since the variance in K rates is enormous: the highest K rates are 5 times as high as the lowest — it would be hard to find a specific skill on which players are more diverse.

          What you might consider doing is tracking how much the variance in different skills narrows as players move up the food chain from A ball to MLB. My guess would be that the variance in some skills narrows, because they are essential for success. BA might be a good example of that. In contrast, there probably isn’t much narrowing with SBs or Ks — because these aren’t essential skills. (On the other hand, age differences may disguise the variance at lower levels: a 19-yr-old in AA may be a future star while a 23-yr-old teammate never makes the majors, but at that moment their skill isn’t so different. So this may or may not work.)

          • We’ll agree to disagree on the first point, then. I can’t say it’s “entirely a function of his other skills” if the baseline for that other production is heavily based on how much he strikes out. But I see where you’re coming from.

            I’m fine with there being better examples of the AK principle then Ks, especially since you’ve shown that it’s at best a difficult argument to make. All of those examples are great.

          • “I can’t say it’s “entirely a function of his other skills” if the baseline for that other production is heavily based on how much he strikes out.”

            David: I’m not sure if we disagree. Are you saying there’s a relationship between a player’s K-rate and other outcomes? I’m sure that’s true: if you told Adam Dunn he had to reduce his Ks even if it meant fewer BBs and HRs, I assume he could do that. So a hitter “buys” other things with his HRs, but how much they buy varies a lot. The guys who buy relatively few BBs and HRs aren’t very good hitters. Is that what you’re saying?

            If so, we’re saying the same thing. The hitters who “get more for their Ks” will perform better in other categories, and we’ll capture it there. And the high-K hitters will tend to be strong in those areas if they survive (and/or have defensive skills).

  • Roher, fantastic research. I really enjoyed the crew analogy. David Pinto, and Guy…really interesting analysis from everyone on this one.

    The idea of survivor bias reminds me of something that Bill James said at the MIT conference a few years ago. He was talking about watching minor leaguers with a scout and the scout said one guy was, “Slow to the ball.” James had no idea what he was talking about. The guy explained he just wasn’t getting his hands around quickly enough. James had never seen this before. Turns out, it’s something that just doesn’t happen with major leaguers (like a guy throwing an 82 mph fastball).

    Really, what we have here is a conditional situation…given that a guy makes the majors, it does not really matter how much he strikes out.

  • I think if someone(I’m a lazy individual) were to gather the data from mlb gameday pertaining to the velocity at which the ball leave the hitters bat(in relation to pitch speed) for all mlb hitter, they would fined that the players who hit the ball the “hardest” would tend to be grouped at the positive end of the correlation spectrum relating to strikeouts and general offensive performance(regardless of what metric is used). i.e. Guys who have marginal(for MLB qualifiers) contact skill and swing the bat with greater velocity will make more of their marginal skills(although producing more K’s) for the obvious reasons that a ball travelling at a greater velocity is harder to field(increasing his BABIP substantially enough to more than offset the increased strikeouts); that the harder you hit a fly ball the more likely it is to be hit out of play(HR); and that a pitcher is more likely to pitch cautiously, potentially walk a hitter that has a stronger record of offensive performance, there by “artificially” improving the hitter’s batting eye(and to some extent potentially covering up for a skill that the hitter is lacking)

  • Maybe this was implied, or was mentioned in the other comments, which I only skimmed, but your analysis seems to only answer ‘why is k-rate not negatively correlated to production?’ and doesn’t answer ‘why is k-rate specifically positively correlated to production?’ (As you said, the correlation is small, but still statistically significant)
    IE- Of the set of players in the MLB who have overcome above average k-rates, shouldn’t there some players who are at replacement level production, some who have MLB-average production, some that are better, and everything in between?
    If that’s true, then shouldn’t production from that set equal production from the set of players who don’t have above average k-rates?
    And if THAT’s true, then shouldn’t k-rate be zero-correlated to production?

    If my understand is right, perhaps the reasoning is that current evaluation methods place too high of an importance on k-rate so there are players with replacement level production, or slightly better production, but above average k-rates, so they aren’t called up. IE- because of evaluation methods, to make the majors (or be moved from AA to AAA etc.) with an above average k-rate, you don’t only have to have enough other tools that your production is good enough, you have to have enough other tools that you’re MORE than good enough and the evaluators can’t ignore you.

  • I’ve heard more and more that strikeouts don’t matter as much as we first thought, but I’ve yet to see the stats on players with lower strikeouts and their value to team wins, instead of individual statistics. A player could strike out a lot and still have a high batting avg, power, and RBI’s. Jim Edmonds was a good example of this. In his peak, he hit over .300 with power. One year, he hit over .400 when making contact. However, what are the TEAM effects of making unproductive outs. When a player strikes out, particulary with men on base, as opposed to making an out while advancing the runners, this hurts the TEAM’s ability to win. If a team starts off the inning with a single and walk (1st and 2nd, nobody out)…then one strikeout by the next player is huge. That would then leave the other team’s pitcher to only need to induce a double play ground ball. That batter that struck out may still hit .310 that year, but his inability to put the ball in play, productively, could cost his team.
    I don’t have the stats in front of me, but I doubt there has every been a team that led the league in strikeouts that went on the win the whole thing. In this past season, none of the top 11 teams in strikeouts made the playoffs. (the Yankees had the 4th lowest strikeout rate). So, in conclusion, I don’t think strikeouts matter to players in terms of earning power, as long as they can put up big power numbers. But, I do think that strikeouts over time can have a negative impact on wins.

  • How about in football, there are some great quarterbacks, who also happen to throw a lot of interceptions. although I’m not sure it strictly meets your requirement, since in general tossing a lot of picks is counterproductive.

  • Very interesting hypothesis, as I began to read I had two possible explanations. One you mentioned; a hitter who strikes out a lot and has made it to the major leagues likely posses another valuable such as power or speed. The other I think would be interesting to explore further. Strikeouts are obviously bad, but without looking up the numbers I believe a high strikeout rate for a batter is often paired with a high walk rate. If you attempt to draw a lot of walks you will undoubtedly strike out several times along the way. The opposite is not necessarily true, but I think it may be enough of a factor to skew strikeout data.

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