The Peter Principle and Regression Toward the Mean

You work hard at your game. You read books and magazines. You practice live and online. You watch videos and TV. You run simulations, you talk to friends, you read discussion groups, and you keep detailed records and notes. Yet, there are forces that conspire to belittle all you've learned, to deny your excellent results, to turn your cash wins into losses, and to tell you whatever gains you've made are illusory.



OK, maybe I'm being overly dramatic. And if you're really doing all that work, I'm willing to admit you're probably at least on the path to being a pretty good player, even if it doesn't come naturally to you. But although I was mostly joking about malevolent forces, there are a few simple principles that could be seen as conspiring to make sure your road to poker success is bumpy.



Two of these forces are logical principles that make no specific reference to poker, yet could not have been more perfectly crafted to reflect the game. The Peter Principle holds that in a hierarchical organization, employees tend to rise through promotion to their level of incompetence. Regression toward the mean is a statistical principle that explains why the results of extreme performers tend to overestimate their true abilities. The one seems to explain, or at least describe, the ebb and flow of poker. The other seems to explain why a player who is killing the games probably isn't as great a player as it seems.



The Peter Principle is often described, informally, in linear terms; each successive job is somehow more demanding than the one below it, and each employee has some maximum level of demands he can handle. In real life (and as originally articulated by Laurence J. Peter, the principle's author), things are more complex. People don't always get promoted to more complex versions of the same jobs. Programmers with excellent technical skills may get promoted to management positions in which those skills are of little use. In fact, it's not even specific to promotion. All sorts of people are hired to do one job just because of their skill at another. Sometimes it's a good idea, other times not.



Does the Peter Principle work with poker? Somewhat. In the real world, so the principle holds, you can rise to your level of incompetence and stay there. In poker, there's a natural force that tends to "unpromote" you, so to speak, and leave your wallet a bit lighter on the way down. However, the Peter Principle does teach us a few important things about the natural consequences of ladder climbing. First, and most importantly, success at one level of poker doesn't guarantee success at the next. Even if the players at the next level are no better, the game may require different skills, skills that may be less well-suited to your natural talents. Second, clearly not everyone is both talented and dedicated enough to learn to beat every game. If your goal is to push your game as far as you can, that puts you on a collision course with failure. While it would be nice to believe you could immediately recognize when you've hit that wall, it's not hard to imagine coming by that recognition the hard way.



Regression toward the mean is somewhat more subtle, but here's a quick primer. Lots of things in the world are determined by a combination of some true value (for example, skill) and some random value (for example, luck). Even when we know luck can play a role, we don't always know what kind of role it's played. Take bowling, for example (I know nothing about bowling, but it seems like a nice example). Suppose the average serious bowler averages 170. When someone bowls 200, we don't know if he's having an unusually good day, a slightly off day, or something in between. But if all we know is that one score, our best guess is that both his true average and the contribution of luck to that particular score were above average. (Bayesian principles can tell us a few things about the balance, but that's a story for another day.) Unfortunately, while the true score won't change much before the next game, you can't count on good luck from one game to the next. As a consequence, when you see someone bowl a 200, and everything else you know about him suggests he should be a 170 bowler, you should expect something closer to that average score the second time. In Bayesian terms, your posterior estimate of the true average will be somewhere between the prior estimate (170) and the new observation (200).



This general mechanism operates across many areas. Whenever you see an extreme performer, the score is more likely to be an overestimate of the true score than an underestimate. Take a second measurement, and you should naturally expect it to be closer to the mean. This is nowhere truer than in poker, where the average player loses money. If someone tells you he's been doing well since starting to play a year earlier, you would be reasonable to guess they're an above-average poker novice. But you'd also be justified in predicting some regression toward the mean. This doesn't mean that everyone who wins at poker is really a loser, and there are likely some players who, even with their impressive results, are actually better players than their results would seem to indicate. But more typically, as the saying goes, you're never as good as you look after a big win, or as bad as you look after a big loss.



Are these two principles similar? Regression toward the mean is a statistical/logical necessity, while the Peter Principle is just a reflection of something organizations do poorly, but conceivably don't have to. Neither promotes the most optimistic outlook, especially if you were trying to enjoy your winning streak. But, they're both useful in promoting a healthy respect for some of the variability in poker outcomes.

Daniel Kimberg is the author of Serious Poker and maintains a web site for serious poker players at www.seriouspoker.com/. You can contact him at [email protected].