Understanding Regression to the Mean

Going into this year's final event at the World Series of Poker, would you have put your money on Phil Hellmuth, who was "due" to win an event, or Phil Ivey, who had already won three bracelets? Would you rather bet on a golfer who is on a hot streak or one who is due to have a good round? In golf, where confidence plays a factor in the outcome, a player's performance is very much dependent on his recent play. If you're flipping a coin, the outcome is independent of past events.

In poker, if you always play your "A" game, your outcome is independent of your previous sessions. But unless you're a robot (or Mark Gregorich), it's likely that your outcome is very much dependent on how you've been running. No one ever said that tilt, or confidence, can't carry over from one session to the next.

Play enough hours and you can compute a meaningful average, or mean, of your expected performance. If your performance starts to vary from that mean, the statisticians will tell you that, in time, it will regress back to its mean. If you've averaged winning one big bet an hour for the past 10 years and you're entering August stuck for the year, statistics are on your side. You would think that all you have to do is show up to win, as the poker gods will put things back in order and allow you to regress to your mean. But the other side of things is that, after having been beaten up for seven months, you're not likely to be the same player who won a big bet an hour for all those years.

Betting on regression to the mean is common in the stock market and is what led to the collapse of Long-Term Capital, a hedge fund made up of Nobel laureates and Wall Street mavens. I'm sure you've been there yourself. When a stock that has been trading at around $50 a share for a year drops to $20, your initial instinct might be that it will rebound to $50, and you'd be tempted to buy. If it had gone to $80, your initial instinct might be that it would regress to $50, and you'd be tempted to sell. But this thinking is flawed, as there's no such thing as a true "mean" for an item that is constantly fluctuating.

The key with stocks is to evaluate the reasons behind the diversion from the mean. If, after examining all the variables, you've determined that very little has changed besides investor sentiment, perhaps the stock will regress back to its "mean" in time. The problem, however, with betting on regression to the mean is that you assume that all variables have remained static. In reality, just like a poker game, the market never stays the same: Interest rates change, risk tolerance changes, and so on. Companies don't remain static, either: Strategies change, product mixes change, and so on. In short, the future performance of a stock is predicated on the future - not the past - and investors who apply regression to the mean to the market usually get burned.

Tech stocks, measured by the NASDAQ composite index, are a perfect example. Investors in March 2000 who got used to seeing the index above 5,000 thought that when it dipped to 4,000, it would regress back to the 5,000 level. The "buy the dips" mentality had made a lot of people rich during the market run-up of the late 1990s. When the index went below 3,000 in late 2000, it looked even more attractive. When it dropped below 2,000 in early 2001, it really seemed like a buying opportunity. More than two years later, the index stands below 1,400. Ouch.

Mason Malmuth takes a closer look at these statistics in his book Gambling Theory and Other Topics. But if you've played poker long enough, you can throw out statistics, as you just know that you can run bad for inordinate lengths of time. The rail is full of players who won consistently for years, started running bad, and whose cries for help to the "regress to the mean poker gods" have been replaced by pathetic bad-beat stories.

So, what the heck does all of this mean to you as a poker player? First, you have to enter every session prepared to play your best. Statistics don't determine whether you win or lose in the long run - how you play your cards does. Second, you constantly need to examine your play. Whether you're on a hot or a cold streak, the key is to know why and make adjustments accordingly. Third, you must understand that, no matter how you play, there is going to be variability in your results. If you're choosing the right games and playing well but still losing, it may be that you're just running bad and there is nothing to worry about. By the same token, if you're winning four or five big bets an hour over an extended period of time, you must understand that it isn't sustainable. I don't think you'll find anyone who thinks Phil Ivey can win 30 bracelets in the next 10 years.

Betting on regression to the mean by buying the dips of the NASDAQ composite has cost investors trillions. Consider that before buying tech stocks at what seem to be cheap prices - or betting on Phil Hellmuth to win an event at next year's World Series.

Greg Dinkin is the author of The Poker MBA: Winning in Business No Matter What Cards You're Dealt, www.thepokermba.com (see the ad in this issue). He is also the director of marketing for the World Poker Tour, www.worldpokertour.com.