How to measure risk intelligence and develop it
A day at the races
I stumbled across a possible answer when I read a paper by two American psychologists that had lain around gathering dust since it was published in 1986. A few years before, Stephen Ceci, not long out of grad school, and his colleague Jeffrey Liker, had approached the owners of Brandywine Raceway to ask permission to conduct a study of their clients. Ceci and Liker identified thirty middle-aged and older men who were avid racetrack patrons and studied them over a four year period. None of the men earned their living by gambling, though all of them attended the races nearly every day of their adult lives.As part of their study, Ceci and Liker asked all thirty men to handicap a number of horse races - ten actual races, plus some other ones they concocted. Handicapping means estimating a horse's chance of winning a race. They found that some of the men were significantly better than others at handicapping. In other words, some of these gamblers were significantly better at estimating the chance that a given horse would win a given race.
It struck me that this ability to estimate probabilities might be the thing I was looking for, the fundamental cognitive ability that lay at the heart of successful gambling. It was Ceci and Liker’s paper that first led me to wonder if the ability to estimate probabilities accurately, and make wise decisions under uncertainty, might constitute a special kind of intelligence. I decided to call it “risk intelligence.”
A test to measure risk intelligence
Risk intelligence can be measured by means of a simple test. First, you need a set of predictions. In horse racing, the predictions are usually about which horse will win a given race. So we list all the possibilities as different predictions: horse A will win, horse B will win, and so on. But the predictions could be about anything, from the weather to the chance of military conflict in different parts of the world.
Next, you assign a probability to each prediction. What is the chance that this prediction will come true? You express your answers as a percentage, where 0% means that there is no chance that it will come true, and 100% means that it is completely certain to come true. For simplicity’s sake, the answers may be restricted to multiples of ten, each 0%, 10%, 20%, and so on.Then you sit back and wait for the race to finish, or whatever other deadline the prediction refers to, and mark each one as true or false.
That’s it. Simple, right? It gets a bit more complicated when you have to mark the test, but the basic idea is not hard to grasp. First, you group together all the predictions to which you assigned the same probability. For example, lets say that there were, during the course of your afternoon at the racetrack, ten horses to whom you gave a ten per cent chance of winning. You count many of those actually won their race, and write the number down next to that category. In the end you should have a table something like this:
This table shows that, of the hundred horses who ran in the races you were betting on, you thought that eight had no chance at all of winning. You were right; none of those horses actually won. Of the ten horses to which you assigned a 10% chance of winning, two of them came first.
Doctors and weather forecasters
To arrive at the numbers in the fourth column, you divide the number in the third column by the number in the second and convert it into a percentage. Ideally, the numbers in the last column should be identical with the numbers in the first column. In that case, if you plotted the figures of the first and last columns against each other on a graph, they would line up on the diagonal line where x = y (which mathematicians call the “identity line”). This indicates perfect risk intelligence. The further away from that diagonal line the points lie, the lower your risk intelligence is.
Take the graph in Figure 1 for example, which displays data from two different studies. The bold line shows the results of a study in which weather forecasters estimated the probability of rainfall. The dotted line shows the results from a study in which doctors estimated the probability that their patients had pneumonia. The weather forecasters displayed very high risk intelligence, as can be seen from the fact that all the points on their line fall on or close to the diagonal line representing a perfect score. When the weather forecasters in the first study estimated the chance of rain the following day at 90 per cent, it rained about 90 per cent of the time. But when the doctors in the second study estimated gave their patients a 90 per cent chance of having pneumonia, only about 15 percent of the patients turned out to have the disease. That means the doctors were likely to recommend more diagnostic tests than was strictly necessary, and to prescribe more treatments than strictly warranted.
How to develop risk intelligence
How come the weather forecasters were so much better than the doctors at estimating probabilities? Sarah Lichtenstein, an expert in the field, suggests that several factors explain the weather forecasters’ success. First, the task for weather forecasters is repetitive. There are only a few things to predict, such as rain and temperature. Doctors, however, must consider all sorts of different things every day, from broken bones to malignant tumors and the correct kind of medication to prescribe.
Second, the weather forecasters in this study had been expressing their forecasts in terms of probability estimates for many years; since 1965, US National Weather forecasters have been required to say not just whether or not it will rain the next day, but how likely they think this is in actual percentage terms. They have had long experience in putting numbers on these things, and as a result they are better at it. Doctors, on the other hand, are under no such obligations. They remain free to be as vague as they like.
Finally, the feedback for weather forecasters (i.e. were their predictions accurate or not?) is clearly defined and quickly received. This is not always true for doctors. Patients may not come back. Diagnoses may remain uncertain or take weeks to be confirmed. Most theories of learning emphasize the need for rapid feedback; the longer the delay between an answer (or, in this case, a prediction) and the knowledge of whether it is right or wrong,, the lower the chance that the later information will enable the learner to profit from it.
These three factors suggest a simple way to improve risk intelligence. First, make predictions regularly about the same kind of thing; focus just on one sport, for example. Secondly, always express your predictions in terms of probabilities; don’t say “I think this horse will win” – say “I think this horse has a 70% chance of winning,” for example. And make sure to write your predictions down before the race starts so you can’t fool yourself afterwards! Finally, when the results of the race are in, score yourself by drawing up a table like the one above.
If you do this over and over again, your risk intelligence will probably improve. You will get better and better at estimating probabilities. And this is one of the key ingredients for successful gambling.
How risk intelligence helps gamblingMost gambling comes down to a competition to see who is better at estimating probabilities. When a bookie offers you 5:1 odds on a horse, he is implicitly estimating the chances of that horse winning the race at 20% or less. You will obviously only take that bet if think the horse has a greater chance of winning. Let’s say you think the horse has a 25% chance of winning. If you are right, then the bookie has offered you longer odds than he should have, and you should come out ahead. Winning at the races is all about looking for these “overlays.” But it’s only an overlay if you are right and the bookie is wrong! In other words, you are pitting your risk intelligence against that of the bookie. In pari-mutuel betting, and in games like Poker, you are pitting your risk intelligence against that of other bettors.
Bookies have several advantages over bettors. They can collect a lot more information, and they can employ whole teams of people to evaluate the odds. But bettors also have an advantage over the bookies. Bookies have to set the odds in a whole range of events and a variety of sports, so spread their expertise thin, whereas bettors can concentrate on just one sport, and indeed on just one specific geographical region or sports league, so they can concentrate their expertise and build a better model of their particular area.
But risk intelligence is not the only key to success; it is just one ingredient in profitable gambling. In addition to estimating probabilities accurately, a successful gambler also needs to manage his or her bankroll effectively, and scour the field for new opportunities. People with high risk intelligence will not succeed at gambling if they do not also acquire these other skills. However, repeated practice at estimating probabilities is a good place to start.
Software toolsThe method I have described here for improving your risk intelligence is simple in theory, but it can be fiddly in practice. Drawing up tables like that above, and plotting the results on a graph, are time-consuming when done with pen and paper. Computers offer ways to automate the whole process and therefore to speed it up considerably.
It is a relatively simple matter to build a spreadsheet that will do the calculations for you. You can download a free one for your own use here
Alternatively, you can also experiment with online tools, such as the free risk intelligence test at www.projectionpoint.com This test uses general knowledge statements rather than predictions, but the psychological skills involved are similar. Instead of estimating the chance that a statement will come true, you must estimate the chance that it is true, right now. In both kinds of exercise, you are in effect putting a number on your own uncertainty. The probability estimate represents how sure you are that the statement is, or will turn out to be, true. For example, take the statement that Africa is bigger than Europe. If you are sure that this statement is true, you will assign it a probability of 100%. If you are sure that it is false, you assign it a probability of 0%. If you have no idea, you will assign it a probability of 50%. If you have a hunch that this statement is true, but aren’t certain, you will assign it a probability somewhere between 50% and 100%. If you have a hunch that this statement is false, but aren’t certain, you will assign it a probability somewhere between 50% and 0%.
Using a general knowledge version of the risk intelligence test can give you a rough idea of your risk intelligence, but it is not as good as using a specific version tailored to the specific area where you are trying to improve your ability to estimate probabilities. For this reason, it is better to design your own tests, using your own predictions. The general knowledge version does have the advantage, however, that it can be scored instantly.
OverconfidencePerhaps the biggest obstacle to developing risk intelligence is overconfidence. By this, I do not mean overly high self-esteem but rather to an unwarranted belief that you are right. Overconfidence in this sense means believing in something more strongly than is justified by the evidence, and thinking you know more than you really do. Underconfidence means thinking you know less than you really do and not having the courage of your convictions. Both are highly problematic for risk intelligence, but overconfidence is much more common than
underconfidence. Indeed, according to the psychologist Scott Plous, “No problem in judgment and decision making is more prevalent and more potentially catastrophic than overconfidence.”
Overconfidence shows up in risk intelligence tests as a tendency to make more extreme probability estimates. For example, an overconfident gambler with a hunch that a horse will win might say it had a 70% chance of winning, when a more cautious gambler might give the horse only a 60% of winning. Conversely, an overconfident gambler with a hunch that a horse will lose might say it had only a 20% chance of winning, when a more cautious gambler might give the horse a more generous 30% of winning. In both cases, the overconfident gambler makes estimates that are closer to the 100% or 0% ends of the spectrum that represent absolute certainty. He is more certain than he should be.
A useful trick for improving risk intelligence, then, is to review your initial estimates and ask yourself, “Am I really that certain? Have I possibly overlooked something?” Given the common tendency towards overconfidence, a small adjustment in the direction of greater uncertainty (i.e. shifting the estimates above 50% downwards, and those below upwards) will usually improve accuracy.
Overconfidence may be the most important cognitive bias that hinders risk intelligence, but it is far from the only one. Psychologists have discovered many other such biases, including optimisim bias, confirmation bias, and hindsight bias. I will examine some of these other biases in my next article, and give some more examples of how risk intelligence can be used to gamble more successfully, and also to make decisions in other areas, such as investment and warfare.
To sum up
To sum up briefly, then: risk intelligence is the ability to make accurate probability estimates. It can be measured by means of a simple test, and improved by taking such tests repeatedly and analyzing the results. But risk intelligence is only one of several ingredients to gambling successfully.