Probability vs. Luck: Lessons Learned From a Day at the Races

 

By Lynda Bourne

Last November, my partner and I spent a lovely day in the country attending the Dunkeld Cup at Mt. Abrupt in Victoria, Australia. The location is very picturesque, and we had a thoroughly enjoyable day. To add to the pleasures of wining and dining, my partner developed a “foolproof method” that allowed him to pick five winners and a placegetter (among the top three) out of seven races with a total of eight bets.

So, should he give up his day job to exploit this newly discovered skill?

The Dunkeld Racecourse with The Grampians Mountains behind.

The horses he chose were not random picks: My partner used a selection method based on a guide that rated horses on their form from 0 to 100. Using a portfolio management approach, he first recognized that the difference between a 97 or 98 rating and a rating of 100 was too small to matter. Every assessment process has a range of error, and a difference of 2 to 3 percent is likely to be well within this range. This approach reduced the panel of potential winners to three or four horses in each race.

The second step in the selection process was to look at the variables. The form guide is printed well before race day, and it had recently rained. A soft track would benefit horses carrying a lighter weight. So out of the prospective panel, we placed our bets on the horse with the lowest weight.

Voilà! Six winners in seven races—a winning formula that would allow us to retire from managing projects and make our fortunes as professional punters … But not so fast.

The probability of repeating a six out of seven winning ratio in the future is very low. How much of our big day boiled down to effective process—and how much was pure dumb luck? That is a risk management question.

Step One: Consider the Probability: The first consideration is how likely was it that someone would pick six out of seven winners? There were several thousand people at the race, and it is highly probable, simply based on random chance, that someone would have a “winning streak” and back six winners using their own system. On this basis, there is a several-thousand-to-one chance of a repeat outcome. Someone will have a similar winning streak in 2020, but probably not us. There is a strong tendency for winners to ascribe the results of random chance to their skill. But pragmatic managers look deeper.

Step Two: Assess All Available Data (Not Just the Highlights): We placed eight bets: Five came in first, one finished third and the other two were placed sixth and seventh, respectively. All we can say for sure is we were likely to select horses that would finish between seventh and first. But as there can only be one winner and two placegetters, horses finishing fourth, fifth, sixth and seventh mean a lost bet. The median position is 3.5—which also means a lost bet. The mean is 2.6, so we may have been slightly in front, but “place bets” do not pay much. Adding in the range options, no horse can do better than first place, but there are many more places between seventh and last. Factor this in, and the margin of success in our small sample becomes doubtful.

So, what are the lessons learned from our day in the country? My take is that good processes help build success—but you should not confuse luck with skill. When Napoleon Bonaparte was criticized for winning battles simply because of luck, he famously retorted: “I’d rather have lucky generals than good ones.” I think we were just lucky.

We may well return to the Dunkeld Cup in 2020. It’s a great day out, and more data is needed to round out this research. In the meantime, applying simple probability analysis to my partner’s winning methodology suggests he needs to keep his day job. That’s a safe bet.