Monte-Carlo or Bust

Monte-Carlo simulations are “computational algorithms that rely on repeated random sampling to obtain numerical results”. The further definition is even more off-putting for non-mathematicians! I will attempt to explain in layman’s terms how an MC Sim is a useful tool in determining accurate percentages and thus, true odds.

A good example of how you can utilise an MC Sim was how I once used it for the 2010 World Cup. Firstly I handicapped the teams in terms of goal superiority. For example, if we top rate Spain, they were on 0.00. Germany may have been 0.2 (0.2 goals inferior to Spain), Brazil 0.3, England 0.6 etc. I then used previous World Cup data to calculate the average goals per game in 1st group game, 2nd group game, 3rd group game, QF, SF, Final. This gave me a prediction for every group game in terms of superiority and total goals. Finally I programmed the draw into the MC sim.

The next stage is to simply decide how many iterations (the number of times the Sim plays the tournament) and hit the Start Button.  Playing the World Cup 10,000 times according to the inputs gave us the % chance of any criteria we wished (winner, group winner, number of goals etc). As the tournament progressed, I had actual results to input as well as altered handicap marks. After every game I would run the MC Sim 10,000 iterations, get the updated percentage chances and bet accordingly. I must have played half a million World Cups!

Interestingly, some markets very closely reflected the MC Sim calculations and yet others were consistently awry. We simply built up big positions over time. Even when you used the handicap marks of the spread companies (which obviously represent the market consensus) there were still some market inefficiencies highlighted by the MC Sim. Admittedly, they tended to be the smaller, more obscure markets, but nevertheless, they were of considerable interest and suggest the market is not always efficient!

The financial markets I trade are an excellent space in which to utilise a MC Sim. You can test a system of trading over 40 years and thousands of trade and believe you are on to a winner! Now put the system through an MC Sim that juggles the results a little….and iterate 50,000 times. The picture is often very different. The real results may lie in the top 10% of the range of potential results thrown up by the 50,000 iterations! Suddenly you may not be so confident as the likelihood of the real results being repeated is just 1 in 10!

How could an Monte-Carlo simulations be used in horse racing? It can be used to produce an odds line. If you can assign ratings to horses and a range away from that rating can be produced by a normal distribution. To understand a normal distribution, think of the height of the male population on a bar graph. The average is 5 foot 10 inches and this height has the most numbers. This will be followed by 5 feet 11 inches and 5 feet 9 inches. The graph looks like a bell with an equal number either side of the 5 feet 10 inches. So, if you assign a horse a rating of 80, then that is its most likely performance, the next most likely is 79 or 81, then 78 or 82 etc, with progressively less chance of running to ratings further away from 80. For racehorse ratings, a more accurate method is to use a negative skewed distribution. Without getting too technical, for racehorse performance, a negative skewed distribution is more accurate than a normal distribution, because a horse is more likely to run below its expected rating than above it. A negative distribution means that 79, 78 77, 76 are more likely than 81, 75,74,73 are more likely than 82 and so on. This is certainly true of exposed horses, but less so of progressive 2 and 3 year olds, when further adjustments are judicial.
To understand this, let us play with some numbers……

Shergar 90…..4/5
Mill Reef 85….11/4
Sea Bird 80…..15/2
Dancing Brave 75…20/1
The Minstrel 70…..100/1


 The MC Sim has run the race 10,000 times and gives you a % chance based upon the ratings. That percentage is then converted into true odds.

To illustrate the point above re negative skewed distributions, let us assume we have a lightly raced, but progressive horse in the race…..let us make Mill Reef lightly raced and progressive. The ratings don’t change but the distribution we apply does. The change can be dramatic. Mill Reef’s percentage chance rises to 45% and he becomes the horse with the best chance, despite having a figure 5lb below Shergar. This is because he has a greater chance of running above his 85 than Shergar does of running above his figure of 90.

Shergar 90….11/8
Mill Reef 85….6/5
Sea Bird 80….12/1
Dancing Brave 75….25/1
The Minstrel 70….100/1


There are downsides to this approach, but, in general terms, it is a method to produce an accurate odds line. Horse racing has many variables that effect the result, some we can incorporate into any ratings….likely effect of ground, distance, draw, jockeyship, fitness etc….but others are more tricky…pace of the race, current well-being of the horse etc.

The Monte-Carlo simulation is only as accurate as the information that is fed into it, but is a great tool for converting that information into real percentages and thus odds.