## More gambling & sail racing in Monte Carlo land

As frequent readers of this blog know, I’m a keen sailor.

Over all these years I’ve been involved in the sail racing circus – either as sailor myself, or as coach or umpire – I’ve always been amazed by the significant variability in sail race results: from one race the the next, the results have a high degree of variation, the winner of yesterday’s race might end up in the middle of the fleet today… In less complex sports, the variability is much much smaller – after all, if Usain Bolt is running 100 m dash, he’s never going to end up outside of the podium…As opposed to Ben Ainslie, who might score a midfleet result any day…

In previous writings on my other blog I’ve been musing about why sail racing has such a high level of variability in the results of races. Briefly, my conclusion was that the variability is because sail racing is a ‘multi-dimensional’ or highly complex sport.

As opposed to sports such as 100m dash, which is pretty much one-dimensional, demanding only the right type of muscle fibres, sail racing is multi-dimensional, that is, in order to succeed, you need to master much more than one dimension of complexity, dimensions such as strategy/tactics/boat handling/rules/physical fitness/aerodynamics/lmeteorology etc.

Having my mind lately on Python and Monte Carlo simulation, I decided to do a Python based simulation on this problem. Here’s the gist of it:

Let’s say that we have identified five factors that determine the performance of a sail racing crew:

• strategy skill (selecting the right side of the course etc)
• tactics skill (dealing with boat-to-boat situations etc)
• boat handling skill
• experience
• equipment quality

Let’s furthermore assign a ‘weight’ to each of these factors:

• strategy weight = 0.9
• tactics skill weight = 0.8
• boat handling weight = 0.7
• experience weight = 0,8
• equipment weight = 0.5

To make a simulation, let’s assign the value of 1.0 for a perfect execution in each of the above five categories, i..e if you execute a 1.0 in any category, you have not made a single mistake in that category, you have executed that dimension flawlessly.

Now, let’s say we have two crews, with the following characteristics:

Crew A has 0.8 in execution level in each of the five categories above.

Crew B has 0.75 in execution level in each of the five categories above.

That is, crew A is clearly a better crew than crew B.

The question then is: who’s going to win the race, crew A or B ?

Well, since Crew A scores 0.8 in each of the five categories, for a total of 5, while crew B scores 0.75 in each category, for a total of 3.75, the result is obvious: crew A wins.

So far, nothing interesting.

But now, let’s leave the territory of determinism in favor for the territory of uncertainty, what some people might refer to as ‘luck’, but what really is caused by the variability within each of the five dimensions.

Let’s introduce some random variability in the skills and performance of each crew, e.g one of the teams might have a ‘bad day’.

Let’s say that  each of the teams have variability in each of the five categories as follows:

teamvariance[‘A’] = [(60,110),(60,110),(80,100),(80,100),(80,100)]
teamvariance[‘B’] = [(90,110),(90,110),(80,110),(80,100),(80,100)]

That is, team A has a factor range of 0.6 to 1.1 in strategy and tactics etc, while team B is a bit more consistent in their performance, with 0.9 to 1.1 in strategy and tactics, the variability of the rest of the parameters being the same for both teams.

Who do you think will be the winner of a long regatta, or series of races…?  Should be team A,  since they are the better team, according to the ‘execution level’ parameters above, right…?

Well, with the numbers above plugged in into a Monte Carlo simulation, it turns out that on average, after 100.000 runs (‘races’), it’s actually team B who’s the winner, despite the fact that nominally, team A is 7% better than team B in each category.

The reason for this is in the variation numbers: if you look above in the team variance table, you can see that team B has much less variability in their performance in strategy and tactics asop to team A. Despite the fact that team A is nominally a better team, team B will still be the winners in the long run, simply because their performance is more consistent, with less variability.

The point here is that as soon as you look at any kind of performance, you must take variability into account, and the more complex the sport, the greater the impact in results of variability.