## The Luck factor in Sports Betting

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Luck plays a very important role in the outcome of our betting activity, much more than many think. It’s true that in the long term the influence of luck tends to zero and the more bets we make the less it will affect our results. But **in the short terms luck can have an amazing influence**, for better or worse.

Most of tipsters and regular bettors know what I am talking about. Anyone who bets regulary has experienced sharp trends in his profit curve, although we use to blame “luck” only when things are moving in the wrong direction and not when we are on fire.

In order to see, from a mathematical perspective, how luck can influence our results, we have made a Monte Carlo simulation. Let’s consider a hypothetical good bettor that would have achieved a 10% yield in a very high number of bets and we can consider this 10% yield his long term “edge” over the market. He makes 400 more bets. These are the parameters:

- Number of bets in 1 year: 400

- Odds: 2.20 (we assume all bets are made at these odds)

- Strike rate: 50%

- Fixed stake: 2 units/bet

- ROI or yield: 10% = (0.50 x (-2) + 0.50 x 2 x 1.20) / 2

- Initial bankroll: 100 units

For ease of calculations, we have used a Fixed Bankroll bankroll management; that is, a 2 units fixed stake is always used. This is how the Monte Carlo simulation works: Excel gives us 400 random numbers between 0 and 1. As the strike rate is 50%, if the number is lower than 0.50 we consider it a lost bet and if the number is higher than 0.50 it’s a won bet. In the first case we lose 2 units and in the second one we win 2.40 (2 x 1.20). This is how the bettor achieves that 10% long term yield. With 400 random numbers we can generate a profit line like the ones we can see below:

This is a sample of 12 results, achieved during a year. We can see that in several of them the magnitude of the bad runs is really sharp, even though in all cases the 10% yield bettor gets to finish the year in profit. Now we carry out this simulation not 12 but 1,000 times. With such a high number of samples we can already obtain very rigurous figures from a statistical point of view. The “maximum drawdown” (maximum peak to trough decline in the period) is 82 units (82% of the initial bankroll) and the average of all drawdowns is 30.9 units. That is, the bankroll of a very good bettor like this one suffers maximum drawdowns of 30.9% on average in a year, using a 2% stake. If we raise it to 3%, the average max. drawdown would be 46.5% and if we get crazy and make 5% our fixed stake the average drawdown would be 77.5%!! Moreover, as we raise the stakes, the number of simulations where we lose all our bankroll and we go bankruptc obviously grows.

**The conclusion is that even for a bettor who is able to generate significant profits in the long term, luck plays a key role in the short term evolution of his bankroll. A bad run will come sooner or later and we should use a sound money management strategy so that the bankruptcy risk won’t be high. Apart from the value we perceive in each of our bets, the staking strategy should obviously be very connected with the odds size. Taking low odds we can risk higher stakes and viceversa. **