Working Out the Maths of Luck 

In the last newsletter we talked about determining whether a tipster has simply being lucky or whether they are in fact a skilful tipster for the long term. Unfortunately there are not many out there that have long term betting histories. This is because either they found out that luck had a lot to do with their successful tipping (that is they made a loss after their initial victories), or they haven’t been around for long enough.

This doesn’t mean that you can dismiss these people. Likewise you may want to work out if your tips are just due to luck or if you tips are actually quite profitable. To work this out, we apply a bit of mathematics.

Okay, so this section will probably be a little complicated, and it involves University standard mathematics that most have either never done or have completely forgotten. Let’s suppose that a tipster has made 100 bets at the line of 1.90 and has recorded of 55 wins and 45 losses. This doesn’t sound that successful, but in fact it is. Betting at a 1.90 line has allowed him to win 4.5 units. Considering that he has bet 100 units, this means that his profit on turnover is . This is a very good profit and most professional punters would be very happy with it.

But was it just a bit of luck that made the tipster win this much or perhaps he actually made some very wise bets? Let’s work this out mathematically.

Scientists always use tests to prove whether events are significantly different from each other. For example a chemist might devise a test that tests whether a drug has a significant positive effect on a patient. Notice that I’m using the word significant here. This means that the chemist is actually testing whether the drug actually has an effect or whether it’s just due to random variations, or luck, that any difference was found.

We can use the same principles here in testing the gamblers record as shown above. What we do when testing such information is assume that each bet that he makes has a 50% chance of winning. Because he is betting on the line for each bet, this is of course a good assumption. Naturally he would want this to be greater than 50% so that he can make a profit, but for the time being we will assume that it is 50%.

Now the punter has recorded a success rate of 55% of his bets, thus meaning he is 5% above the average if he was just blindly betting on any bet. To test whether this is due to luck or wise betting we have to use what is called the “binomial test” or the “one sample z-test for proportions”. There are many websites outlining this on the web should you wish to do a search, and even though I’m going to go through a few details below, I won’t bore you with all the mathematics.

Firstly we work out the z value. The p value is determined by the following rule:

Here the small p is the 55% that the tipster correctly tipped. The capital P is the 50% that we would normally expect and the n is the number of bets that he made. Putting these values into the above equation gives:

Now unfortunately here we get a bit more complex. Basically we have to look up normal distribution tables to determine what this means. We have to convert this to a probability. Here you can either use the normal distribution tables that you can find on the web or better still use excel.

In Excel type in “=1-normdist(1,0,1,true)” and you should get an answer of 15.8%. This means that despite his very good record of a 4.5% profit on turnover, there is a 15.8% chance that it’s just due to luck. This is despite over 100 bets! This clearly shows that a betting history of 100 bets is not sufficient to prove that you are not just lucky.

Typically in science, if the probability is under 5% then we can conclude that there is significant evidence to suggest that the results are not due to luck and that he has made some very wise bets. So if you were this particular tipper, how can you prove if it is luck or not? There are two ways to do so. One, the better percentage difference from 50% that you tip the lower the chances are, using the above calculations, that your tips are only successful due to luck.

But more likely the case, the more bets you make, even if the return is the same, the less chance that it’s due to luck. And that links back nicely to what I was saying previously about the long term. The longer the successful history of a gambler, the better they are. Let’s prove this by giving some more examples. We’ve actually made a table below that gives the probabilities that the gambler above has succeeded due to luck. We’ve basically given him the 5% edge that he had previously, but changed the number of bets that he has made. 

The information gives some startling results. Firstly it suggests that anywhere under 100 bets is hardly enough evidence that a gambler actually making wise bets even if they are making 4.5% profit on investment. Following streaks is ludicrous as such a small number of bets has been proven, as shown above, may just be lucky.

Remember that I said that 5% is the general “cut-off” to where we can conclude that one is a successful tipster because of wise bets as opposed to luck? Well as shown above even 250 bets is not sufficient history for this at the given profit on investment. That’s right you need at least 275 bets and then still there is a 5% chance that the tipster, or your bets, have just been lucky and not skilful.

In an AFL or NRL season there are approximately 185 games. This means that you would need at least two years worth of data to believe that a tipster is actually quite good. This backs up the statements that I was saying before about the long term.

Of course the mathematics change a little if you were to work this out when gambling on games that are not a 50% probability of winning, but the meaning behind the above analyse is sound. Gambling, just like property and stock market investment, is all about the long term. Every professional gambler knows this, we’ve proven it, and now you know it too.

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