*We make no apologies for the scientific equations and terms in this article, but this just goes to show the depth our analysts will go to in order to be successful.*

It can take years to develop the knowledge and skills required to become a successful punter. Then one day, you try something different and go on a winning run that lasts longer than you expect.

The next question you might be asking yourself is: have I finally found the winning formula, or did I just get lucky?

One way we can answer this question is with statistics.

Last week, Rowan provided the perfect introduction to the relationship between statistics and punting. This week, I take his work a step further and show you how you can use statistics to answer that fundamental question: are my results due to luck or skill?

## Sample Size & Confidence

As Rohan discussed last week, statistics is all about sample size and confidence. The larger your sample size, the more confident you can be in your results.

For example, if you had 1000 bets at the line (i.e. 1000 x 50/50 bets) and you’re showing a 10% P.O.T., you can be pretty confident have a winning strategy. Conversely, if you had 10 bets at the line and showed 10% P.O.T., it was most likely due to luck.

Those conclusions are pretty straight forward but what about 200 bets? How confident can you be in your 10% P.O.T. then? Are 200 bets enough to know you have a profitable method?

The method I’m about to show you is one way to answer these questions. The example we’ll use is a sample of 200 line bets with a 58% strike rate (116 winners) and a 10% P.O.T. record.

That makes the average price on each bet around $1.90. Once you understand the process below, you’ll be able to test it on any set of results to see how confident you can be in your method.

## Hypothesis Tests

Hypothesis tests are one of the methods statisticians use to answer questions about their data. The question we really want to know is how confident can we be that we have a profitable method based on our sample? The only way we can find out is by testing the sample.

The data that makes up our sample is simply the profit on each bet. In our relatively simple example, if we bet $100 per bet, our data is 116 winning bets that have a profit of $90 each and 84 losing bets that have a profit of -$100 each.

Your personal record will have a whole range of different profit values based on how much you outlaid on each bet and the prices you took and that is fine.

For those familiar with statistics, the test we’re about to perform is the “one-sample t-test for a population mean”. That’s a long name but I’ll break it down into this 5-step procedure:

## Step 1

When you perform this test, you create two hypotheses that are basically the opposite of one another. There are some fancy symbols here, but all you need to know is that we have two hypotheses:

H0: µ = $0 profit (our method is not profitable)

Ha: µ > $0 profit (our method is profitable)

## Step 2

Next we need to decide how confident we want to be that our method is profitable. It’s totally up to you how confident you want to be. You can choose any level of confidence you want.

The standard is 95% confidence, so in our example, I’ll say that we want to 95% confident that our method is profitable. Instead of saying “95% confident” though, in hypothesis testing, we say we want a “significance level” (α, alpha) of 0.05:

α = 0.05

## Step 3

Next we calculate what is called the “critical value”. The critical value is like our measuring stick. You could look up a “one-tailed t table” to find the critical value but an easier way is to use this Excel formula:

=TINV(2 x α,sample size – 1)

In our example, we would enter:

=TINV(0.10,199)

because α = 0.05 and our sample size is 200.

Excel should return the “critical value” of 1.65 (rounded to 2 decimal places).

## Step 4

Next we need to calculate the “test statistic”. The test statistic is compared to the critical value to determine whether our method is profitable or not. We have more fancy symbols here, so let me explain:

Test statistic t = (xbar – µ0)/(s/sqrt(n))

- xbar is the mean (average) profit of our sample, which is $10
- µ0 is the $0 profit in our first hypothesis
- s is the standard deviation of the sample, which can be calculated with the Excel formula =STDEV(data range), which is $94 in our example
- n is the sample size, which is 200 (you need to find the square root of that in the equation)

Using that information:

Test statistic t = (xbar – µ0)/(s/sqrt(n))

Test statistic t = (10 – 0)/(94/sqrt(200))

Test statistic t = 1.51

## Step 5

Now we can work out whether our method is profitable or not.

Our test statistic (1.51) is smaller than our critical value (1.65). Because it is smaller, we cannot reject the first hypothesis. We cannot reject the statement that “our method is not profitable”.

Therefore, at the 5% significance level, we cannot support our second hypothesis that our method is profitable. In other words, it looks like our profitable results were based on luck more than skill.

## How Confident Do You Want To Be?

In the test above, I mentioned that it is up to you how confident you want to be that your method is profitable. The more confident you want to be, the more likely the test will fail. So what about if we were happy to be 90% confident that our method is profitable?

Using the same steps as above, we end up with the same test statistic (1.51) but this time our critical value is 1.29.

Now our test statistic (1.51) is larger than our critical value (1.29). Because it is larger, we can reject the first hypothesis. We can reject the statement that “our method is not profitable”.

Therefore, at the 10% significance level, we can support our second hypothesis that our method is profitable. In other words, it looks like our profitable results were based on skill and not luck. Nice one!

The only difference between this test and the first one is that we are willing to be a little less confident in the result. 90% confidence also means there’s a 10% chance your results are not profitable.

There are few certainties in punting and statistics is the same. The next question is: are you willing to accept that chance?