If you are reading this article, you are probably already aware of basic statistics and probability. After all, you do not have to have a PhD in Maths to calculate odds. However, the terms we use here are not used in everyday activities, and it could be tough for a beginner to understand all of the information that is provided here, especially if you are a not a maths whizz.

Moreover, since betting and sports go hand in hand, sports fans can see what a real betting site is about through SportsBettingSitez. This website is perfect for both beginners and seasoned punters; we recommend you check them out before reading all of the information provided below. Also if you are a newbie, you should read their guide - it will make everything that we will explain below much clearer.

We will start off this guide with a few words about the binomial distribution. This is quite suitable for 50-50 propositions such as Asian handicap markets or point spread, and others in which the odds for all sides are close to even money, or a bit smaller after the bookie applies its betting margin. However, it is quite common for punters to wager on all sorts of various prices with different stakes such as match betting in tennis or 1X2 in soccer.

In situations like this one, you can rely on the t-distribution, as well as the popular t-test for statistical significance. In this guide, we will explain how you can use it to your advantage to measure a betting tipster's performance.

The Range of a Tipster's Record
The t-distribution is quite similar to the normal distribution, which is shaped like a bell. Moreover, for numbers and bets above about 30, it is to all purposes and intents the same thing. We use the t-test to investigate the possibility that profit from a series of bets might have happened by chance. For example, a return of 120% from 100 bets at the odds of 10.00 or longer is probably the consequence of luck. However, the same returns from betting odds-on prices will indicate skill.

The smaller the possibility is, the more probable it is that something else is explaining their profitability such as the skill level of the punter. What the t-test does is compare the bettor's observed return to a theoretical expectation, which is defined by the market they are betting in.

Typically, this is the loss equivalent to the bookie's margin, or break even if the punter is going that extra step to find the best odds with the help of an odds comparison tool. Afterwards, the results are analysed to determine if the difference is statistically significant.

At this point, it should be obvious that the bigger the profitability is, the t-score will be larger, and the betting history will be more statistically significant. This means that it is more likely that skill played a big part, rather than luck. The t-score is equivalent to a punter's excess median (average) return over expectation.

So the longer the history is, the more likely it is that skill is at work, rather than luck. For example, consider that two bettors both have a 120% ROI (return on investment). However, the first one managed to achieve it from 10 wagers, and the second one from 1,000. It is obvious which one of them is most likely to be a skilled punter.

It is normal to have some doubts, so you should consider the coin tossing probability. It is quite more likely to land a six or more heads from six tosses, rather than landing 600 or more heads from 1,000 if we assume only chance. Moreover, if someone lands 600 or more heads, you might suspect that the coin is biased.

So you will most likely conclude that a punter with an extended period of profitability is demonstrating skill, rather than chance. Thus, the t-score is equivalent to the square root of the number of wagers.

Short vs. Long Odds
However, the influence of the betting odds is less intuitive. In fact, an ROI of 120% from wagering odds around 1.25 are a much better indicator of skill, instead of proportional profitability from odds around 5.00. Thus, wagering on longer odds (lower probability outcomes) is riskier if we assume the equivalent stakes since it is at the mercy of random variability.

In other words, the returns are more elusive. For example, 19 or 21 winners at odds of 5.00 will give returns of 95% or 105%. In opposition, 79 or 81 winners at odds of 1.25 will display 98.75% or 101.25% gain over turnover. Thus, betting longer odds indicates taking a larger risk for a bigger reward. You can see the influence of the wagering odds using the standard deviation (SD) in losses and profits of the betting history. For example, for the level staking, the SD will look like this:

In this case, r represents the punter's return, and o is the median odds for the wagering history. The SD in losses and profits betting at odds of 5.00 is over eight times larger than betting at 1.25. If we assume that the expected returns that are only based on luck are 100%, the t-score will look like this:

In this case, n represents the number of wagers. Therefore, the t-score for proportional returns as well as the length of the betting history is more than eight times smaller wagering at odds of 5.00 compared to 1.25.

By now, it should be apparent that the superior yields that were accomplished by betting longer odds are not particularly a sign of better forecasting skills. The exact amount of luck will distribute a larger percentage returns.

Thus, the comparisons of wagering histories that consider solely rate returns (which is quite common when you rank tipsters) are substantially misleading. If we take the betting odds into consideration, the t-score will provide a measure of the quality of the risk-adjusted return more than expectation.

How to Calculate Chance
The final thing you have to do is to convert the t-score into a p-value (probability). If you have a Microsoft Excel, it will be much easier, as it has a TDIST function. TDIST comes from t (t-score), Degrees of Freedom (number of separate pieces of data, which is equal to the number of bets -1) and tails.

The tails can be either one or two depending if the t-test is one-tailed or two-tailed. Since we are only interested if a profit is statistically significant, we will use the first one. Alternatively, you can use an online calculator in which you can place these values.

Clearly, the median odds at which a punter makes a bet have a large impact on whether their profitability is considered as skilful or lucky. A return of 120% from 100 bets at odds of 10.00 or longer should be regarded as a consequence of luck.

So, if a bettor shows the identical return wagering odds-on prices, it will be more likely that the profitability has ascended because of their skill level. Therefore, when you compare betting histories from tipsters, it will not be enough to only analyse their percentage returns, you will also have to analyse the odds and the length of their records.

If you found this guide useful, we recommend that you check out our Stat Centre for the Premier League Overview. body check tags ::