How to calculate statistical significance of a hypothesis I have

Question

First of all, I'm a stats newbie. I have no formal education in stats, nor did I do well in math classes. I'm sorry if my question is phrased poorly.

I want to know how to calculate statistical significance to see how much a variable (i.e experience) contributes to wins in the sports, specifically MMA.

I've been tracking my W/L bets on a spreadsheet, and identified the number of times I bet on a fighter because I think he has enough experience to win the fight, regardless if he's the underdog or the betting favorite.

I want to know if I have a large enough sample to confidently say that what I'm observing is statistically significant. I want to be able to calculate that on my own. What would that formula look like?

Some numbers that I have: Total bets: 65 Win %: 51.56%

Bet on Experience Wins: 14 Bet on Experience Losses:7 Bet on Experience Win % 66.67%

Answer 1

The statistical significance of your sample is dependent on the distribution of your null hypothesis.

For example, if your null hypothesis is that you have a probability $p$ of guessing the correct winner of any fight, you could find the probability of guessing X of 65 fights correctly using the probability density function of the binomial distribution:

$P(\text{X correct}) = {65 \choose X}(p)^X(1-p)^{65-X}$

To get the significance of your sample, you would get the probability of guessing that many or more correctly by calculating this probability for each possibility. So if you guessed 33 correctly, you would sum the probabilities of guessing 33, 34,35,...,65 correctly to find the significance, referred to as the p-value.

p-value = $\Sigma^{65}_X {65 \choose x}(p)^X(1-p)^{65-X}$

The interpretation of this probability is subjective, and you should set a limit beforehand on what you'd find meaningful. The default value for many people is 0.1 or 0.05, so if your calculated probability value is less than that mark, you have reason to believe you are better at guessing the outcome than the suggested p-value.

You can adjust the null hypothesis probability distribution to take into consideration a better prediction rate of based on fighters with experience or other parameters.