How To Mathematically Verify Betting Strategy Results

In sports betting, success often hinges on navigating the fine line between chance and skill. So how do you know if your strategy is working?

This detailed analysis of 317 Premier League football bets, placed over two seasons using my Fickle Football Fan Formula, aims to determine whether the promising results can be attributed to luck or a strategic advantage.

Understanding this process will enable you to evaluate a strategy’s viability.

 

My Strategy’s Results

The Fickle Football Fan Formula utilised a recency bias selection method which yielded a 5.51% ROI from 317 £10 lay bets placed on the betting exchange. This produced a profit of +£299.40 after subtracting a 2% commission on winning bets.

However, these results will not factor into the following mathematical test where I aim to find out if the win rate which lead to the positive outcome was luck, or skill.

£10 Lay Bets on Fickle Fan Formula - All Time

 

Average Implied Probability & Win Rates

To analyse the results, I calculated the average implied probability and observed win rates.


Average Implied Probability

Each bet from the dataset was assigned with an implied probability derived from the odds taken on the betting exchange.

For instance, a lay bet placed at odds of 3.0 implied a winning probability of 1 – (1 / 3.0) = 66.66%. This means that a “backer” of the same outcome faced an implied 33.33% chance of winning.

Across the 317 lay bets placed in the Fickle Football Fan Formula, the average implied probability is 51.12%. This figure reflects the expected likelihood of each bet winning based on the market’s assessment of the selections.

Learn more about implied probability.


Observed Win Rate

Out of the 317 bets, 171 lay bets resulted in a win. This gives an observed win or “strike” rate of 53.94%, which is slightly higher than the average implied probability.

The strike rate was calculated simply as 171 divided by 317.

Learn more about strike rates.

 

P-value Analysis: Testing For Luck or Strategy

To assess whether the observed win rate from the 317 football bets can be attributed to luck or strategy, a p-value analysis was performed. Several values were required, including those calculated in the previous section:

  • Total bets (N) = 317
  • Number of wins = 171
  • Observed win rate ≈ 0.5394 (or 53.94%)
  • Average implied probability (μ) from odds = 0.5112 (or 51.12%)

The following three steps show how I calculated the p-value for my betting results.


1. Standard Error (SE) Calculation

Firstly, the standard error (SE) was computed to assess the variability of the observed win rate around the mean implied probability. Here’s the calculation:


2. Z-score Calculation

Secondly, the Z-score was computed to measure how many standard deviations an observed win rate is away from the mean implied probability (μ). Here’s the calculation:


3. P-value Determination

Lastly, the P-value was computed to help determine the strength of evidence against the “null hypothesis” — in order to assess whether the observed win rate significantly differs from the average implied probability.

Using the Z-score of approximately 1.007, I looked up the corresponding p-value from the standard normal distribution table:

P(Z > 1.007) ≈ 0.1562 (one-tailed)

This means that under the normal distribution, we would expect to observe a value with a Z-score greater than 1.007 around 15.62% of the time.

Since 0.1562 is greater than typical significance levels like 0.05, it suggests that the deviation is not statistically significant. Therefore the null hypothesis is not rejected.

Note: The decision to use a one-tailed or two-tailed test depends on the specific research question and hypothesis being investigated. In this analysis, the objective was to conduct a one-tailed test to determine if my observed win rate significantly exceeds the implied probability. However, if the goal were to assess whether there is a significant difference between the observed win rate and the implied probability in any direction, a two-tailed test would be appropriate, as follows:

 

Results Interpretation: What Does It Mean?

When conducting statistical tests, such as calculating p-values, we usually compare our observed data (the win rate from the bets) against the “null hypothesis” to determine if our observations are likely due to chance or if they are meaningful.

The calculated p-value of approximately 0.1562 indicates that there is not sufficient evidence to reject the null hypothesis. This means that the observed win rate of 53.94% does not statistically differ from the average implied probability of 51.12% at the usual significance level (e.g., α = 0.05 or 5%).

So the observed win rate is in line with the expected win rate implied by the odds. The positive outcome of the strategy is, unfortunately, most likely down to random variation rather than a systematic advantage in the betting strategy.


Conclusion

While the Fickle Football Fan formula showed a positive Return on Investment (ROI), from a mathematical standpoint, there is no clear evidence that this selection method will consistently generate profit in the future. However, it is encouraging that there is no indication of losses.

Interestingly, just one month before the end of the season, when results were favourable, the same test indicated statistical significance and suggested a likely advantage for me. However, a downturn at the season’s end brought the results right back in line with expectations.

Further data collection and testing could strengthen these findings and provide deeper insights into the strategy’s effectiveness. There could be room to refine this strategy to produce better results. But for now, I’ll take the winnings, put the Fickle Fan Formula on the shelf, and look towards new experiments.


If any mathematicians out there have any suggestions for improving this type of analysis, I’m open to hearing them.

Toby @ Punter2Pro
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