World Cup 2022 - Applying Statistics To Betting Odds #2

Hello there!

Being someone who has a keen interest in Statistics, it's always fun and interesting to put some of the knowledge into practice and real life applications. In this case, I am referring to betting odds.

But before I begin, I thought I should put out a big and bold disclaimer that this is solely a textbook practice and it's not meant to encourage anyone to bet because statistics is always about probabilities and my analysis is just meant to be a fun exercise (and this means I could be way wrong!).

This post is a continuation of the earlier post so you might want to refer to it for background.
Post #1

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Predicting Total Goals In World Cup 2022

Now that we have 8 more matches or should I say, data points, after 2 days of matches, let's see if we can better model the final outcome.

The first observation was WOW, how fast the tables have turned with regard to the odds. From a supposedly low scoring tournament, we have seen a whooping 24 goals from the last 8 matches, including a 4-1 match between Croatia and Canada, a 3-3 draw between Cameroon and Serbia and a 3-2 match between Ghana and South Korea.

As such, the betting odds adjusted to call 155-165 goals as the most probable outcome. But is it true? Let's take a look at the model.

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Where We Are

After 32 matches:

• Total Goals: 81
• Mean (average goals per match): 2.53 (up from 2.38 previously)
• Variance: 4.39 (down from 4.59 previously)

As there are a total of 64 matches, we are halfway through and there are 32 matches to go. Using the data of 32 matches played as a sample, we can apply lambda (λ), or mean, of 2.53. So the mean goals for the remaining matches would be 32 * 2.53 = 81.

So we are assuming the remaining goals for 32 matches (X) would follow a Poisson distribution with mean 81, i.e. X ~ Po(81).

Looking back on the betting odds:

• If we needed the total goals to be less than 155, that means we can only afford to have 73 more goals given the current tally is 81. Punching the numbers into Excel/Google Sheet, P(X <= 73) = 20.39%.
• If we needed the total goals to be between 156 to 165, that means we want to have 74 to 84 more goals given the current tally is 81. Punching the numbers into Excel/Google Sheet, P(74 <= X <= 84) = 45.32%.
• If we needed the total goals to be more than 165, that means we want to have 85 or more goals given the current tally is 81. P(X >= 85) = 34.29%.

Presenting these numbers in a table and including the betting odds in the earlier screenshot:

Comparing the odds by models vs the betting odds, the value sits with "More than 165 Goals". With 50% of the tournament gone, the model predicts a 34% chance of it happening.

This time, I am going to stick my neck out and say that "More than 165 Goals" has a good chance of happening.

• Compared to 2 days ago, we have more data points and have lesser matches left, so there is less uncertainty.
• Like I mentioned in the earlier posts, the final 16 matches have a chance of additional 30 minutes of extra time if they end as a draw at full time. More minutes of playing means more chance for goals.

Of course, the same caution applies.

• The model is based on the assumption that the goals follow a Poisson Distribution. (Which might or might not be true)
• I have used the sample mean based on the current 32 matches, which might or might not be reflective of the full 64 matches. If you use a different mean, the results would be different.
• The mean and variance for the 32 matches are STILL very different for now, so a Poisson distribution might not be a strong fit. But I will observe as the matches go on.

In conclusion, on balance, I will take a chance on an outcome with a decent likelihood at odds more than 3! Wish me luck!

With that, thanks for reading! Really appreciate it if you have gone this far. As usual, let me know any thoughts that you have!