World Cup 2022 - Applying Statistics To Betting Odds #1

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!).

Alright, with that disclaimer out, let's get to the main post!

Predicting Total Goals In World Cup 2022

So today I stumbled upon one of the betting odds for the total goals for the World Cup 2022 tournaments. For those who are not familiar with reading these odds, this means if you were to bet $100 on "Less than 155" @ 2.30 odds, and if it turns out correct, you are paid $230, i.e. $100 your bet + $130 profit. (Note: I am sure there are many bookmakers out there so their odds might vary or be better. Of course, like what I have said earlier, it's meant to be textbook and not an encouragement for anyone to bet based on my analysis.)

So how does Statistics feature here? In my view, goals typically follow a Poisson Distribution.

According to Wikipedia:

The Poisson distribution can be applied to systems with a large number of possible events, each of which is rare. The number of such events that occur during a fixed time interval is, under the right circumstances, a random number with a Poisson distribution.

Again, in my view, the events can be "goals" and during a fixed time interval can be "one match".

• The variables under Poisson distribution range from 0 to infinity (no negative values), and the number of goals in 1 match ranges from 0 to theoretically infinity as well, and you can't have a negative amount of goals in a match.
• Also, two events cannot happen at the exact time. This is true to goals as well, i.e. you can't have 2 goals scored at the same time because there is only 1 ball on the pitch.
• Now the tricky part is, the events are supposed to be independent. I am not 100% sure if goals in a match are considered independent, but I think it can be a loose assumption, since we can't really predict the next goal when a goal is scored or not.
• For Poisson distribution, the mean and variance are assumed to be the same. Typically, based on my faint memory, this applies to be the goals scored per match, but for World Cup 2022, currently we are 24 matches in, I observed that the mean and variance are quite different. So that's something to take note as well.

Where We Are

After 24 matches:

• Total Goals: 57
• Mean (average goals per match): 2.38
• Variance: 4.59 (very different from Mean)

As there are a total of 64 matches, there are 40 matches to go. Using the data of 24 matches played as a sample, we can apply lambda (λ), or mean, of 2.38. So the mean goals for the remaining matches would be 40 * 2.38 = 95.

So we are assuming the remaining goals for 40 matches (X) would follow a Poisson distribution with mean 95, i.e. X ~ Po(95).

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 97 more goals given the current tally is 57. Punching the numbers into Excel/Google Sheet, P(X <= 97) = 60.74%.
• If we needed the total goals to be between 156 to 165, that means we want to have 98 to 108 more goals given the current tally is 57. Punching the numbers into Excel/Google Sheet, P(98 <= X <= 108) = 30.74%.
• If we needed the total goals to be more than 165, that means we want to have 109 or more goals given the current tally is 57. P(X >= 109) = 8.52%.

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

On first glance, it seems than there is some value in betting "Less than 155" given that the odds are 2.30 and there is a relatively high chance of around 61% of it happening. But finally, you need to take note of the following:

• 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 24 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 (2.38) and variance (4.59) for the 24 matches are very different for now, so a Poisson distribution might not be a strong fit. But I will observe as the matches go on.
• Finally, the most important factor in my opinion, for the final 16 matches, if they end with a draw after 90 minutes, there is extra time of 30 minutes and goals scored in the extra time count towards the tally as well. So that's a potential of 480 additional minutes to account for, but of course, not every match will end up in a draw. (In case you are wondering, penalty shootout goals are not counted.)

In conclusion, statistically, the "Less than 155 Goals" odds of 2.30 offer very good value but because of the considerations stated above, I think there's more observing to do and hopefully with a few more matches in the coming days, we can get a clearer picture.

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