Horses in the Race🏏
Tracking the progress of the Cricket World Cup
How many teams are still in the “running” at the 2023 Cricket World Cup?
In theory, the answer is “10” because no team is as yet eliminated. In practice, a few teams (e.g. India, South Africa and Australia) are far more likely to qualify — and so the answer should be far less. But what exactly is it? Read on to find out.
The 2023 Men’s ODI Cricket World Cup includes 10 teams. First, each of the 10 teams play each other in a group stage consisting of 45 matches. The top four teams from the group stage, then qualify for the semi-finals, the winners of which play the final.
At the beginning of the group stage, all 10 teams have some chance of qualifying for the semi-finals — though some more than others. As the group stage progresses, some teams become more likely, and others less likely.
At the time of writing (after 29 of the 45 matches of the group stage were complete), the probability of qualifying (computed by me) were as follows.
[See 2023 Cricket World Cup 🏏, if you want to know more about how these probabilities were computed.]
You might have noticed the number “4.9” above, with the suffix “Horse Race”. This was my (somewhat tongue-in-cheek) way of quantifying the number of teams that had a realistic chance of qualifying for the semi-finals.
How is this computed? Before we get to numbers, let me describe its intuitive meaning first.
The Intuition
Suppose all 10 teams have the identical probability of qualifying for the semi-final. Since, there are 4 teams in the semi-finals, the probability of each team qualifying would be 40%.
How suppose the group stage have progressed, and the 4 teams are already decided. Then these four teams each have a 100% probability of qualifying, while all the other teams have 0% probability.
What if we could define a metric that computed to “10” in the former case, and “4” in the latter case.
The Numbers
The “Horse Race” metric is the square of the number of teams in the semi-final stage (i.e. 4² = 16) divided by the sum of the squares of the probabilities of each team qualifying.
Hence, former case describe above we get 16 / (10 x 40% x 40%) = 16/1.6 = 10. In the latter case we get, 16 / (4 x 100% x 100%) = 16 / 4 = 4.
If 3 teams had already got semi-finals spots, and two other teams had 50% odds, while the other 5 were eliminated, we get 16 / (3 x 100% x 100% + 2 x 50% x 50%) = 4.57.
At the time of writing, India has almost cemented a semi-final spot. South Africa and Australia likewise, with New Zealand not far behind. Then Pakistan, Sri Lanka and Afghanistan have an outside chance, followed by the Netherlands, England and Bangladesh who are all but eliminated. The “4.9” number roughly tells us that there are 5 teams in the race.
