WCMI And Winner SP Distribution
In sports markets, the probabilities implied by the prices on offer are a proxy for the collective knowledge of the betting public for that particular event. By adapting Shannon's Entropy formula, we generated our own "Wisdom Of Crowd Market Index" (WCMI) metric for summarizing this collective knowledge on a scale from [0..1].
Insights From Real-World Data
Recently, we ran an analysis on a sample of 509 UK horse races, each with at least eight runners. Our findings provided interesting insights into the WCMI's behaviour and its relation to the market dynamics. Specifically, we looked at the average starting price of the winning horse across the different WCMI ranges.
Let's take a look at the distribution of starting prices across different WCMI ranges:
| Label | Min | Max | Count | SP Median | SP MAD |
|---|---|---|---|---|---|
| A | 0.00 | 0.09 | 77 | 6.50 | 2.17 |
| B | 0.10 | 0.19 | 216 | 5.00 | 2.00 |
| C | 0.20 | 0.29 | 159 | 4.00 | 2.00 |
| D | 0.30 | 0.39 | 51 | 1.91 | 0.41 |
The distribution of starting prices was measured using the Median Absolute Deviation (MAD), a robust measure of the statistical dispersion.
Our findings can be summarised as follows:
- Only six races had a WCMI of 0.40 or higher.
- Strong negative correlation between WCMI ranges and average starting prices of winners.
- Dispersion of average starting prices of winners is similar across WCMI ranges except for 'D', which is visibly narrower.
As expected, this suggests that when the market is less informed (lower WCMI), the starting prices tend to be higher.
The above graph is for illustrative purposes only and should not be interpreted as definitive!
Implications For Sports Trader
| Label | Min | Max | Count | SP Median | SP MAD |
|---|---|---|---|---|---|
| ST | 0.25 | 0.39 | 127 | 2.63 | 1.01 |
For the Sports Trader, the general advice would be to concentrate on the 25% of races with a WCMI range of [0.25..0.39] where the consensus is on the relative strength at the top of the market.
Implications For Convex Bettor
| Label | Min | Max | Count | SP Median | SP MAD |
|---|---|---|---|---|---|
| CB | 0.00 | 0.15 | 226 | 6.00 | 2.25 |
By contrast, for the Convex Bettor, we would recommend focusing on the 44% of races with a WCMI range of [0.00..0.15] where the consensus is on the relative weakness at the top of the market
That said, you should always evaluate what works for you - given your particular risk profile.