Comparing two season totals seems straightforward until the underlying mix of fixtures changes. A higher overall hit rate can coexist with a lower hit rate in every group. Before concluding that a research filter improved, inspect what contributed to each denominator.
A numerical example with no match-data claims
Let A and B represent two groups of fixtures. In period one, the selected outcome occurs in 8 of 10 A fixtures and 18 of 90 B fixtures. Together that is 26 out of 100, or 26%.
In period two, it occurs in 63 of 90 A fixtures and 1 of 10 B fixtures. The total is now 64 out of 100, or 64%. Yet A has fallen from 80% to 70%, and B has fallen from 20% to 10%. These are constructed counts used to explain the arithmetic, not observed results from any competition or product.
| Group | Period one | Period two |
|---|---|---|
| A | 8/10 = 80% | 63/90 = 70% |
| B | 18/90 = 20% | 1/10 = 10% |
| Combined | 26/100 = 26% | 64/100 = 64% |
The denominator contains the explanation
The second period contains many more fixtures from A, where the outcome is more frequent. The overall rate is a weighted average of the group rates, using each group's share of observations as its weight. Changing those shares changes the meaning of the combined comparison.
There is no arithmetic contradiction. The aggregate answers what happened in each observed mixture. The group comparisons answer what happened within A and B separately. Treating those as the same question produces the misleading interpretation.
Add a comparison with fixed weights
For illustration, give A and B equal weight in both periods. Period one becomes 0.5 × 80% + 0.5 × 20% = 50%. Period two becomes 0.5 × 70% + 0.5 × 10% = 40%. Holding the mixture fixed makes the within-group deterioration visible.
Equal weights are a choice, not a universal standard. In an actual study, the target population may suggest different weights. State the choice before interpreting the result and report the observed total separately from the standardised comparison. Selecting weights after seeing which produce a preferred conclusion defeats the purpose.
Check the composition of an odds archive
New competitions, missing seasons and changes in price coverage can alter the fixture mix. Football-Data's collection and coverage notes illustrate why the documentation accompanying an archive matters. In your own study, tabulate counts by season, competition, price band and market before comparing a single headline percentage.
This exercise does not remove statistical uncertainty. A group containing ten fixtures still has a small denominator. It establishes a prior question: are the periods describing comparable populations? Only after answering that should a higher total be discussed as possible evidence of an improved method.
Sources and method
Calculations and scenarios are original teaching examples, not observed match data, product performance or predictions. Sources support the stated concepts and methods. This article was prepared with AI assistance; sources and calculations were checked.
- Football-Data: data coverage and collection notes — accessed 14 September 2026