Proofset Academy · Lesson 2.5

The true probability versus the odds

Odds give a probability. The only question that matters is whether that probability is higher or lower than the true chance of the outcome. This lesson gives the central rule of any bet, shows why a single match proves nothing, and presents what Proofset has measured against the market.

Know the central rule: p > 1 ÷ odds.

Test the rule on odds and probabilities of your choice.

Understand why you cannot beat the market without knowing more than it does.

See that a winning bet was not necessarily a good bet.

Know what a well-calibrated probability is.

Read the Proofset measurements against the market, with their margins of error.

Part 1

The central rule

Let us call p the true probability that a bet wins. A bet makes sense in only one case:

p > 1 ÷ odds

In other words, the true chance must exceed the implied probability of the odds, margin included (lessons 2.3 and 2.4). It also works the other way round: for a true probability p, the smallest odds that make sense are 1 ÷ p. For p = 60 %, that is 1,67. Proofset shows minimum odds built on this principle on its cards (module 5).

Odds 1,80, p = 52,6 %

1 ÷ 1,80 = 55,6 %. The true chance is lower: the bet makes no sense.

Odds 1,80, p = 60 %

60 % exceeds 55,6 %: the bet makes sense.

Odds 1,25, p = 85 %

1 ÷ 1,25 = 80 %. 85 % exceeds 80 %: the bet makes sense, even at low odds.

Part 3

When you know no more than the market

If you have no information beyond what the market has, the best estimate of the true probability is that of the market without margin (lesson 2.4). But this is always lower than the implied probability of the odds, since the margin is added to it. The rule is therefore never met.

What this means

Betting “at random”, or on gut feeling, amounts to choosing, every time, a bet whose true chance is lower than the one the odds assume.

What would be needed

An estimate of the true probability better than the market’s, proven over a large number of matches. This is very difficult: the market brings together a great deal of information.

One match proves nothing; a hundred matches start to tell a story

Take a bet whose true chance is 60 %. Run 100 simulated matches. Each dot is a match: green if won, orange if lost. Run it several times and watch the streaks.

Won: 0Lost: 0Longest losing streak: 0

Key takeaway: over 100 matches, the number of wins hovers around 60, but it changes from one run to the next, and streaks of 4 or 5 losses happen often (module 4). A winning bet was not necessarily a good bet; a losing bet was not necessarily a mistake. A method is judged over hundreds of matches, not on a single one.

Part 5

A well-calibrated probability

A probability is well calibrated when it keeps its word: across all matches announced at 70 %, the favourite should win about 70 times out of 100. An overconfident estimate (“90 %” that wins only 70 times out of 100) makes you believe the rule is met when it is not.

Illustration: the diagonal is perfect calibration. The orange curve shows an overconfident estimate, as an example.

For Proofset, checking calibration is part of the method: a displayed probability must match a measured win rate. Module 6 shows how this is checked.

What Proofset has measured against the market

On its matches with odds, Proofset compared the favourite’s share of wins with the probability the market gave, with the margin removed. When the favourite wins more often than the market predicted, Proofset’s estimate knew more than the market on that group of matches.

Group of matches	Matches	Favourite wins	Market predicted	Difference (± at 95 %)
All ELO favourites	2 931	62,8 %	59,9 %	+2,9 ± 1,6
ELO favourite ≥ 65 % and 100 % dominant	141	85,8 %	77,7 %	+8,1 ± 5,6

Proofset database, matches from 01/06 to 13/10/2026 with odds (ATP, WTA, Challenger), de-duplicated database. Report “ELO + Domination versus the market” of 14/10/2026. It is not known at what time each set of odds was recorded.

Reading: the combination of ELO and Domination wins clearly more often than the market predicted, +8,1 points over 141 matches. The margins of error are wide because the groups are small: over 141 matches, the difference can range from +2,5 to +13,7 points. These are measurements of the past; they do not guarantee the future. Module 6 explains how they were made.

Why it matters for a bet

Only one question matters: does the true probability exceed 1 ÷ odds? Everything else (form, name, motivation) only matters if it changes p.
Without more information than the market, the answer is always no, because of the margin.
Judge over time: a single result says nothing about the quality of a decision. Only hundreds of matches, with their margins of error, allow a conclusion.

Part 7

Test yourself

7 questions. You need 6 correct answers to pass the lesson.

0 / 7