Most sports predictions give you one number: "Team A will score 2 goals" or "Player X will hit 15 aces." Our models give the chance of every possible result instead. That list of chances is a probability distribution, and this guide shows how to read one, no statistics background needed.
What is a probability distribution?
It answers one question: what can happen, and how likely is each result?
Instead of "we expect 24 total points", a distribution says: 5% for 20 points, 8% for 21, 12% for 22, 15% for 23, 18% for 24, and so on. You see the likely results and the unlikely ones side by side.
Why it matters
Two forecasts can both say "about 24". One can be almost sure of it and the other barely more than a guess. Only the distribution tells them apart.
Reading the distribution chart
The chart below is a made-up example for total points in a match. Each bar is one possible result, and its height is how likely that result is.
Example: Probability Distribution
How to read this chart
The peak is the most likely result. The width is the uncertainty: a narrow shape means the model is fairly sure, a wide one means many results are possible. The dashed line marks the expected value, the average result.
Four things a distribution tells you
- Expected value (mean): the average result, weighting every outcome by its chance.
- Most likely result (mode): the single value with the highest chance, the top of the curve.
- Spread (variance): how far results can wander. Narrow means more certainty, wide means less.
- Skew: whether the long tail sits on the high side or the low side.
The mean and the mode are not always the same. In a skewed distribution the average is pulled toward the long tail.
The cumulative distribution function (CDF)
The distribution answers "how likely is exactly this result?". The CDF answers "how likely is this result or anything lower?"
That makes it the chart for over/under questions. For the chance of 24 total points or fewer, find 24 on the horizontal axis and read the height of the curve.
Example: Cumulative Distribution Function (CDF)
How to read this chart
The CDF always climbs from 0% to 100%. For "X or fewer", find X on the horizontal axis and read the percentage. For "more than X", subtract that percentage from 100%. Where the curve is steep, many results are packed together.
Three worked examples
With the example CDF above:
- 22 points or fewer: find 22, read about 31%.
- More than 26 points: 26 reads about 80%, so 100% minus 80% gives about 20%.
- Between 23 and 26 points: 80% at 26 minus 31% at 22 gives about 49%.
Distribution or CDF: which chart for which question
Both charts come from the same numbers. They answer different questions:
| Question | Chart | Example |
|---|---|---|
| What is the most likely result? | Distribution | The peak sits at 24 points |
| How sure is the model? | Distribution | A narrow shape means more certainty |
| Chance of going over or under a number? | CDF | Read the curve at that number |
| Chance of landing inside a range? | CDF | Upper value minus lower value |
What you see that a single number hides
The tails
A long tail on one side means very high or very low results are more likely than the average suggests. A single prediction never shows it.
Same average, different stories
Two matches can share an expected value of 24 while one has a narrow curve and the other a wide one. The first is a confident forecast, the second an open one.
Where you will find these charts
Our match pages show a distribution and a CDF for the totals and spreads we model, for example:
- total points, goals or games in a match
- player statistics such as tennis aces and double faults, or NBA points, rebounds and assists
The match winner is shown as a probability for each side.
Note: the distributions come from neural network models trained on past matches. They describe what tends to happen, not what will happen, and we publish how well they match real results.
See real distributions
The match analysis pages carry distribution and CDF charts for upcoming games.
In short
A distribution shows every result and its chance. The CDF turns the same numbers into "this or fewer" and "more than this". Together they tell you what is likely, how likely, and how much else could still happen.