When analyzing sports, most predictions give you a single number: "Team A will score 2 goals" or "Player X will hit 15 aces." But what if you could see the full picture—not just what's most likely to happen, but the probability of every possible outcome?
At PredixSport, our AI models don't just predict single values. They generate complete probability distributions that show you the likelihood of each possible result. This guide explains how to read and interpret these powerful analytical tools, even if you have no statistics background.
What Is a Probability Distribution?
Think of a probability distribution as a visual answer to the question: "What are all the possible outcomes, and how likely is each one?"
Instead of saying "we expect 24 total points," a distribution shows you something far more valuable: there's a 5% chance of 20 points, 8% chance of 21 points, 12% chance of 22 points, 15% chance of 23 points, 18% chance of 24 points, and so on. You see the complete landscape of possibilities.
The Key Insight
A single prediction hides uncertainty. A probability distribution reveals it—showing you not only what's most likely, but how confident the model is and what range of outcomes you should realistically expect.
The Probability Distribution Chart
Let's look at a practical example. The chart below shows a probability distribution for total points in a hypothetical match. Each bar represents a possible outcome, and the height shows how likely that outcome is.
Example: Probability Distribution
How to Read This Chart
The peak shows the most likely outcome (the "mode"). The spread shows uncertainty—a narrow distribution means more confidence, while a wide spread indicates greater uncertainty. The dashed line marks the expected value (average prediction).
What You Can Learn from a Distribution
- Expected Value (Mean): The weighted average of all outcomes—what the model predicts "on average"
- Most Likely Outcome (Mode): The single value with the highest probability—the peak of the curve
- Spread (Variance): How spread out the possibilities are—narrow means more certainty, wide means less
- Skewness: Whether outcomes lean toward higher or lower values
The Cumulative Distribution Function (CDF)
While the probability distribution answers "how likely is exactly this outcome?", the CDF answers a different but equally important question: "What's the probability of the outcome being less than or equal to this value?"
This makes the CDF incredibly useful for over/under analysis. Want to know the probability of under 24 total points? Just look at where 24 intersects the CDF curve—it directly gives you that probability.
Example: Cumulative Distribution Function (CDF)
How to Read This Chart
The CDF always rises from 0% to 100%. To find the probability of "under X," find X on the horizontal axis and read the percentage on the vertical axis. For "over X," subtract that percentage from 100%. The steeper the curve, the more probability is concentrated in that range.
Practical CDF Examples
Using the CDF chart above, you can quickly answer questions like:
- "What's the probability of under 22 points?" → Find 22 on the x-axis, read ~25% on y-axis
- "What's the probability of over 26 points?" → Find 26 (~75% under), so ~25% over
- "What's the probability of exactly between 22-26 points?" → 75% - 25% = 50%
Distribution vs. CDF: When to Use Each
Both charts come from the same underlying data but answer different questions:
| Question Type | Use This Chart | Example |
|---|---|---|
| What's the most likely outcome? | Distribution | The peak shows 24 points is most probable |
| How confident is the prediction? | Distribution | Narrow spread = high confidence |
| Probability of under/over a threshold? | CDF | Read directly from the curve at that point |
| Probability within a range? | CDF | Subtract lower bound from upper bound |
Why This Matters for Sports Analysis
Understanding probability distributions gives you a significant analytical advantage:
Richer Information
A single prediction tells you one thing. A distribution tells you everything—the expected outcome, alternative scenarios, and how much uncertainty exists. This is the difference between a guess and informed analysis.
Identify Edge Cases
Distributions reveal when extreme outcomes are more likely than you'd expect. A long "tail" on one side might indicate potential for surprisingly high or low results that single predictions would miss entirely.
Compare Scenarios
When two predictions have the same expected value but different distributions, they tell very different stories. One might be highly confident while another has massive uncertainty—information you'd completely miss with single-point predictions.
Our Unique Approach
At PredixSport, we're one of the few sports analytics platforms that provide full probability distributions for our predictions. While most services give you a single number, our AI models—trained on extensive historical data—generate complete probability curves for metrics like:
- Total points/goals/games in a match
- Individual player statistics (aces, assists, rebounds, etc.)
- Match winner probabilities
Note: Our probability distributions are generated by deep learning models trained on large datasets of historical matches. The distributions reflect statistical patterns and tendencies, not certainties. Sports outcomes are inherently unpredictable, and these tools are designed to enhance your analytical understanding, not guarantee results.
See Our Probability Distributions in Action
Explore our match analysis pages to see real probability distributions and CDF charts for upcoming games across multiple sports.
Conclusion
Probability distributions and CDFs are powerful tools that transform how you understand sports predictions. Instead of relying on single-point estimates that hide uncertainty, these visualizations reveal the complete picture—showing you not just what's likely, but how likely, and the full range of realistic possibilities.
Whether you're analyzing total points in basketball, goals in soccer, or aces in tennis, understanding these charts gives you a deeper, more nuanced view of what our AI models are actually predicting. It's the difference between hearing "expect around 24" and seeing exactly why 24 is expected, how confident that prediction is, and what other outcomes remain entirely plausible.
This is the foundation of modern sports analytics—and now you have the knowledge to read it like a professional.