Shot Probability and Expected Goals Calculator
Combine entered individual shot probabilities into expected goals and a full independent-shot goal-count distribution.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sum Bernoulli means and convolve individual shot-success distributions to calculate the Poisson-binomial goal-count probabilities.
Expected goals=Σp; variance=Σp(1−p); score PMF=convolution of [1−p,p] for each shot
Worked example
Independent shot probabilities of 10%, 20% and 50% sum to 0.8 expected goals. The probability of at least one goal is 1−0.9×0.8×0.5=64%.
Assumptions and input details
1–200 entered shot probabilities. This is a probability-combination tool, not an xG model trained on shot locations or tracking data. Independence, calibration and the meaning of every entered probability are assumptions. Rebounds and game-state dependence can invalidate the score distribution. No live match data, bookmaker odds or betting action is used.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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