Gaming Frame Rate A/B Test Formula
Learn how average FPS difference, relative uplift, standard error, and approximate confidence bounds are calculated for two gaming benchmark variants.
This calculator estimates whether the average FPS difference between Variant A and Variant B is large relative to normal run-to-run variation. It is useful for comparing controlled changes such as graphics settings, drivers, hardware configurations, or game patches.
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Approximate 95% Confidence Interval for FPS Difference
Where:
First find how many FPS Variant B gains or loses versus Variant A. Then calculate the uncertainty from each variant's FPS variation and number of runs. Adding and subtracting 1.96 times that uncertainty gives an approximate 95% range for the true FPS difference.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| averageFpsA - Variant A average FPS | The mean frames per second measured for the baseline variant. | FPS |
| averageFpsB - Variant B average FPS | The mean frames per second measured for the changed or challenger variant. | FPS |
| fpsStdDevA - Variant A FPS standard deviation | The amount FPS results vary from run to run for Variant A. | FPS |
| fpsStdDevB - Variant B FPS standard deviation | The amount FPS results vary from run to run for Variant B. | FPS |
| sampleSizeA - Variant A benchmark runs | The number of comparable FPS observations for Variant A. | number |
| sampleSizeB - Variant B benchmark runs | The number of comparable FPS observations for Variant B. | number |
Step-by-Step Calculation
Calculate the average FPS difference
A positive result means Variant B has a higher average FPS; a negative result means it is slower.
fpsDifference = averageFpsB - averageFpsA
Calculate the percentage FPS uplift
This expresses the FPS change relative to the Variant A baseline.
fpsUplift = (fpsDifference / averageFpsA) * 100
Calculate the variance contribution from Variant A
Higher run-to-run variation increases uncertainty, while more benchmark runs reduce it.
varianceA = pow(fpsStdDevA, 2) / sampleSizeA
Calculate the variance contribution from Variant B
This is the corresponding uncertainty contribution for Variant B.
varianceB = pow(fpsStdDevB, 2) / sampleSizeB
Calculate the standard error of the difference
The standard error estimates how much the measured FPS difference may vary across comparable samples.
standardError = sqrt(varianceA + varianceB)
Calculate the performance difference score
This expresses the observed FPS difference in standard-error units. A larger absolute score indicates a clearer difference relative to measured variation.
zScore = fpsDifference / standardError
Calculate approximate confidence bounds
These bounds provide an approximate 95% interval for the underlying average FPS difference.
confidenceLower = fpsDifference - 1.96 * standardError; confidenceUpper = fpsDifference + 1.96 * standardError
Comparing two graphics configurations
Find the FPS difference
128 - 120
8 FPS
Find the relative uplift
(8 / 120) * 100
6.67%
Calculate Variant A variance contribution
pow(12, 2) / 50
2.88
Calculate Variant B variance contribution
pow(14, 2) / 50
3.92
Calculate standard error
sqrt(2.88 + 3.92)
2.61 FPS
Calculate 95% margin
1.96 * 2.61
5.12 FPS
Calculate confidence range
8 - 5.12 to 8 + 5.12
2.88 to 13.12 FPS
Final Result
Variant B is 8.0 FPS faster than Variant A, a 6.67% uplift. The approximate 95% confidence interval is 2.9 to 13.1 FPS.
Assumptions
- ✓Benchmark runs use broadly comparable scenes, game versions, graphics settings, hardware conditions, and measurement methods.
- ✓The observations within each variant are treated as independent measurements.
- ✓The supplied standard deviations reasonably describe run-to-run FPS variation.
- ✓The normal approximation used for the 95% interval is most informative when each variant has several repeated runs.
Limitations
- !Average FPS does not measure frame-time consistency, stutter, 1% lows, input latency, or visual quality.
- !Changing scenes, background activity, thermal behavior, shader compilation, and game updates can affect results beyond the tested change.
- !The interval is approximate and depends on accurate run counts and standard deviations.
- !A statistically clearer difference may still be too small to matter at a chosen display refresh rate or for a specific game.
Common Mistakes to Avoid
Entering one benchmark pass as though it represents many independent runs.
Comparing different scenes, resolutions, graphics presets, or benchmark durations between variants.
Using the FPS standard deviation from individual frame times when the input is intended to represent variation among benchmark-run results.
Treating a positive average FPS result as proof of better frame pacing or lower input latency.
Using percentage uplift without checking the absolute FPS difference and confidence range.
Related Formulas
Frequently Asked Questions
How do you calculate FPS difference between two benchmark variants?
Subtract Variant A average FPS from Variant B average FPS. A result above zero means Variant B is faster on average.
How is FPS uplift calculated?
Divide the FPS difference by Variant A average FPS, then multiply by 100. This gives the percentage change relative to the baseline.
What is the standard error in an FPS A/B test?
It estimates uncertainty in the difference between the two average FPS values using each variant's standard deviation and number of runs.
What does an approximate 95% FPS confidence interval show?
It shows a plausible range for the underlying average FPS difference based on the entered benchmark data. A range entirely above zero indicates the measured gain is more clearly separated from observed variation.
What does a negative FPS difference mean?
It means Variant B averaged fewer FPS than Variant A. The confidence range helps show whether that observed loss is clear relative to normal variation.
Is a high performance difference score always important for gaming?
No. It indicates a clearer measured difference relative to variation, but practical importance also depends on the absolute FPS change, frame pacing, display refresh rate, and gameplay goals.
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