Published by Sean Carr
Fixed Cost vs Pixel Cost: A Resolution Ladder With R^2 = 0.99993
Frame time was a clean linear function of shaded pixels, and an earlier 'quartering pixels saved ~20%' figure did not survive the full curve.
At a Glance
Linear fit on p50
R^2 = 0.999931
Fit on p50: F = 2.6416 ms, k = 0.5707 ms/Mpix, R^2 = 0.999931. p99 fit R^2 = 0.999999.
4K to 1080p frame-time reduction
48%
4K to 1440p: 1.548x ratio, about a 35.7% frame-time reduction. 4K to 1080p: a 48% reduction.
p50 frame time, native 4K
7.373 ms
p50 frame time: 1080p 3.812 ms; 1440p 4.763 ms; native 4K fullscreen 7.373 ms.
Pixel term share at native 4K
64%
At native 4K, pixel term 4.74 ms = 64% of the frame; at 1080p it is 31%.
| Telemetry Metric | Measured Value | Context & Observability |
|---|---|---|
| Linear fit on p50 | R^2 = 0.999931 | Fit on p50: F = 2.6416 ms, k = 0.5707 ms/Mpix, R^2 = 0.999931. p99 fit R^2 = 0.999999. |
| 4K to 1080p frame-time reduction | 48% | 4K to 1440p: 1.548x ratio, about a 35.7% frame-time reduction. 4K to 1080p: a 48% reduction. |
| p50 frame time, native 4K | 7.373 ms | p50 frame time: 1080p 3.812 ms; 1440p 4.763 ms; native 4K fullscreen 7.373 ms. |
| Pixel term share at native 4K | 64% | At native 4K, pixel term 4.74 ms = 64% of the frame; at 1080p it is 31%. |
| Held-out rung residuals | ±0.04 ms | Held-out rungs land within ±0.04 ms of the fit (residuals +0.001, -0.013, +0.039 ms). |
| Pixel cost equals fixed cost | 4.63 Mpix | Crossover where pixel cost equals fixed cost: 4.63 Mpix. |
| Present pass share at 4K | 97% | At 4K, the present pass (GPU shading plus present) was 7.129 ms of the 7.373 ms frame (97%). |
| Native 4K p99 | 7.807 ms | Every rung met the 8.33 ms (120 FPS) target at p50 and p99; native 4K p99 was 7.807 ms. |
Published by Sean Carr
View & print executive brief version →Executive Summary & Core Finding
We measured frame time at six render extents from 1080p to native 4K and fit T = F + k·P. On the three native rungs, p50 frame time fit with R^2 = 0.999931, and three resampled rungs landed on the same line within 0.04 ms. Dropping from 4K to 1080p cut frame time by 48%, not the roughly 20% an earlier spot measurement had suggested.
Method
Data collected Aug 7, 2026; written up October 2026.
August 7, 2026, NVIDIA GeForce RTX 5080, 3840x2160 160 Hz display, MAILBOX present mode verified on every rung, quiet machine.
Each rung ran 1030 frames of a deterministic playing scene with a fixed camera; the first 30 frames were dropped and 1000 measured.
The fit used least squares over the three 1:1 native rungs; the other three rungs were held out as validation.
True shaded extent was taken from the engine's own log rather than the swapchain size.
What We Measured
Frame time at six render extents, 1080p to native 4K
Linear fit on p50
R^2 = 0.999931
Fit on p50: F = 2.6416 ms, k = 0.5707 ms/Mpix, R^2 = 0.999931. p99 fit R^2 = 0.999999.
4K to 1080p frame-time reduction
48%
4K to 1440p: 1.548x ratio, about a 35.7% frame-time reduction. 4K to 1080p: a 48% reduction.
p50 frame time, native 4K
7.373 ms
p50 frame time: 1080p 3.812 ms; 1440p 4.763 ms; native 4K fullscreen 7.373 ms.
Pixel term share at native 4K
64%
At native 4K, pixel term 4.74 ms = 64% of the frame; at 1080p it is 31%.
Held-out rung residuals
±0.04 ms
Held-out rungs land within ±0.04 ms of the fit (residuals +0.001, -0.013, +0.039 ms).
Pixel cost equals fixed cost
4.63 Mpix
Crossover where pixel cost equals fixed cost: 4.63 Mpix.
Present pass share at 4K
97%
At 4K, the present pass (GPU shading plus present) was 7.129 ms of the 7.373 ms frame (97%).
Native 4K p99
7.807 ms
Every rung met the 8.33 ms (120 FPS) target at p50 and p99; native 4K p99 was 7.807 ms.
What We Think It Suggests
- For this scene on this GPU, resolution behaved as a near-linear lever, and the cost tracked shaded pixels rather than the swapchain size. A half-scale render presented into a 4K swapchain cost 3.813 ms, within 0.001 ms of native 1080p at 3.812 ms.
- The earlier ~20% figure was most likely confounded by vsync quantization or a windowed-mode clip that hid the true render extent. Logging the true shaded extent per rung was what made the curve clean.
Limits
- The fit has only three points; a high R^2 on three points says the points are collinear, not that the model holds across all resolutions.
- One light scene at one camera anchor on one GPU. Later builds with more content measured much slower 4K frames, so these absolute numbers describe this scene only.
- The source of the earlier ~20% figure is not in this record, so the confound is an explanation, not a demonstrated cause.
Detailed Analysis & Field Observations
We measured frame time at six render extents from 1080p to native 4K and fit T = F + k·P. On the three native rungs, p50 frame time fit with R^2 = 0.999931, and three resampled rungs landed on the same line within 0.04 ms. Dropping from 4K to 1080p cut frame time by 48%, not the roughly 20% an earlier spot measurement had suggested.
Data collected Aug 7, 2026; written up October 2026.