this formula estimates the perceptual quality of digital video files by considering key properties that affect viewer experience. each factor in the formula scales in a specific way with changes in the underlying video file properties. below is a summarized description of how each factor influences the overall quality score.

• resolution factor: increases logarithmically with the video resolution. baseline: 640x480, 0.3072 megapixel
• frame rate factor: increases logarithmically with the frame rate. baseline: 30
• bit depth factor: increases logarithmically with the bit depth. baseline: 8
• bitrate factor: modeled using a sigmoid function relative to the optimal bitrate. baseline: resolution * bitdepth * framerate * codec_factor
• codec factor: adjusts the optimal bitrate based on codec efficiency relative to a baseline codec. baseline: h264
• quality score: additive aggregation with weighted contributions from each factor

the score is suitable for estimating quality in contexts where detailed subjective testing is impractical. furthermore, it can aid in decision-making for video encoding settings, streaming quality selection, or benchmarking.

get_quality_score = (width, height, framerate, bitdepth, bitrate, codec) ->
  codec_efficiencies =
    av1: 1.5
    h264: 1.0
    h266: 2.0
    hevc: 1.7
    vp8: 0.9
    vp9: 1.3
  codec_factor = 1.0 / (codec_efficiencies[codec] or 0.8)
  resolution = width * height
  optimal_bitrate = resolution * bitdepth * framerate * codec_factor
  bitrate_factor = 2.0 / (1 + Math.exp(-0.001 * (bitrate - optimal_bitrate)))
  resolution_factor = Math.log2(resolution / (1920 * 1080) + 1)
  framerate_factor = Math.log2(framerate / 30.0 + 1)
  bitdepth_factor = Math.log2((bitdepth - 6.0) / 2.0)
  score = 0.4 * resolution_factor + 0.3 * framerate_factor + 0.2 * bitdepth_factor + 0.1 * bitrate_factor
  Math.max 0, Math.round(score * 10 - 1)

640x480 30 8 9000000 h264 -> 3
640x480 30 8 25000000 h264 -> 3
640x480 30 8 75000000 h264 -> 5
640x480 30 8 100000000 h264 -> 5
640x480 30 8 200000000 h264 -> 5
640x480 30 8 9000000 av1 -> 3
640x480 30 8 25000000 av1 -> 3
640x480 30 8 75000000 av1 -> 5
640x480 30 8 100000000 av1 -> 5
640x480 30 8 200000000 av1 -> 5
640x480 30 10 9000000 h264 -> 5
640x480 30 10 25000000 h264 -> 5
640x480 30 10 75000000 h264 -> 5
640x480 30 10 100000000 h264 -> 7
640x480 30 10 200000000 h264 -> 7
640x480 30 10 9000000 av1 -> 5
640x480 30 10 25000000 av1 -> 5
640x480 30 10 75000000 av1 -> 7
640x480 30 10 100000000 av1 -> 7
640x480 30 10 200000000 av1 -> 7
640x480 60 8 9000000 h264 -> 5
640x480 60 8 25000000 h264 -> 5
640x480 60 8 75000000 h264 -> 5
640x480 60 8 100000000 h264 -> 5
640x480 60 8 200000000 h264 -> 7
640x480 60 8 9000000 av1 -> 5
640x480 60 8 25000000 av1 -> 5
640x480 60 8 75000000 av1 -> 5
640x480 60 8 100000000 av1 -> 7
640x480 60 8 200000000 av1 -> 7
640x480 60 10 9000000 h264 -> 7
640x480 60 10 25000000 h264 -> 7
640x480 60 10 75000000 h264 -> 7
640x480 60 10 100000000 h264 -> 7
640x480 60 10 200000000 h264 -> 9
640x480 60 10 9000000 av1 -> 7
640x480 60 10 25000000 av1 -> 7
640x480 60 10 75000000 av1 -> 7
640x480 60 10 100000000 av1 -> 7
640x480 60 10 200000000 av1 -> 9
640x480 120 8 9000000 h264 -> 7
640x480 120 8 25000000 h264 -> 7
640x480 120 8 75000000 h264 -> 7
640x480 120 8 100000000 h264 -> 7
640x480 120 8 200000000 h264 -> 7
640x480 120 8 9000000 av1 -> 7
640x480 120 8 25000000 av1 -> 7
640x480 120 8 75000000 av1 -> 7
640x480 120 8 100000000 av1 -> 7
640x480 120 8 200000000 av1 -> 9
640x480 120 10 9000000 h264 -> 9
640x480 120 10 25000000 h264 -> 9
640x480 120 10 75000000 h264 -> 9
640x480 120 10 100000000 h264 -> 9
640x480 120 10 200000000 h264 -> 9
640x480 120 10 9000000 av1 -> 9
640x480 120 10 25000000 av1 -> 9
640x480 120 10 75000000 av1 -> 9
640x480 120 10 100000000 av1 -> 9
640x480 120 10 200000000 av1 -> 9

1920x1080 30 8 9000000 h264 -> 6
1920x1080 30 8 25000000 h264 -> 6
1920x1080 30 8 75000000 h264 -> 6
1920x1080 30 8 100000000 h264 -> 6
1920x1080 30 8 200000000 h264 -> 6
1920x1080 30 8 9000000 av1 -> 6
1920x1080 30 8 25000000 av1 -> 6
1920x1080 30 8 75000000 av1 -> 6
1920x1080 30 8 100000000 av1 -> 6
1920x1080 30 8 200000000 av1 -> 6
1920x1080 30 10 9000000 h264 -> 8
1920x1080 30 10 25000000 h264 -> 8
1920x1080 30 10 75000000 h264 -> 8
1920x1080 30 10 100000000 h264 -> 8
1920x1080 30 10 200000000 h264 -> 8
1920x1080 30 10 9000000 av1 -> 8
1920x1080 30 10 25000000 av1 -> 8
1920x1080 30 10 75000000 av1 -> 8
1920x1080 30 10 100000000 av1 -> 8
1920x1080 30 10 200000000 av1 -> 8
1920x1080 60 8 9000000 h264 -> 8
1920x1080 60 8 25000000 h264 -> 8
1920x1080 60 8 75000000 h264 -> 8
1920x1080 60 8 100000000 h264 -> 8
1920x1080 60 8 200000000 h264 -> 8
1920x1080 60 8 9000000 av1 -> 8
1920x1080 60 8 25000000 av1 -> 8
1920x1080 60 8 75000000 av1 -> 8
1920x1080 60 8 100000000 av1 -> 8
1920x1080 60 8 200000000 av1 -> 8
1920x1080 60 10 9000000 h264 -> 10
1920x1080 60 10 25000000 h264 -> 10
1920x1080 60 10 75000000 h264 -> 10
1920x1080 60 10 100000000 h264 -> 10
1920x1080 60 10 200000000 h264 -> 10
1920x1080 60 10 9000000 av1 -> 10
1920x1080 60 10 25000000 av1 -> 10
1920x1080 60 10 75000000 av1 -> 10
1920x1080 60 10 100000000 av1 -> 10
1920x1080 60 10 200000000 av1 -> 10
1920x1080 120 8 9000000 h264 -> 10
1920x1080 120 8 25000000 h264 -> 10
1920x1080 120 8 75000000 h264 -> 10
1920x1080 120 8 100000000 h264 -> 10
1920x1080 120 8 200000000 h264 -> 10
1920x1080 120 8 9000000 av1 -> 10
1920x1080 120 8 25000000 av1 -> 10
1920x1080 120 8 75000000 av1 -> 10
1920x1080 120 8 100000000 av1 -> 10
1920x1080 120 8 200000000 av1 -> 10
1920x1080 120 10 9000000 h264 -> 12
1920x1080 120 10 25000000 h264 -> 12
1920x1080 120 10 75000000 h264 -> 12
1920x1080 120 10 100000000 h264 -> 12
1920x1080 120 10 200000000 h264 -> 12
1920x1080 120 10 9000000 av1 -> 12
1920x1080 120 10 25000000 av1 -> 12
1920x1080 120 10 75000000 av1 -> 12
1920x1080 120 10 100000000 av1 -> 12
1920x1080 120 10 200000000 av1 -> 12

3840x2160 30 8 9000000 h264 -> 11
3840x2160 30 8 25000000 h264 -> 11
3840x2160 30 8 75000000 h264 -> 11
3840x2160 30 8 100000000 h264 -> 11
3840x2160 30 8 200000000 h264 -> 11
3840x2160 30 8 9000000 av1 -> 11
3840x2160 30 8 25000000 av1 -> 11
3840x2160 30 8 75000000 av1 -> 11
3840x2160 30 8 100000000 av1 -> 11
3840x2160 30 8 200000000 av1 -> 11
3840x2160 30 10 9000000 h264 -> 13
3840x2160 30 10 25000000 h264 -> 13
3840x2160 30 10 75000000 h264 -> 13
3840x2160 30 10 100000000 h264 -> 13
3840x2160 30 10 200000000 h264 -> 13
3840x2160 30 10 9000000 av1 -> 13
3840x2160 30 10 25000000 av1 -> 13
3840x2160 30 10 75000000 av1 -> 13
3840x2160 30 10 100000000 av1 -> 13
3840x2160 30 10 200000000 av1 -> 13
3840x2160 60 8 9000000 h264 -> 13
3840x2160 60 8 25000000 h264 -> 13
3840x2160 60 8 75000000 h264 -> 13
3840x2160 60 8 100000000 h264 -> 13
3840x2160 60 8 200000000 h264 -> 13
3840x2160 60 8 9000000 av1 -> 13
3840x2160 60 8 25000000 av1 -> 13
3840x2160 60 8 75000000 av1 -> 13
3840x2160 60 8 100000000 av1 -> 13
3840x2160 60 8 200000000 av1 -> 13
3840x2160 60 10 9000000 h264 -> 15
3840x2160 60 10 25000000 h264 -> 15
3840x2160 60 10 75000000 h264 -> 15
3840x2160 60 10 100000000 h264 -> 15
3840x2160 60 10 200000000 h264 -> 15
3840x2160 60 10 9000000 av1 -> 15
3840x2160 60 10 25000000 av1 -> 15
3840x2160 60 10 75000000 av1 -> 15
3840x2160 60 10 100000000 av1 -> 15
3840x2160 60 10 200000000 av1 -> 15
3840x2160 120 8 9000000 h264 -> 15
3840x2160 120 8 25000000 h264 -> 15
3840x2160 120 8 75000000 h264 -> 15
3840x2160 120 8 100000000 h264 -> 15
3840x2160 120 8 200000000 h264 -> 15
3840x2160 120 8 9000000 av1 -> 15
3840x2160 120 8 25000000 av1 -> 15
3840x2160 120 8 75000000 av1 -> 15
3840x2160 120 8 100000000 av1 -> 15
3840x2160 120 8 200000000 av1 -> 15
3840x2160 120 10 9000000 h264 -> 17
3840x2160 120 10 25000000 h264 -> 17
3840x2160 120 10 75000000 h264 -> 17
3840x2160 120 10 100000000 h264 -> 17
3840x2160 120 10 200000000 h264 -> 17
3840x2160 120 10 9000000 av1 -> 17
3840x2160 120 10 25000000 av1 -> 17
3840x2160 120 10 75000000 av1 -> 17
3840x2160 120 10 100000000 av1 -> 17
3840x2160 120 10 200000000 av1 -> 17

7680x4320 30 8 9000000 h264 -> 18
7680x4320 30 8 25000000 h264 -> 18
7680x4320 30 8 75000000 h264 -> 18
7680x4320 30 8 100000000 h264 -> 18
7680x4320 30 8 200000000 h264 -> 18
7680x4320 30 8 9000000 av1 -> 18
7680x4320 30 8 25000000 av1 -> 18
7680x4320 30 8 75000000 av1 -> 18
7680x4320 30 8 100000000 av1 -> 18
7680x4320 30 8 200000000 av1 -> 18
7680x4320 30 10 9000000 h264 -> 20
7680x4320 30 10 25000000 h264 -> 20
7680x4320 30 10 75000000 h264 -> 20
7680x4320 30 10 100000000 h264 -> 20
7680x4320 30 10 200000000 h264 -> 20
7680x4320 30 10 9000000 av1 -> 20
7680x4320 30 10 25000000 av1 -> 20
7680x4320 30 10 75000000 av1 -> 20
7680x4320 30 10 100000000 av1 -> 20
7680x4320 30 10 200000000 av1 -> 20
7680x4320 60 8 9000000 h264 -> 20
7680x4320 60 8 25000000 h264 -> 20
7680x4320 60 8 75000000 h264 -> 20
7680x4320 60 8 100000000 h264 -> 20
7680x4320 60 8 200000000 h264 -> 20
7680x4320 60 8 9000000 av1 -> 20
7680x4320 60 8 25000000 av1 -> 20
7680x4320 60 8 75000000 av1 -> 20
7680x4320 60 8 100000000 av1 -> 20
7680x4320 60 8 200000000 av1 -> 20
7680x4320 60 10 9000000 h264 -> 22
7680x4320 60 10 25000000 h264 -> 22
7680x4320 60 10 75000000 h264 -> 22
7680x4320 60 10 100000000 h264 -> 22
7680x4320 60 10 200000000 h264 -> 22
7680x4320 60 10 9000000 av1 -> 22
7680x4320 60 10 25000000 av1 -> 22
7680x4320 60 10 75000000 av1 -> 22
7680x4320 60 10 100000000 av1 -> 22
7680x4320 60 10 200000000 av1 -> 22
7680x4320 120 8 9000000 h264 -> 22
7680x4320 120 8 25000000 h264 -> 22
7680x4320 120 8 75000000 h264 -> 22
7680x4320 120 8 100000000 h264 -> 22
7680x4320 120 8 200000000 h264 -> 22
7680x4320 120 8 9000000 av1 -> 22
7680x4320 120 8 25000000 av1 -> 22
7680x4320 120 8 75000000 av1 -> 22
7680x4320 120 8 100000000 av1 -> 22
7680x4320 120 8 200000000 av1 -> 22
7680x4320 120 10 9000000 h264 -> 24
7680x4320 120 10 25000000 h264 -> 24
7680x4320 120 10 75000000 h264 -> 24
7680x4320 120 10 100000000 h264 -> 24
7680x4320 120 10 200000000 h264 -> 24
7680x4320 120 10 9000000 av1 -> 24
7680x4320 120 10 25000000 av1 -> 24
7680x4320 120 10 75000000 av1 -> 24
7680x4320 120 10 100000000 av1 -> 24
7680x4320 120 10 200000000 av1 -> 24