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How Delta-E 2000 Scoring Works in ToonTone

Why Color Scoring Needs Science


When you pick a color in ToonTone and see your score, you might wonder: why not just compare how far apart the red, green, and blue values are? The answer lies in a fundamental truth about human vision — our eyes don't perceive all colors equally.


Try this mental experiment: imagine shifting a pure blue by 20 RGB units versus shifting a pure green by 20 units. The green shift looks much more dramatic to human eyes, even though the "mathematical distance" is identical. This is because our retinas have different types of cone cells with unequal sensitivities across the visible spectrum.


This is exactly why ToonTone uses Delta-E 2000 (written ΔE₀₀) — the gold standard in color science for measuring perceptual color difference.



The Journey from RGB to a Score


Step 1: RGB → Lab Color Space


Your monitor displays colors in RGB (Red, Green, Blue). But RGB is a device-dependent color model — the same RGB values look different on different screens. More importantly, RGB doesn't map to how humans actually see color.


The CIELAB color space (commonly called "Lab") was designed in 1976 to be perceptually uniform. It separates color into three channels:


  • L* — Lightness (0 = black, 100 = white)
  • a* — Green to Red axis
  • b* — Blue to Yellow axis

    • The conversion from RGB to Lab involves two intermediate steps:


    1. RGB → XYZ: A linear transformation using a standard illuminant (we use D65, which simulates daylight)

    2. XYZ → Lab: A non-linear transformation that applies cube-root compression to match human perception


    This means that equal distances in Lab space correspond roughly to equal perceived differences — a critical property for fair scoring.


    Step 2: The CIEDE2000 Formula


    Once both colors (your guess and the target) are in Lab space, we apply the CIEDE2000 formula. This is not a simple Euclidean distance. It's a sophisticated formula published in 2000 by the International Commission on Illumination (CIE) that accounts for several perceptual effects:


    Lightness Weighting (SL)

    Humans are less sensitive to lightness differences in very dark or very light colors. CIEDE2000 applies a compensation factor that reduces the impact of lightness differences at the extremes.


    Chroma Weighting (SC)

    More saturated colors need a bigger change to look different. The formula scales the chroma (saturation) difference accordingly — a 5-unit chroma difference in a muted color looks more dramatic than the same 5-unit difference in a vivid color.


    Hue Weighting (SH)

    Our sensitivity to hue changes varies across the spectrum. We're particularly bad at distinguishing blues from purples, but very good at telling apart greens from yellows. The formula includes hue-dependent weighting to account for this.


    Rotation Term (RT)

    There's an interaction between chroma and hue in the blue region of the color space. A correction term rotates the hue/chroma difference plane in the blue region, improving accuracy for blue-purple colors.


    The final formula combines these weighted differences:


    ΔE₀₀ = √[(ΔL'/kLSL)² + (ΔC'/kCSC)² + (ΔH'/kHSH)² + RT·(ΔC'/kCSC)·(ΔH'/kHSH)]

    Where kL, kC, and kH are parametric factors (we use the default 1:1:1 ratio).


    Step 3: Delta-E → Score


    Once we have the Delta-E value, we map it to a 0-100 score using a simple linear scale:


    Delta-EScorePerception

    |---------|-------|------------|

    0100Identical — you nailed it! 1-296-100Barely noticeable difference 2-590-96Slight difference, excellent match 5-1080-90Noticeable but close 10-2060-80Clearly different colors 20-3530-60Very different 35-500-30Wrong color family 50+0Completely wrong

    Your total game score is the sum of all 10 rounds, giving a maximum of 1000 points.



    Why This Matters for Gameplay


    Using perceptual color distance instead of raw RGB math means ToonTone's scoring actually reflects how "right" your answer looks to a human observer. It would be unfair if guessing a slightly wrong shade of blue scored the same as guessing a slightly wrong shade of green when one error is visually more obvious than the other.


    It also means the hint system provides genuinely useful information. When we show you the hue and saturation range, those values correspond to perceptual categories you can actually reason about — "it's a warm orange, not a cool orange" or "it's highly saturated, not muted."



    The Hint Penalty


    Using a hint costs 30% of your round score. This means:


  • If you would have scored 90 without a hint → you get 63
  • If you would have scored 60 without a hint → you get 42
  • If you would have scored 30 without a hint → you get 21

    • The penalty is multiplicative, not additive. This makes hints most costly when you would have scored well anyway, and relatively less painful when you're genuinely lost. The strategic calculation: is the hint likely to improve your raw score by more than 43%? (Since you need 1/(1-0.3) = 1.43x your unassisted score to break even.)



    Fun Facts


  • The original Delta-E formula from 1976 (ΔE*ab) is just the Euclidean distance in Lab space. It's fast to compute but inaccurate — especially for saturated colors and blues.
  • CIEDE2000 is used by paint manufacturers like Benjamin Moore and Sherwin-Williams to ensure batch consistency.
  • Display calibration tools like X-Rite and Datacolor use ΔE₀₀ as the primary accuracy metric.
  • A trained colorist can typically distinguish Delta-E differences of about 1.0. Untrained observers need about 2.5 to notice a difference.

    • Play ToonTone and see how your color memory stacks up against industrial-grade color science!