Game Accuracy not explained well on website

[cmwetherell]

The page on the Lichess accuracy metric talks about Win% and Accuracy% as a move by move metric, but doesn't discuss the gameAccuracy function defined in the source code below. In the game review section, the "information" button near the Accuracy % for the game links to the page without any discussion of the comprehensive game accuracy.

Just sharing this picture as an example. The blue "i" made me think the page I was going to would explain Game Accuracy.

I think this page would be improved if there is a more clear explanation of converting the move by move Accuracy% to game accuracy. For example, why was volatility weighted and harmonic means chosen? Why are they averaged? Why is the volatility clamped to 0.5 - 12? I'd find this information interesting, I think others would as well.

lila/modules/analyse/src/main/AccuracyPercent.scala

Lines 77 to 111 in d816175

	def gameAccuracy(startColor: Color, cps: List[Eval.Cp]): Option[ByColor[AccuracyPercent]] =
	val allWinPercents = (Eval.Cp.initial :: cps).map(WinPercent.fromCentiPawns)
	val windowSize = (cps.size / 10).atLeast(2).atMost(8)
	val allWinPercentValues = WinPercent.raw(allWinPercents)
	val windows =
	List
	.fill(windowSize.atMost(allWinPercentValues.size) - 2)(allWinPercentValues.take(windowSize))
	.toList ::: allWinPercentValues.sliding(windowSize).toList
	val weights = windows.map { xs => Maths.standardDeviation(xs).orZero.atLeast(0.5).atMost(12) }
	val weightedAccuracies: Iterable[((Double, Double), Color)] = allWinPercents
	.sliding(2)
	.zip(weights)
	.zipWithIndex
	.collect { case ((List(prev, next), weight), i) =>
	val color = Color.fromWhite((i % 2 == 0) == startColor.white)
	val accuracy =
	AccuracyPercent.fromWinPercents(color.fold(prev, next), color.fold(next, prev)).value
	((accuracy, weight), color)
	}
	.to(Iterable)
	// cps.zip(weightedAccuracies) foreach { case (eval, ((acc, weight), color)) =>
	// println(s"$eval $color ${weight.toInt} ${acc.toInt}")
	// }
	def colorAccuracy(color: Color) = for
	weighted <- Maths.weightedMean:
	weightedAccuracies.collect:
	case (weightedAccuracy, c) if c == color => weightedAccuracy
	harmonic <- Maths.harmonicMean:
	weightedAccuracies.collect:
	case ((accuracy, _), c) if c == color => accuracy
	yield AccuracyPercent((weighted + harmonic) / 2)
	ByColor(colorAccuracy)

[kraktus]

For example, why was volatility weighted and harmonic means chosen? Why are they averaged? Why is the volatility clamped to 0.5 - 12?

As far as I remember, these were just heuristics tweaked manually until it matched the most with what a human would feel about accuracy. It is not a scientific metric.