tutor peers rating range using gaussian distribution

build.sbt

@@ -272,7 +272,7 @@ lazy val importer = module("importer",
 
 lazy val insight = module("insight",
   Seq(common, game, user, analyse, relation, pref, socket, round, security),
-  Seq(scalatags) ++ reactivemongo.bundle
+  Seq(scalatags, breeze) ++ reactivemongo.bundle
 )
 
 lazy val tutor = module("tutor",

modules/insight/src/main/Question.scala

@@ -13,11 +13,22 @@ case class Question[X](
 
 object Question:
 
+  private val peerDistribution = {
+    // based on https://lichess.org/stat/rating/distribution/blitz
+    // https://hq.lichess.ovh/#narrow/stream/1-general/topic/tutor.2C.20let's.20build.20it.20together/near/2159478
+    import breeze.stats.distributions.*
+    Gaussian(1465d, 394d)(using Rand)
+  }
+
   case class Peers(rating: MeanRating):
     def ratingRange: Range =
-      // based on https://lichess.org/stat/rating/distribution/blitz
-      val diff = Math.ceil(0.0002647 * Math.pow(rating.value, 2) - 0.80735 * rating.value + 635.4411).toInt
-      Range(rating.value - diff, rating.value + diff)
+      val cdf = peerDistribution.cdf(rating.value) // percentile of player given rating
+      val proportion     = 0.03 // probability density function, i.e. proportion of players
+      val (lower, upper) = (cdf - proportion, cdf + proportion)
+      Range(
+        peerDistribution.inverseCdf(lower atLeast 0).toInt atLeast 0,
+        peerDistribution.inverseCdf(upper atMost 1).toInt atMost 4000
+      )
     def showRatingRange =
       val rr = ratingRange
       s"${rr.min}-${rr.max}"

project/Dependencies.scala

@@ -33,6 +33,7 @@ object Dependencies {
   val uaparser    = "org.uaparser"               %% "uap-scala"    % "0.14.0"
   val apacheText  = "org.apache.commons"          % "commons-text" % "1.10.0"
   val bloomFilter = "com.github.alexandrnikitin" %% "bloom-filter" % "0.13.1_lila-1"
+  val breeze      = "org.scalanlp"               %% "breeze"       % "2.1.0"
 
   object specs2 {
     val version = "5.2.0"