diff --git a/other/world.ts b/other/world.ts
index 09b765f..828081c 100644
--- a/other/world.ts
+++ b/other/world.ts
@@ -57,7 +57,9 @@ export default class World {
   private width: number;
   private height: number;
   private minSpawnDistance = 10;
-  private maxMoveDistance = 2;
+  private minMoveDistance = 2;
+  private maxMoveDistance = 9;
+  private moveDistanceChangePow = 0.45;
   private newBotRadius = 5;
   private maxFoodRadius = 3;
   private initialFoodCount = 200;
@@ -105,6 +107,12 @@ export default class World {
     return { x, y };
   }
 
+  private getMaxBotMoveDistance(radius: number): number {
+    const speedRatio = Math.pow(this.newBotRadius / radius, this.moveDistanceChangePow);
+    const normalizedSpeed = speedRatio * this.maxMoveDistance;
+    return Math.max(this.minMoveDistance, normalizedSpeed);
+  }
+
   private getAvailableSpawnPositions(newEntityRadius: number): number[] {
     const takenPositions: Set<number> = new Set();
 
@@ -235,10 +243,12 @@ export default class World {
       throw new Error(`Bot with id ${botId} not found`);
     }
 
+    const maxBotMoveDistance = this.getMaxBotMoveDistance(bot.radius);
+
     const distance = World.distance(bot, { x, y });
-    if (distance > this.maxMoveDistance) {
+    if (distance > maxBotMoveDistance) {
       // compute closest possible x and y
-      const { x: newX, y: newY } = World.computeClosestXYWithinDistance(bot, { x, y }, this.maxMoveDistance);
+      const { x: newX, y: newY } = World.computeClosestXYWithinDistance(bot, { x, y }, maxBotMoveDistance);
       x = newX;
       y = newY;
     }