Is this still true? (Since "Energy spent on control" is renamed to "Control points for .." and nothing is shown above reserved rooms anymore.) 

The impact factor of a tower can be calculated by the function below. I post this here since I dont think this is any kind of magic.

It took me while to figure out that the falloff is actually linear (by the post of dissi above)

var towerRangeImpactFactor = function(distance) {
  if(distance <= TOWER_OPTIMAL_RANGE) {
   return 1
  }
  if(distance >= TOWER_FALLOFF_RANGE) {
    return 1 - TOWER_FALLOFF
  }
  var towerFalloffPerTile = TOWER_FALLOFF / (TOWER_FALLOFF_RANGE - TOWER_OPTIMAL_RANGE)
  return 1 - (distance - TOWER_OPTIMAL_RANGE) * towerFalloffPerTile
}

then the damage can be calculated with

var damage = TOWER_POWER_ATTACK * towerRangeImpactFactor(distance)