New players enter the system and must be absorbed. Their arrival is say, Poissonian (maybe it’s Erlang), their steady-state rank distrubtion, say, Gaussian. They enter at the median and impart some disruption until they reach their correct rank (which isn’t actually precise, accurate, or correct but let’s pretend).
All smurfs are alts. The fraction is unknown. The best-case, min-disrupt scenario is that:
- All alts are perfect clones of some main (no smurfing, A=1).
- People who use alts are uniform by rank (hardcore and high ranked players don’t alt more or less than casuals and low ranks, B=1).
- The number of alts per person is rank uniform (hardcore players don’t have more or less alts, C=1).
Even if 1,2,3 hold perfectly (it’s almost impossible for this to be the case) - you have at least as much disruption as new players. So the statement ‘every alt corrupts the ladder’ is valid. Because we don’t periodically reset or adapt SR payouts by population.
But you can actually make data-free arguments on (2) and (3) that show how hard it is to achieve B,C = 1, and how k>0 entrants into the system actually force B,C to become lower (again, because of how the ladder saturates with SR).
But this is just a thought experiment. We already have countless evidence that shows A<1 (smurf to alt ratio), and with reasonable threshold arguments you could bound some lower values for B,C (who uses alts and how many).
Very quickly, the disruption imparted by duplicate accounts (alts) increases faster than new players. Recall, pumping SR into a ladder causes inflation (with geometric dissipate) and encourages constant-sum, pay2win equilibria to emerge, that effecitvely punish and tax the lone-account player.
Mobility gets harder, your rank becomes less meaningful, you have more usurped games, SR no longer tracks skill scarcity just account winrates (which are changed by alt saturation), and Scott is happy calling it an esport.