My most accurate and very complicated simulation of a ladder in AoE2 DE

Histograms (left - ELO of each player from bottom to top, right - distribution of players with ELO range)

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Top15 of a simulated ladder

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Top15 of a real ladder (23 december 2019)

1. Skill (20 real players with precise tweak of their skill based on a voobly) Skill affects on a win probability Every game skill of the player is increasing. More skill and games means less increasing. After a lose skill is increasing more.
2. Rating. Starting rating is 1000. First 10 games gives 2x more ELO. Top 100 gains 2x less rating.
3. Weakness and strongness (only for real players for now). Some players are always playing better or worse against an others. For example, Nili killing Hera, and Villese killing Vinch. Those traits are only slightly increasing/decreasing probability of win.
4. Online. Every session players joining in the queue. The higher probability of online the more games. Some noobs has only 0% online and playing up to 2 times.
5. Matchmaking. Pairing two close opponents. Difference in 50 ELO = they play 100%. Difference in 100 ELO = they play 25%. 200 ELO = 12.5%. 400 ELO = 6.25%. If more then players don't play.
6. New players. Very hard problem to tweak. I have newbies and "elders" Gaussian variance of skill for noobs: 1000 +-. For "elders": 1400 (skill is relative value and does not affect ELO directly)
7. Every session there is 4 new random players in the system

It was very fun to play with parameters and observe how different values affect a simulation. For example, the more random good player the more and faster top players gets a 2K+ ELO. The bigger amount of players in general does not affect a top players too much (but a small amount is ruins everything). I have even more observations, maybe i will post my work in progress later. Make it top please!

You can notice how accurate a simulation: Daut has exact #10 place with exact 63% winrate (but somehow 100 more games