Awesome, someone else who does simulations and math experiments.

Quote:

**Lamcho**:

Just after i did my previous i started writing a script that calculates the fowling:

- You have the categories from bronze to diamond

- You have pool of players (100'000 in my tests)

- You make them all play equal number of games (200 in my tests)

- You assigns skill value to every category, for the purpose of the test we will greatly exaggerate players skills assigning 1 to bronze, 2 to silver, .. 5 to diamond. i.e. team of 5 bronze players is equal to team of 1 diamond player, 2 silvers are equal to bronze and gold ant etc.

- All players start with the same elo points.

- All players are grouped in pairs of teams in such way, that the teams in each pair have as close as possible elo that can be found in certain elo range.

- A game is "simulated" in each pair, The simulation is the flowing:

* the team with larger skill sum wins (note that ELO rating is not included in any calculations)

* if both teams have equal skill sum it is randomly decided which team wins (both have 50%, 50% chance)

* each team have X% chance to have an AFK player, if it have it, their skill sum is reduced by 20%.

* each team have Y% chance to have troll player (or not fully functioning player), if they have it, their skill sum is reduced by 5%

- After the matches all players have their ELO points updated by flat amount subtracted added depending on lose / win.

- Players are paired in teams again, and the loops go on for as many iterations entered.

- After all N matches have been played for every player all of then are sorted by their ELO value, and divided in the described divisions (for example you you had 100 positions for diamond at start the 100 player will highest elo will be placed there, if you had 1000 positions for bronze the 1000 players with lowest elo will be placed and so on for every division).

- The new position for every person is reviewed and compared to his skill. (The skill that match calculations depend on) This rules should describe much stable system than LoL ladders system, however after running many simulations here are the results:

- Placement in low tiers (bronze, silver, gold) is getting worse when increase AFKs, Trolls and surprisingly played games.

- Placement in high tiers (platinum, diamond) is improving when increase played games, AFKs & Trolls have low impact.

The numbers:

I've used some stats from last year for people / division distribution:

Bronze - 47900,

Silver - 42100,

Gold - 7500,

Platinum - 1900,

Diamond - 600

If you consider you will have only 1 AFK every 20 games (i wish..) and 1 Troll every 20 games and every player makes 200 games you get that you have estimated correctly about 75% (most simulations ware actually lower percentage) of the players in your game.

26% (12682 people) of all people in Bronze are not supposed to be here but they are.

28% (11744) are not supposed to be in Silver (Some of them are from Bronze, Gold and Plat)

7% (544) are not supposed to be in Gold.

6% (119) in Patinum

2% (13) in Diamond

If you pump up the AFKs and Trolls up to 1 every 5 games you end up with numbers around 30 - 35% for bronze and silver, 10 - 12% in gold and plat and diamond stay almost the same. Overall there are about 20-28% of the people displaced incorrectly (up or down) only with 1 division and 2-5% displaced with 2 or more, however 2% of 10,462,982 (all ranked players) are 209,260 people. The simulation do not consider into effect thinks like tilting, anger, frustration and etc.

In conclusion, to have a good time in the game you need to be Korean with lots of free time.

You're not taking in to account that a player may be excellent on one champion in one position, but completely inept at others. I don't think that should matter in this simulation since flexibility could just be part of the "skill" stat, but it's a variable that might change things. As is the ability to work together when there's three players who want the same position.

200 games might not be enough. I played around 300 games last season, and I think I could still have climbed a few divisions if I had played more.

Your system of assigning integer skill values to players might skew the stats. I don't think there are Diamond players who belong in Bronze and vice versa, not in your simulation nor in the game for real, but there might be low Silvers in high Bronze and vice versa, which would look no different in the numbers of players who aren't where they belong.

I don't think the 20% reduction of skill sum is a good approximation of what an afk does to a game. Rather, I would just ignore the afker's contribution to the skill sum entirely.

A "troll player" can be anything from an intentional feeder to a Twisted Fate adc. I think you should use different categories of "trolls", from the types that effectively turn the game into a 4v6, the ones who take something experimental that didn't work out, and the ones who take something unconventional that the enemy team doesn't know how to deal with. These would all potentially (and erroneously) be called trolls.

Your simulation is more in-depth than mine, and I'd really like to see the code behind it.