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From Reddit - "Ranked math: the role of luck (season 11)"

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Quality Poster
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17,320 battles

Hi all,


From Reddit - "Ranked math: the role of luck (season 11)":





I computed this by tracking probability weights through a Markov process as time move forwards in steps (games). This was not a Monte Carlo simulation, so the accuracy is limited only by machine precision effects.


  • Start at Rank 12 with one star, as per a player just achieving Rank 12 for the first time and getting that bonus star. Rank 12 is irrevocable. 44 stars (including the starting star) from the beginning of Rank 12 are needed to rank out.

  • The result of each game is independent and identically distributed according to the player's "true" win rate, which is fixed for each series. Note that this may not be the actual win rate over the season depending on the roll of the dice. It's also not completely realistic in that win rate depends on the competition, which in turn depends on rank and timing within the season. But at least this should give a rough idea of what to expect.

  • Chance of keeping a star if losing is fixed at 1/6. As usual, better players may be more likely to keep their star, but it's hard to estimate and only so many series can be intelligibly plotted, so I just fixed it at this value.


  • Since there are only 6 players per team, a slightly greater fraction of stars get saved compared to the previous (full) Ranked season. This reduces the number of games needed by a little. Low win rates benefit the most from this effect... but the constant factor is the player, not the win rate. Weak players will be a greater drag on their team, which will easily overwhelm this effect by reducing their "true" win rate. In constrast, strong players will have a better chance to carry, increasing their "true" win rate.

  • One interesting factor is that Rank 12 and Rank 11 only have two stars this time around. Since Rank 12 is irrevocable and getting to Rank 11 awards a bonus star, players who bounce between these two ranks may end up injecting more stars into the system than before.

Previous seasons



Leo "Apollo11"

  • Cool 3

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1 hour ago, LemonadeWarrior said:

I play Ranked for fun.

I play ranked for the "WTF that's hilarious" effect. Get rewarded every time. 

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I only plan to play a single match... Just to gain the rewards from last season... Nothing is set in stone but for now just one.

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