In Old Champ Select, You Got Your Desired Role ~64.8% of the Time

Over 155 ranked games, I got my desired role 70.97% of the time. What was my desired role? Mid. Supposedly that lane is the most in-demand. I never dodged based on lane that I got, and I never insta-locked.

Here's the math of the old system, assuming each role had 20% of players preferring it:

When I am first pick, the chance I get my role is 1. When I am second pick, the chance I get my role is 0.8. For 3rd pick, 0.64. For 4th, 0.48. and for last pick, I still have a 0.32 chance of getting my desired role.

Weighting each of these factors given that they each occur in one out of five games, we arrive at the following: The chance that I get first pick and also get my desired role is 0.2 The chance that I get 2nd and my role is 0.16. For 3rd pick, 0.128 Fourth, 0.096 And last, 0.064.

Summing all of these together results in a probability of 0.648 that I get my role, if the underlying assumption of equal role distribution is true, and that players will always take their first choice if a team mate also wants it who is after them in pick order.

I think that 155 games is a reasonable sample size. I got my role more often than my model here predicts. Generally the only thing I would say in champ select was "Prefer mid".

I am interested in seeing how often I get my primary role in the new system. I don't have enough info yet, having only played eleven games with the new system... but there is at least one thing I can be confident in... I'll get my worst role less. I'm pretty happy about that. Now I can set up all my rune pages for my two preferred roles. New players will also have an easier time acquiring champion pools for their role of choice. That's cool.

Thanks for reading, hope you found it somewhat interesting.

Edit: Slight math error as posted above. Thanks to Llanite for helping me realize error. Final chance should be 60%, not 64.8%.