Honor in Summoner's Rift and Twisted Treeline - probabilities

Well, hello there.

I've had a discussion with Voldymort@EUNE about probability to receive honor in specific gamemode(5v5 vs 3v3) and I promised to have my take on it. He also stated that he might make it into a post through the magic of copy-paste, when he is relatively sure about the numbers. But I am overconfident so, obviously, I am stealing his idea and writing this post myself.

Here we go!

---

First of all, players are incentivized to honor other people due to spilling some honor upon themselves in the process. While, obviously, not every player honors every game, be it out of spite or genuine righteous fury, we will ignore this aspect for now and count the probability for the case of "everyone honors someone".

The second assumption is that all players have equal chance to receive honor, which is, obviously, not the case - out of 4 people you are more likely to honor someone outstanding, but let's assume that noone is toxic or awesome. We have a game of 5 average Joes.

The third is a valuable disclamer that makes our life simple - receiving a honor point, obviously, doesn't interact with your chance to receive other honor points, which simplifies our calculations even further.

This is basically what we are calculating: https://www.youtube.com/watch?v=s5DWg4o6h8Q In this case there were 3 missiles, each having a chance of 20% to hit a specific target independently 20%*20%*20% = 0.8% chance for it to happen. Easy.

---

Summoner's Rift:

We have four free honor points. Assuming that each player has equal chance to receive each specific point, we are dealing with 25% chance per point and they roll independently. Here is an easy way to calculate the odds of honors hitting you:

1. 25%(obviously)
2. (the previous was a hit)25%*25% = 6.25%
3. (two previous were hits)6.25%*25% = 1.5625%
4. (three previous were hits)1.5625%*25% = 0.390625%

This is quite a lottery. https://www.youtube.com/watch?v=ymPpIzaanhY

Twisted Treeline

We have two free honor points. Assuming that each player has equal chance to receive each specific point, we are dealing with 50% chance per point and they roll independently. Here is an easy way to calculate the odds of honors hitting you:

1. 50%(obviously)
2. (the previous was a hit)50%*50% = 25%

https://imgur.com/2oNu26e

---

If we take into account that people don't honor in, let's assume, 10% games, we have our chances reduced by 10%(we are only interested in this disappointment if it would otherwise roll successfully) on each step, which means:

SR would be 22.5% 22.5%*22.5% = 5.0625% 22.5%*22.5%*22.5% = 1.1390625% 22.5%*22.5%*22.5%*22.5% = 0.256289062%

TT would be: 45% 45%*45% = 20,25%

How and where did I fuck that up? https://www.youtube.com/watch?v=k7HMQuoISNg