MrL1193
Inkling Cadet
Your model reaches an incorrect conclusion because there's an error in it, and it's really quite a silly error to make. Brace yourself for a math lesson, because here it comes.Let's assume that it takes 100 points to reach max level. You get 1 point for losing, 10 for winning. And let's assume that there are bad players, and good players, evenly split on each team. Good players always win against bad players, and win half the time against good players. Bad players always lose to good players, and will win half the time against other bad players. If we take this to be true, it means that good players will win 75% of their matches, and bad players 25%. That means that good players will play, on average, about 13 matches before stopping, and bad players 31 matches.
Now let's take mirror matches into account. Let's assume that the more popular team will face a mirror match 25% of the time, and the less popular team only 10%. With these numbers, you can see that out of those 13 and 31 matches, on the more popular team, 4/13 matches will be mirrors for the good, and 8/31 for the bad. In turn, on the less popular team, you have 2/13, and 4/31.
Now you can see the issue. On the less popular team, good players will be playing about 11 matches against the enemy team, and bad players 27. But on the more popular team, you have 9 matches for the good players, and 23 for the bad. Even though the more popular team will still have less bad players playing against the other team due to mirrors, 71.875% of their matches versus the less popular team will be played by bad players, compared to the 71.053% of the less popular team. This difference is what explains the discrepancy due to team popularity. And keep in mind that these mirror match percentages of 10/25 are just an estimate.
Your fatal error was... Rounding.
Yes, really. Rounding.
You know all those percentages you pulled out at the end? You were basing them on rounded numbers. That's the only reason they came out different for each team. But see, the thing is, you weren't supposed to use rounded numbers for your calculations. Yeah, I know that no single player is actually going to play 3.25 mirror matches (mid-match DC's don't count), but that number isn't supposed to represent what any one player actually did. It's an average of the whole matches played by millions of players. That means that some played 3 or fewer mirror matches, while others played 4 or more mirror matches, and it averaged out to 3.25 per player.
So now, let's take another look at your model, this time with the correct numbers in place (marked in red).
Well, would you look at that. The percentages of matches played by bad players are identical for each team after all. (70.4545%) Who would have guessed?Let's assume that it takes 100 points to reach max level. You get 1 point for losing, 10 for winning. And let's assume that there are bad players, and good players, evenly split on each team. Good players always win against bad players, and win half the time against good players. Bad players always lose to good players, and will win half the time against other bad players. If we take this to be true, it means that good players will win 75% of their matches, and bad players 25%. That means that good players will play, on average, about 13 matches before stopping, and bad players 31 matches.
Now let's take mirror matches into account. Let's assume that the more popular team will face a mirror match 25% of the time, and the less popular team only 10%. With these numbers, you can see that out of those 13 and 31 matches, on the more popular team, 3.25/13 matches will be mirrors for the good, and 7.75/31 for the bad. In turn, on the less popular team, you have 1.3/13, and 3.1/31.
Now you can see the issue. On the less popular team, good players will be playing about 11.7 matches against the enemy team, and bad players 27.9. But on the more popular team, you have 9.75 matches for the good players, and 23.25 for the bad. Even though the more popular team will still have less bad players playing against the other team due to mirrors, 70.4545% (23.25/33) of their matches versus the less popular team will be played by bad players, compared to the 70.4545% (27.9/39.6) of the less popular team.
You can try to make all the flawed mathematical models you want, but you can't change the facts. If the proportion of skilled players is the same for each team, then neither team has an inherent advantage, regardless of mirror matches, skilled players leaving early, or anything else. If one team wins more than the other, it's because they had a greater proportion of skilled players, better internet connections, or some other factor that created an inequality; the matchmaking has nothing to do with it (aside from perhaps a slight psychological effect created by differing wait times, but mirror matches actually help alleviate that, rather than making it worse).