This content is already somewhat invalidated because I didn’t realize that you could lose 2 pips at a time until just now, so most of these numbers will be overstated. Also, not sure if these already exist anywhere already. But as I said, I like maths. Assumptions and details are below for those interested.
Essentially, I’m trying to simulate the time it would take to get through a division with 6 tiers that allowed tier dropping. The simulation grants 1 pip per win and deducts 1 pip per loss subject to a floor of 0 pips.
For a 50% win probability, which the matchmaking system theoretically targets, you have about a 6% chance of getting 30 pips within 200 games, a 20% chance of getting 30 pips within 350 games, a 35% chance to do so within 500 games, a 50% chance to do so within around 710 games, and a 65% chance to do so within 1,000 games. 1,000 games roughly equates to basically playing ranked PvP as a full time job for a month for a 65% chance to go up a division.
If you can run at a 51% win probability, your situation is quite a bit better (I feel like it’s possible to run as high as a 53% probability without being a super awesome player, but admittedly have no real backing for that other than my impression that no matchmaking system is perfect enough to get everyone at an expected 50%). At a 51% win rate, you’ll be through the division after only 300 games with a 25% chance. You have a 50-50 shot of finishing within 500 games, and your 1,000 game odds rise to 83%. To paraphrase, 1 out of every 6 legitimately better-than-average players will not escape the division after about 250 hours of work.
If you are so awesome that you can manage a win rate of 55%, which is an exceptional achievement over a large sample size, you have a 50-50 shot of being done after 225 games, a 94% chance of finishing within 500, and only a 0.1% chance of not finishing after a month of full time work.
Now, these numbers are admittedly off due to multi-pip losses, possible tanking by opponents (or teammates), and certainly other factors that I probably haven’t considered. But they should be a somewhat fair approximation of the time commitment involved. Moreover, they’re not especially difficult to come up with, so (at least in my mind) it was likely decided that this type of time commitment was acceptable when setting it up.
Assumptions, details, and more musings:
The assumptions I’m using are that a win is worth +1 pip, a loss is -1 pip (unless you currently have no pips in which case it’s meaningless), and there are 30 pips to advance a division (which I believe is the case for the first division that allows tier-dropping). The simulation runs off games until it hits a point where 30 pips have been achieved. This is similar to finding the point where wins exceed losses by 30, but because losses are ignored when the total pip count is zero, it’s not exactly the same question. I run the scenario 10,000 times to get a distribution, and I stop counting if 30 pips haven’t been achieved after 1,000 games in any given iteration.
The win probabilities referenced implicitly assume that matches aren’t being thrown by the opposing side. In reality, and as somebody else discussed, due to MMR concerns it makes sense to tank for a while after hitting a new division to lower your own MMR to raise your later win probability through easier matches. The extension of that argument is that if everyone else follows a similar strategy, your win probability will be even higher when you actually try to win, as the expected number of tankers on the opposing side will be higher than on your side (since there would be 4 potential tankers on your team versus 5 on the other team, and during the “tanking” phase of the system). This is further exaggerated if you actually use a full team who buys in to that same strategy, thereby lowering your expected number of tankers to 0.