Hearthpwn

The average calculations here are a good rule of thumb, but if you consider the fact that a season is of finite length, the average time to reach legend among those who do so successfully is actually shorter than calculated. Stopping at a fixed time means that a lot of very long paths that contribute to the calculated average stop before they reach Legend.

The distribution of waiting times to reach Legend is fat-tailed (roughly inverse Gaussian). If you can play 500 games starting at rank 5 + 0 stars, you have about a 95% chance of reaching Legend, and yes you'll get there on average (assuming you do) in about 220 games, but the most likely outcome is that you get there in somewhere around 150 games.

(I'm using a simulation that assumes exponentially decreasing winRates as you go up ranks: At rank 1 it's 53.25%, which gets us a 55.1% win rate among all the matches played in the simulations I did, including those where you linger at lower ranks or fall back.)

Some fun factiods:

The expected max drawdown in terms of stars (your largest fall from the previous highest rank in the run) is about 10, with a standard deviation of nearly 5. So even at this win rate, it's not uncommon to fall back two full ranks or more from the highest rank you've previously attained during a 500-game run.

The expected longest losing streak in a 500-game run is about 6 games.