This is a quantitative comparison between the current ensured draw system and the upcoming mileage system as described in the dev notes. I assume that the nominal 5-6* draw rate stays the same across both systems, at 5.08%. If you don't remember stats or you just don't care about how these numbers were obtained, you can skip down to ===(RESULTS)===.

Start by calculating the average number of draws you'd have to do to get a 5* under the current system.

Your chance of getting a 5* in exactly 1 draw is obviously 0.0508.

Your chance of getting a 5* in exactly 2 draws is (1-0.0508)*0.0508. This is because you have to fail to get a 5* once (1-0.0508) and then you also have to succeed the second time (0.0508)

More generally, your chance of getting a 5* in exactly n draws is (1-0.0508)^(n-1)*0.0508 as long as n is less than 44. If n is 44, then you have (1-0.0508)^(43)*1 because you only have to fail 43 times, your 44th success is guaranteed.

Weight each number from 1 to 43 by the chance that it'll take that many draws to get a 5*, then add them all up.

I did this by typing the following into Wolfram Alpha: sum of (1-0.0508)^(n-1)*0.0508*n for n from 1 to 43

It gave me 13.02. Then, add onto it the chance that it'll take 44 draws, multiplied by 44: 13.02+44*(1-0.0508)^43 = 17.70. So on average, it takes 17.70 draws to get a 5*. That results in a rate of...

===(RESULTS)===

5.65% for the current system.

The new mileage system is much simpler to calculate. Assuming the normal draw rate stays the same, your rate of 5*s per draw is:

7.08% if you use your mileage for a season 1 box.

5.75% if you use your mileage for a season 1-2 box. Note that it is ever so slightly higher than what we have right now.

5.28% if you use your mileage for a season 2 box.

===(CONCLUSION)===