Medals Guide

[ChickenWing]

A lot of people have been complaining about the amount of failure when upgrading the amount of stars. The goal of this post is to understand better the statistics behind the star system, which should help people plan the amount of medals they need to get to another safe spot.

First, the safe spots for blue medals are at 0, 1, 4, 7, and 9 stars. This means that once you reach this amount of stars on a hero, you can't lose stars below this amount.

First, we need to look at the stats for specific star levels: Here is the amount of success for passing from one star level to the next and what's at stake:

0 to 1: 100% (safe spot)
1 to 2: 88% (safe spot)
2 to 3: 72% (lose 1 star if it fails)
3 to 4: 56% (lose 1 star if it fails)
4 to 5: 45% (safe spot)
5 to 6: 32% (lose 1 star if it fails)
6 to 7: 20% (lose 2 stars if it fails)
7 to 8: 14% (safe spot)
8 to 9: 10% (lose 1 star if it fails)

If you look closely, whenever you fail between 4 and 6 stars, you fall back to 4 stars, and whenever you fail between 7 and 8 stars, you fall back to 7 stars. This means that two groups can be created. In those two groups, you must chain two or three successes to get to the next safe spot, which means you must multiply the amount of success from each star level to get your real chance of success to get to the next safe spot.

4 to 7 stars: 45% x 32% x 20% = 2.88%
7 to 9 stars: 14% x 10% = 1.40%

This explains why so many people think it is harder than the statistics shown and, in fact, IT IS harder.

Now, the amount of success will vary from one person to another according to the bell curve, which is a way of explaining the distribution of outcomes in statistics. Here's what it looks like:

picture-normal-distributin-curve-and-graph.jpg

In short, 34% of the people will find it a bit easier than my statistics, 34% a bit harder, 13.5% a lot easier, 13.5% a lot harder, and the rest will either never get there or get there first shot.

4 to 7 stars
Within 34.72 attempts from the safe spot (100/2.88)

Blue hero: minimum 35 blue medals, maximum 104 blue medals (requires a maximum of 3 blue medals per attempt; 3 x 34.72)

Purple hero: minimum 70 blue medals, maximum 208 blue medals (requires a maximum of 6 blue medals per attempt; 6 x 34.72)

Gold hero: minimum 105 blue medals, maximum 312 blue medals (requires a maximum of 9 blue medals per attempt; 9 x 34.72)

7 to 9 stars
Within 71.43 attempts from the safe spot (100/1.4)

Blue hero: minimum 72 blue medals, maximum 142 blue medals (requires a maximum of 3 blue medals per attempt; 2 x 71.43)

Purple hero: minimum 144 blue medals, maximum 284 blue medals (requires a maximum of 6 blue medals per attempt; 4 x 71.43)

Gold hero: minimum 216 blue medals, maximum 428 blue medals (requires a maximum of 9 blue medals per attempt; 6 x 71.43)


Thus, to get a gold hero from 4 stars to 9 stars, the average person will need between 321 and 740 blue medals. 50% of the people will perform better than that; 50% will perform worse than that. Are you part of the ones below the normal distribution?