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?

[jkwongfl_7919855]

last sentence- below* not "bellow"
purple star analysis?
im too lazy to check your math right now, but seems legit

[ChickenWing]

I stand corrected! The maths are a bit simplified, but the averages I provide should be correct.

[ChickenWing]

I can't write a purple medal guide; I would need the stats but don't have access to them.

[Herby]

I can't write a purple medal guide; I would need the stats but don't have access to them.

9-10: 50%
10-11: 40%
11-12: 30%
12-13: 20%
13-14: 15%

You lose 1 star if you fail any attempt.

Don't have a 14 star hero yet, so I don't know 14-15 odds.

[ChickenWing]

9-10: 50%
10-11: 40%
11-12: 30%
12-13: 20%
13-14: 15%

You lose 1 star if you fail any attempt.

Don't have a 14 star hero yet, so I don't know 14-15 odds.

Thanks for those number. My understanding of statistics is not enough to allow me to calculate anything out of this, though. I was able to calculate with the safe spots because they offered a single path. The fact that you can always fall back by one star means that there is an infinite amount of paths and, thus, of possibilities. If I can't calculate the possibilities, it certainly shows that the outcomes are a lot worse than the ones for blue medals.

[Andy]

Are the stats comulative? In other words if I try to go from 8 to 9 on a Gold (or the main) do I need to have all the medals available at the same time or cam I do 100 today and some more when I get space for more and am able to gather them? 216 medals is 44 slots and 428 86 slots.

[JezebelMD_6540395]

Well, let's see. To have 740 stars, you'd need 148 slots in your inventory since a slot can hold only 5 stars max!!! Kinda out of the question, I'd say.

[ChickenWing]

This is just an average of the amount of medals you'll need to spend before you get there. You don,t need to have all of them at once to succeed. However, the average player will have spent between 321 and 740 blue medals to get from 4 to 9 stars.

[Revan]

Awesome. You did the math that I had no interest in taking the time to do.