Speed Kills - How to Find the Best Speed Mods

"sjkerhfgdjhd;1002890" wrote:

"Woodroward;1002846" wrote:

"sjkerhfgdjhd;1002833" wrote:

"Woodroward;1002822" wrote:

"sjkerhfgdjhd;1002612" wrote:
Here are the odds for each colour of mod to upgrade speed. The numbers are the odds for a mod to upgrade speed at least that many times, and then I put the odds of upgrading that many times but no more in brackets where applicable.

Green
0 upgrades, 0%
1 upgrade, 100%

Blue
0 upgrades, 25%
1 upgrade, 75%(50%)
2 upgrades, 25%

Purple
0 upgrades, 29.64%
1 upgrade, 70.36%(44.44%)
2 upgrades, 25.92%(22.22%)
3 upgrades, 3.7%

Gold
0 upgrades, 31.65%
1 upgrade, 68.25%(42.18%)
2 upgrades, 26.17%(21.09%)
3 upgrades, 5.08%(4.69%)
4 upgrades, 0.39%

As you can see, while the odds of getting a single upgrade drops off steadily, for the good mods where speed has upgraded at least twice it only goes up as the quality increases. I would still say it is worth buying green mods with a speed secondary if they have one of the valuable primary stats, but probably not otherwise, unless you have a lot of credits to spare. But once you start to get good fast mods for your arena team even blue mods may not be desirable unless the secondary and/or set bonus fit well on your team.

These numbers aren't correct either. Some of them are, but not all of them.

What formula are you using to calculate these stats?

Green and blue are good.
Purple
3 stats revealed is a 1/3 chance each of 3 upgrades.
That means a 33% chance of exactly 1 upgrade, or a 33 + 10.89 + 3.59 = 47.48% chance of at least 1 upgrade.
.33 * .33 = 10,89 % chance for exactly 2 upgrades 10.89 + 3.59 = 14.48% chance of at least 2 upgrades.
.33 * .33 * .33 = 3.59% chance for 3 upgrades

Gold
4 stats revealed is a 1/4 chance each of 4 upgrades
That means a 25% chance of exactly one upgrade, or a 25 + 8.2 = 33.2% chance of at least 1 upgrade.
.25 * .25 = 6.25% chance of exactly 2 upgrades, or an 6.25 + 1.95 = 8.2% chance of at least 2 upgrades
.25 * .25 * .25 = 1.56% chance of exactly 3 upgrades, or a 1.56 + .39 = 1.95% chance of at least 3 upgrades.
.25 * .25 * .25 * .25 = 0.39% chance of exactly 4 upgrades

Nope, you are calculating the wrong way. The second upgrade on a gold mod is not a 25% chance of a 25% chance, it is a 25% chance of a 75% chance. You can easily verify this by considering the odds of speed not upgrading. Since the odds of speed not upgrading once is 75%, the odds of it not upgrading four consecutive times is .75 to the fourth power, or 31.64%. The other 68.36% of cases must then all have at least one speed upgrade.

The hardest part of math isn't doing the calculations right, it's knowing which calculations to do in the first place. But don't feel too bad, earlier today I made a mistake in calculating how many different Clash Royale decks are possible and ended up off by 180 zeros on my answer.

Still trying to figure out how you came up with a purple mod having a 44% chance of exactly one upgrade when it is clearly 33%

The 44% isn't supposed to be the odds of there being one upgrade after the first upgrade, it is the odds of there being exactly one upgrade after you have done all three of the upgrades possible on a purple mod. When a purple mod with speed hits level 3 there is a 1/3 chance that speed will upgrade. When it hits level 6 then 1/3 of the upgraded ones will upgrade again and no longer be exactly one, but 1/3 of the ones that weren't upgraded will get their first upgrade, and there are twice as many of those, so you will gain more than you lose. You will have 1/9 with two upgrades, 4/9 with one, and 4/9 with none. The third upgrade is just another iteration, with 1/27 at 3 upgrades, 6/27 at 2 upgrades, 12/27 at one upgrade, and 8/27 at no upgrades. 12/27 is 44.44% repeating.

"ljcool110;1003054" wrote:
Ok, well you guys have proven the difficulty in calculating the exact odds for each speed increase since nobody can agree.

As for the article, it should be updated. I am sure you all will let me know if the updated version is not correct, but I am confident that it is.

To be fair, after researching and contemplating, I think the person I was in discourse with is correct in their methods. I did come up with slightly different figures when I used them, but that could be accounted for by the difference in using rounded decimals vs fractions. Fractions are more accurate, so I would guess that their's is also more accurate.