Portal Summons Odds - Visualized

It is understandable to look at the individual cards in a given portal, especially the number of 5* heroes, and think of the odds as being “flat” or even. They aren’t. This post tries to help people understand the odds in a more visual manner. It won’t help ease the disappointment with your umpteenth 3*, but it might help better explain why you received it vs one of the many 5* cards you just scrolled through.

I plan on updating this post as new portals roll out or as I have time to research. Open to suggestions on formatting and the like.

The visualizations/spinner doohickie comes from Picker Wheel

Best to worst odds for a non S1 Legendary hero or Costume (Nov 2022)

Portal Odds
HA10 Legendary 5%
HA10 Costume 5%
Costume Chamber 2.5%
CF2 2.5%
Black Friday 2.5%
Super Elemental (Green) 2.3%
Covenant of Champions 1.9%
Tavern of Legends 1.9%
S2/S3/S4/S5 1.6%
Christmas 1.6%
Halloween 1.5%
W3K 1.2%
AQ 1.2%
Mighty Pets 1%
Styx 1%

Best to worst odds for a non S1 Epic (Nov 2022)

Portal Odds
HA8 30%
Black Friday 26.5%
CF2 26.5%
Super Elemental (Green) 20.5%
S2/S3/S4/S5 14.6%
Covenant of Champions 11.9%
AQ 8%
Halloween 5.7%
Christmas 5.7%
W3K 5.7%
Mighty Pets 5.7%
Syx 5.7%

Halloween 2022

Hero Level Heroes Odds
Event 5* 6 1.5%
Event 4* 3 5.7%
Event 3* 3 14.2%
S1 5* 20 1%
S1 4* 22 20.8%
S1 3* 23 56.8%

Christmas 2022

Hero Level Heroes Odds
Event 5* 7 1.6%
Event 4* 3 5.7%
Event 3* 3 14.2%
S1 5* 20 0.9%
S1 4* 22 20.8%
S1 3* 23 56.8%

Challenge Festival 2 - as of Dec 2022

  • No S1 heroes
Level Heroes Odds
5* Featured 3 1%
5* 19 1.5%
4* 10 26.5%
3* 7 71%

Super Elemental (Green) - Dec 2022

Event Heroes Odds Non S1 Non S1 Odds
Featured 2 0.2% - 0.2%
5* 45 2.3% 41 2.1%
4* 21 26.5% 16 20.5%
3* 19 71% 13 48%

Tavern of Legends - as of Nov 2022

  • The number of HOTM will increase month over month
Hero Level Heroes Odds
Featured HOTM 5* 3 1%
HOTM 5* 53 0.9%
S1 5* 20 0.6%
S1 4* 22 26.5%
S1 3* 23 71%

Black Friday Nov 2022

  • CF1 = original challenge event heroes now in Challenge Festival 1
  • CF2 = Villains, Starfall Circus, Slayers, Bard
  • Ele = Super Elemental
  • Masq = Masquerade - whatever Fortuna/Jove are
Level Heroes Odds
5* Featured 2 0.2%
5* 263 2.3%
4* 77 26.5%
3* 70 71%
Level Heroes S2 S3 S4 S5 AQ CF1 CF2 CofC Garg HOTM Kal Magic Masq Pets Ninja Seasonal Styx Ele W3k
5* Featured 2 0.2% 2
5* 263 13 18 21 14 8 25 21 8 6 64 7 6 2 5 10 18 5 2 10
4* 22 9 10 5 5 3 11 9 2 2 0 1 2 0 2 3 7 3 0 3
3* 24 8 10 5 5 2 8 6 3 2 0 2 2 0 2 0 10 2 0 3

Tower of Styx - as of Nov 2022

Hero Level Heroes Odds
Styx 5* 8 1%
Styx 4* 3 5.7%
Styx 3* 2 7.9%
S1 5* 20 1.5%
S1 4* 22 20.8%
S1 3* 23 63.1%

War of the 3 Kingdoms - as of Nov 2022

Hero Level Heroes Odds
Event 5* 8 1.2%
Event 4* 4 5.7%
Event 3* 3 7.9%
S1 5* 20 1.3%
S1 4* 22 20.8%
S1 3* 23 63.1%

Covenant of Champions - as of Nov 2022

  • There is a 45% chance to draw a non S1 3* or 4*
  • 75% chance to draw a non S1 5* (non featured).
  • CF1 = original challenge event heroes now in Challenge Festival 1
Level Heroes Odds S1 S2 S3 CF1 CofC Kal Ninja
5* Featured 6 1.6% 1 1 2 1 1
5* 20 0.9% 5 3 3 9
4* 22 26.5% 12 2 2 4 2
3* 24 71% 13 1 2 5 3

Alliance Quest - as of Oct 2022

Hero Level Heroes Odds
Event 5* 8 1.2%
Event 4* 3 8%
Event 3* 2 23.7%
S1 5* 20 1.2%
S1 4* 22 18.5%
S1 3* 23 47.3%

Costume Chamber - as of Oct 2022. All S1 heroes have 1 costume by this point

Type Level Heroes Odds 2nd Costume
S1 Featured 5* 2 1.3% 2
S1 5* 18 1.2% 6
S1 4* 22 26.5% 2
S1 3* 23 71% 0

Mighty Pets - as of Nov 2022

Type Level Heroes Odds
Mighty Pet 5* 5 1%
Mighty Pet 4* 2 5.7%
Mighty Pet 3* 2 7.9%
Epic Trainer 4* 5 1%
Rare Trainer 3* 5 10%
S1 5* 20 1.5%
S1 4* 22 19.8%
S1 3* 23 53.1%

Season 5 - as of Oct 2022

Type Level Heroes Odds
S5 5* Featured 3 1%
S5 5* 11 0.6%
S5 4* 5 14.6%
S5 3* 5 51.6%
S1 5* 20 0.9%
S1 4* 22 11.9%
S1 3* 23 19.6%

Season 4 - as of Oct 2022

Type Level Heroes Odds
S4 5* Featured 3 1%
S4 5* 19 0.6%
S4 4* 5 14.6%
S4 3* 5 51.6%
S1 5* 20 0.9%
S1 4* 22 11.9%
S1 3* 23 19.6%

Season 3 - as of Oct 2022

Type Level Heroes Odds
S3 5* Featured 3 1%
S3 5* 15 0.6%
S3 4* 11 14.6%
S3 3* 9 51.6%
S1 5* 20 0.9%
S1 4* 22 11.9%
S1 3* 23 19.6%

Season 2 - as of Nov 2022
5* Featured includes 2 S2 and 2 HOTM

Type Level Heroes Odds
S2 5* Featured 4 1.3%
S2 5* 13 0.3%
S2 4* 9 14.6%
S2 3* 7 51.4%
S1 5* 20 0.9%
S1 4* 22 11.9%
S1 3* 23 19.6%

TC20 - Odds interpreted by player base

Type Level Heroes Odds
S1 5* 20 5%
S1 4* 22 20%
S1 3* 23 75%

HA10
5% Chance to receive a non S1 hero. There is an additional 5% chance to receive a costume if the hero has one as a separate roll not shown here.

HA8 - as of Oct 2022

Type Level Heroes Odds
CF1 4* 10 30%
S1 4* 22 70%

33 Likes

Reserved for use if needed

1 Like

This is awesome! Really puts things in perspective. Much appreciated

Will you bring doing this for other portals?

Yep! My plan is to insert them into the OP. I haven’t researched each season’s portal. I figure we will roll through them in short order.

3 Likes

These are really fantastic! Thank you for making them :slight_smile:

1 Like

The chart below TC20 seems to be backwards, unless I’ve been doing something wrong I don’t get 75% 5*.

Whoops! Corrected. Thanks!

Thank you for this. Much appreciated.

2 Likes

I think being a bit more consistent through all of them might help with visual comparability

  1. Always start at exactly 12 o´clock with all of them, currently some are and some are not

  2. Keep the same order: Most of them start with S1rare>S1epic>S1legendary, then move on to whatever the interesting part of the portal is, but in S4 you´ve mixed it up for some reason.
    I think it´s a good idea to start with S1 in all portals, to show right off the bat how much garbage is to be expected. Makes it easier to compare portals and find the ones with less garbage.

An additional idea:
Use the colours as well to show garbage. So make all S1 in greyscale, while adding the nonS1 in shades of a color.
Also use the shades to go from weak to strong colour (rare to legendary) to show the most interesting bits most clearly. Probably best to use the same shade for each rarity, but do keep the separate bits for each hero. That way it is more obvious that say Aderyn and Bertulf have the same chance of popping up.

Bonus draws are difficult to correctly incorporate, but do improve a very important section, so I would definitely try to somehow include them, maybe add an additional slice next to the pie chart? Not sure if your graphics tool is capable of doing that, but it would show the point that you get an extra bit on top of your regular pull. And especially in the HA 10 it´s actually a rather big part of the desired outcome. The hotm may be less important, because it´s the same everywhere, but still it´s a bonus that makes those horrible odds slightly better :slight_smile:

Nice effort! Keep them coming!

2 Likes

Oh nice thank you that’s so awesome Pie Charts Are the Worst

Bonus draws @1.3%, is an extra. It is not part of the regular 100% for each summon.

Pie chart is usually 100%. To add Bonus draw in would make the pie chart 101.3%. It would not representative of the actual summon odds for each portal.

1 Like

Well done, I love how well these visuals are organised!

1 Like

hence you put an additional slice next to the 100% pie chart.

This is so great. I want these to be implemented into all posts that are relevant- hopefully it can help :pray:

1 Like

The hotm is a bonus draw that occurs as an independent event alongside every portal pull. Because it is an independent event, it does not affect the odds of a portal outcome. You might get an extra 5* from one of your pulls, but the probability of getting that extra 5* doesn’t change the underlying probabilities for an event hero. It is a separate event (that occurs simultaneously, but is still separate), with its own probability distribution of outcomes.

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Which is why I think the pie chart is good as it is. 100%.

1 Like

I’ve added S3 and went ahead and did HA8 for S&Gs. Too bad HA10 doesn’t operate like HA8 :wink:

4 Likes

[quote=“nicos, post:11, topic:281071”] Pie Charts Are the Worst
[/quote]

As the linked article notes at the end, pie charts are good for one thing: showing what a fraction looks like. Which is exactly what we really need most here. It shows you graphically just how tiny that 1% or 2.5% chance of getting something you want really is.

Here are a couple more handy numbers. With a 2.5% overall chance of Legendaries and 1% HOTM, on a 10- pull, the chance of getting no Legendaries at all is about 70.2%. On a 30-pull, the chance of no Legendaries is about 34.6%.

On a 10-pull, the chance of pulling exactly 1 Legendary is about 25.2%, so the chance of more than 1 is about 4.6%. On a 30-pull, the chance of pulling exactly 1 Legendary is about 37.4%, so the chance of more than 1 is about 28.0%.

This might be fun to see on a pie chart: a chart where you could enter the chance for getting what you want (2.5%, for example) and then maybe a slider for number of pulls so you can see graphically how your chances change between pulling zero, 1, or more than 1 as you pull more times in total.

total = 84.90% ???

1 Like