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Mining for Bits

How are critical stars distributed?

Rating: 2 votes, 5.00 average.

Me, of course. I need a place to write down my observations.

tl;dr: It uses a weighed table based on each servant's personal criticalWeight and 3 random cards are given 50, 20 and 20 extra criticalWeight.

There's a concept of 'critical weight'. It's called that because it's used for a weighed table. Tally up all the results and you get 100%, and each value is a fraction of the pie. So [20 30 50] adds up to 100 and thus the chances become [20% 30% 50%]. If it's [10 5 7 3] then it adds up to 25 and the chances are [40% 20% 28% 12%].

First, the game assigns base weights to three of the five cards. 50, 20 and 20.. The cards are then shuffled.
Second, it adds the card's servant's criticalWeight, multiplied by their critical focus factor (This is what Gil's Collector EX does and whatnot), to each card.
What are these criticalWeights? These:

servant criticalWeight
Mashu Kyrielite 99
Artoria Pendragon 102
Artoria Pendragon (Alter) 99
Artoria Pendragon (Lily) 102
Nero Claudius 102
Siegfried 97
Gaius Julius Caesar 99
Altera 102
Gilles de Rais 98
Chevalier d'Eon 102
Emiya 145
Gilgamesh 153
Robin Hood 150
Atalanta 148
Euryale 156
Arash 147
Cu Chulainn 87
Elizabeth Bathory 90
Musashibou Benkei 89
Cu Chulainn (Prototype) 88
Leonidas I 89
Romulus 90
Medusa 194
Saint George 205
Edward Teach 198
Boudica 196
Ushiwakamaru 204
Alexander 205
Marie Antoinette 201
Saint Martha 205
Medea 50
Gilles de Rais 48
Hans Christian Andersen 48
William Shakespeare 50
Mephistopheles 50
Wolfgang Amadeus Mozart 49
Zhuge Kongming (El-Melloi II) 50
Cu Chulainn 49
Sasaki Koujirou 102
Hassan of the Cursed Arm 97
Stheno 104
Jing Ke 98
Charles-Henri Sanson 102
Phantom of the Opera 98
Mata Hari 98
Carmilla 98
Heracles 10
Lancelot 10
Lu Bu Feng Xian 9
Spartacus 9
Sakata Kintoki 9
Vlad III 9
Asterion 9
Caligula 9
Darius III 9
Kiyohime 9
Eirik Bloodaxe 9
Tamamo Cat 10
Jeanne d'Arc 99

Yes, Riders and Archers will attract the most stars (plus minus the skew caused by those base weights I mentioned before. Also RNG)
And Gil? Well he'll prolly get ALL THE STARS. The bling extends to his gameplay.

Third, the game tallies up the total weight. Like I said, weighed table.
Fourth, it goes one by one with each star you got. It will roll a random number between 0 and [totalWeight]. Whichever slot corresponds to the number will get the crit star. Imagine it as dividing a dartboard into 5 sections in proportion of each card's criticalWeight and then throwing a dart. Wherever the dart hits, that card gets +X (where X is 11% as of this writing) crit chance.
Fairly simple, really. But now you know why Berserkers never get crits. Unless they luck out and get that base 20 or 50 criticalWeight, their slice of the pie is literally zero almost zero.

Interestingly the devs have a system so cards would get X bonus crit rate for every Y stars they get, but the parameters that control it are both set to 0. I guess they realized it'd go nuts too quickly.

Updated September 4th, 2015 at 12:55 AM by Kyte



  1. GundamFSN's Avatar
    Huh so Riders are actually crits monster.

    No wonder Alexander always hogs crit stars like crazy.
  2. Aedra's Avatar
    Thx for your analysis. I've been wondering for a while
  3. Aedra's Avatar
    thx for the update..

    at least berserker is not 0 anymore :v
  4. magnetic_fan's Avatar
    Could you find out how skills like Gilgamesh's Collector EX and the Bazett concept equipment act on critical weight? Something like (RNG + criticalweight) * (1 + X from critical focus factor)?

    Because in your servant profile draft Gilgamesh's Collector EX has Star focus up from 300% to 600%, which in Japanese wiki is 30 to 60. Some of my fellow player get confused and think 30 to 60 is directly added to critical weight like (RNG + criricalweight + X from focus)

    スキル名 CT スキル効果 Lv1 Lv2 Lv3 Lv4 Lv5 Lv6 Lv7 Lv8 Lv9 Lv10
    抑制A 7 自身にスター集中状態を付与(3T) 20 20 20 20 20 20 20 20 20 20
    &スターを大量獲得 5 6 7 8 9 10 11 12 13 15
    無窮の武練A+ 7 自身にスター集中状態を付与(3T) 20 23 26 29 32 35 38 41 44 50
    コレクターEX 7 自身にスター集中状態大を付与(3T) 30 33 36 39 42 45 48 51 54 60
    追い込みの美学C 6 自身にスター集中状態大を付与(1T) 50 55 60 65 70 75 80 85 90 100
    By the way, people from Chinese forums noticed that difference within the same class comes from Luck of the servant. Same with deathRate from Magic and starRate from Agility. Turned out the ability rank is a important part of the model when DW&TM design servant stats.

    Hope Luck doesn't effect material drop rate lol.
    Updated September 12th, 2015 at 09:11 AM by magnetic_fan
  5. Kyte's Avatar
    Second, it adds the card's servant's criticalWeight, multiplied by their critical focus factor (This is what Gil's Collector EX does and whatnot), to each card.
  6. magnetic_fan's Avatar
    I see. So in Gilgamesh's case, (50/20/0 + 153) * 1 without Collector on, and (50/20/0 + 153) * 300% with Collector Lv1. Is that right?

    Thank you so much for your consideration.
  7. Kyte's Avatar
    Remember 300% = 3
  8. Aedra's Avatar
    After the patch, I notice that there are a lot more chance to get 100% critical chance for 2 cards or more now. Somehow it feel like they change stars distribution to ignore the card that already 100%. Can you check it up if you have time?

    or maybe just my imagination....
  9. Kyte's Avatar
    Maybe they capped it, doesn't really matter.
  10. Northfish's Avatar
    Are you sure the added star weight is multiplied by star focus bonus itself without plus 1? Fate GUDAGUDA Order just increase star focus rate by 1% when it is not in max limit, and the performance in game is obviously not (RNG + weight) * 1%. Or there is difference between CEs and skills?