Battle Points: Critical Formula Revealed!

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Critical Formula Revealed!

 

Even though the Critical system has been part of Wizard101 for close to three years, it is amazing just how little is known about it.

My last post on the subject, Critical Intel, debunked some of the ‘common’ knowledge in the arena about Critical… but what is the actual truth behind it all? It was hiding in plain sight with the help of the following two observations:

  1. Destiny’s and Milt’s analysis of the Skyscream Hood (80 critical) and the Skyscream Cape (41 critical) showed that regardless of level, the Hood would always give 9% more Criticals than the Cape, corresponding to a ratio of just below 4.5 Critical rating to 1% chance.
  2. Dead Sparrow’s Critical build showed that at Level 30, 4.5 Critical rating corresponds essentially EXACTLY to 1% Critical chance (e.g. gear with 5 Critical gives a 1% boost; gear with 8-10 Critical gives a 2% boost).
  3. The minimum percentage that KI assigns to any statistic from gear is exactly 1 percent; for example, if you have a pet with Spell-Proof, it will always give exactly a minimum of 1 percent resist even if Strength, Agility, and Power are all at zero.

These were the clues that enabled me to unearth the formula on how to determine critical chance from a given piece of gear!

 

How to determine Critical Chance at Level 90

  1. Divide your Critical rating by the fraction 40/9 (which is approximately 4.44).
  2. Subtract 4 from the result.
  3. If the result is greater than 1, you now have the Critical chance you get from this piece of gear.
  4. Otherwise, the gear will add exactly 1 percent to your critical chance.

Here are two examples to show how this works.

Skyscream Hood: 80 Critical gives you a percentage of 80/(40/9) – 4 = 14%, which KI indeed displays as 14%.

Woodland Tribal Hood: 148 Critical gives you a percentage of 148/(40/9) – 4 = 29.3%, which KI indeed displays as 29%.

 

How to determine Critical Chance at other levels

Below Level 90, the only change to the rules is what you subtract at Step 2. At Level 50 or below, the amount you subtract is 0, so you simply divide your Critical Rating by 40/9 to get a percentage. For example, Dead Sparrow’s pet Hunter had a Critical rating of 25, which corresponded to a percentage of 25/(40/9) = 5.625%, which was indeed rounded up to 6%. However, if you gave Hunter to a Level 90 wizard, you would need to subtract 4 percent and end up with = 1.625%… barely enough to round to 2%.

After Level 50, the amount you subtract goes up by 1% for every 10 levels. For example, at Level 60, you simply subtract 1% in Step 2 instead of 4%. That Skyscream Hood? At Level 60, its Critical percentage is now 80/(40/9) – 1 = 17%, which is indeed displayed as 17.

This is most likely why people thought Critical was linear (read: you divide the rating by a fixed number, such as 5, to get a percentage) for so long: at level 60, Critical percentages are generally within rounding error of what you would expect from Critical being linear.

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But what about Block?

A similar formula works for Block; testing has confirmed that Block indeed works the same way (the percentage is indeed computed item by item). The rules at Level 90 are as follows:

  1. Divide your Block rating by the fraction 40/11 (which is approximately 3.64).
  2. Subtract 4 from the result.
  3. If the result is greater than 1, you now have the Block chance you get from this piece of gear.
  4. Otherwise, the gear will add exactly 1 percent to your block chance.

Here are two examples to show how this works.

Courtly Dirk: 11 Block gives you 11/(40/11) – 4 = -0.975%, less than 1%, which means you get 1% Block at Promethean.

Walkers of the Hungry Dead: 93 Block gives you 93/(40/11) – 4 = 21.575%, which is indeed displayed as 22%.

 

How to determine Block at other levels

Below Level 90, the only change to the rules is what you subtract at Step 2. At Level 50 or below, the amount you subtract is 0, so you simply divide your Block Rating by 40/11 to get a percentage. After Level 50, the amount you subtract goes up by 1% for every 10 levels. For example, at Level 60, you simply subtract 1% in Step 2 instead of 4%.

 

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Leave A Comment!

  • Thank you, mmailliw, for cracking the code! The relationship between critical chance and % has always baffled me, but this makes sense.
    I love this series of articles on the math behind critical & block.

    I guess the big takeaway here for me is that gear with less than 18 critical or 15 block is useless for my level 90. Thank you!

  • I’ve been looking for this for a long time. Thanks you so much for sharing this with us! πŸ™‚

  • Your findings here probably saved me a lot of aggravation, because I was considering buying the Diego Ring/Athame which each have 15 crit for my Level 90. Sadly, they would have done nothing for me, and I would have sacrificed important stats to use them. Glad someone figured this stuff out before I wasted my time and effort.

    • ChoGath

      Mathemagicians and scientific experimentation 4tw πŸ™‚

  • Katherine Light

    Is it possible that critical and block, while displayed singularly when you break it down by gear, are actually calculated cumulatively? EG, if you have 4 pieces of gear with 12 block each, they would each individually be worthless but that KI actually figures out block based on the summation of the stats? I just have a hard time imagining there being top level no auction, otherwise great stat-giving gear put in place that APPEARS to have good stats but where the block is actually a complete fake-out of a stat. That seems overly deceptive on the part of those who design the gear. “Look at this wand, it gives you a bit of crit block! ….. lolz nope, I lied.” I just have problems wrapping my head around the designers doing that.

    • Anything is possible, but if this is true then the crit percentages it shows you for gear are way off at high levels.

      Edit: I guess what I’m saying is: Either way you look at it, the stats are misleading. Either it’s telling you false numbers, or it’s telling you the right numbers(rounded to nearest %) and what Will says is true.

      • mmailliw

        Actually I looked at your video testing where you tested 240 Critical at Level 80 with 30% Vengeance vs 136 Block and cast 4 Fire Elves of which 3 went Critical and none were blocked.

        Under both theories, the most likely result is for 3 of the 4 Elves to go Critical and exactly one of those Critical Elves to go blocked… but there is a *slightly* higher chance of seeing 3 go Critical and 0 of those get blocked under my theory (9.9% chance) than under Katherine’s (7.7% chance).

        To test it better we would really need a test like what I described to Katherine above (5 gear pieces with 10 Block Each vs a wand that gives 30-60 Crit)…

    • So, I’m not completely certain about this because I haven’t done an exhaustive study of all the gear in game, but I think you will not find level 90 gear with less than +18 critical or less than +15 block. I don’t think there is useless gear for any level because the stats scale. BUT! If your level 90 equips a level 56 ring, for example, that only gives +9 block… THAT would be useless.

      This ties in to mmailliw’s last article http://www.duelist101.com/news/issues/battle-points-critical-intel/

      where he describes how low critical and block ratings correspond to very low percentages.

      • mmailliw

        I was thinking about this for a while and (besides the new warlord gear) there is only really one exception to this.

        I) The block from Courtly Dirk (Level 76; 11 block) is NOT QUITE worthless at the level you can first craft it because the cutoff for ‘counting’ at Level 76 is 9.36 (and at Level 80 it is still ‘only’ 10.8, corresponding to a change of approximately 0.05%) even though it will never increase your block chance by more than half a percent.
        II) The block from the Storm Caiman’s Cruel Fang, though (Level 86; also 11 block) now IS worthless because the cutoff at Level 86 is 12.96 which is above 11.

        In both cases, though, the crafted athame in question gives enough other stats in terms of health, attack boost, power pips, and healing to still be part of a viable PvP build even ignoring block (which rarely is the main consideration in choosing athames anyway).

        • Katherine Light

          Yes, it was the Storm Caiman’s Cruel Fang I was thinking of, as well as the Waterworks Robes (which I know many who don’t craft are still using at max level for it’s resist). There’s also the Storm Caiman’s Tailbiter Ring, which is only 18, so isn’t completely useless but is pretty much negligible. It seems odd to me that they’d build stats into the gear knowing the stats are a fake-out.

    • mmailliw

      Actually, this looks like it should be pretty easy to test: stage a “match” between a Level 90 with 5 pieces of gear each at 10-12 block and a Level 90 opponent with, say, 30 to 60 Critical rating solely from wand and see how many wand hits get blocked!

      If my theory is correct, then every single critical should go through (because the block is worthless).

      If your suggestion is correct, then every single critical hit should be blocked (even with the 60 Critical vs 50 block, the Critical percentage is 9.3% with Block percentage 9.8%).

      Nick’s testing of the Level 80 Critical build actually seems to provide *slightly* stronger evidence for my theory than your suggestion… but neither had been ruled out.

      • Katherine Light

        That sounds like a fantastic test! I’d love to help test it out sometime, if you’re willing, just to confirm it.

        • mmailliw

          Me too! I can bring a 60/60 wand and wear nothing else and if you have 5 different pieces of 10-block gear I can whack you with wand hits until 1 of 3 things happen:

          I) I am blocked all the time (confirming your suggestion)
          II) I am never blocked (confirming my theory)
          III) I am blocked SOME of the time (which would suggest an alternate theory: e.g. that the formula is used except that KI always ensures that each piece of block-granting gear grants at least some minimum block % such as 0.5% or 1%)

          I’m thinking immediately after tomorrow’s second M4C event ends (which I believe would mean around 7P Pacific); does that work for you?

          • Katherine Light

            It does indeed! I’ll need a bit of times to scrounge up pieces with exactly 10 block, lol, but at the bazaar I should be able to manage it.

          • I just tested this with CelestialMoon. I used 10-10-10-10-11 block items, and she used a wand with exactly 60 crit. I blocked 4/10 crits. So, it’s neither.

            The gear didn’t have 0 block, but it didn’t take the total and add them together either. I am under the assumption that there’s a minimum amount of block that any piece of gear with block stat can give. Will thinks this would be .5% so it will always round up to at least 1%. It’s hard to say without more data though.

          • mmailliw

            With a minimum of .5%, 26% of Criticals should be blocked; with a minimum of 1%, the number becomes 52% (and 40% is right in the middle between these two). I would suspect that this minimum number works like resist number: is it known what the minimum value of resist for a pet is?

          • mmailliw

            LOL we should be able to get a bit of testing in between 7 and 730 tomorrow then (a pirate thing ended up going to round 3)… to find out whether the magic number is 0.5 or 1.0!

          • mmailliw

            lol ready now: want to meet in arena realm scarecrow if this time works?

          • Katherine Light

            Hey! I just finished taking care of things after Batten Down the hatches – sorry I’m late, but I’ll head right over and see if you’re still there. πŸ™‚

  • Anthony FireSword

    Ah, this does my heart good to hear this. Now fire and storm have a very good chance of scoring a crit against ice opponents who opt to use the thaurmature’s chill waders for the 5 extra resist over the frost shrine slippers’ 10 resist, but that the cost of 65 block! That extra resist isnt doing much good when placed against a 2X multiplyer, now isnt it (assuming the block the rest of their gear provides isnt enough to get more than a ‘lucky’ block in). πŸ˜€

  • {iGnite}

    This is amazing; Now we just need to know how these stats are calculated in-battle.

  • izabera

    are you saying these rounding errors?

    lvl 90 staff of the storm caiman: 100 crit, displays as 19%
    (100-18)/4.5=18.22222

    knightly helm: 140 crit, displays as 28%

    (140-18)/4.5=27.11111

    • Hmmm… we’ll have to ask mmailliw to take a look at these and possibly tweak the formula.

      • mmailliw

        If the “18” is really “17 7/9” (160/9) and the “4.5” is really “4 4/9” (40/9), then the 1 point per level relationship can still hold, along with Izabera’s data. (This would ALSO confirm that KI always rounds halves up because three of the data points, including both of the ones Izabera pointed out, now end in a .5.)

    • mmailliw

      More data! Yummy!

      Looking at these and the rest of my chart, I have concluded that the actual ratio value is somewhere in the interval [4.407, 4.421]. I was so excited to see 4.5 that I jumped on it; however, it seems like the data refuses to be that “nice”… both 4.41 and 4.42 agree with the data though.

      • mmailliw

        EDIT: I now think the formula looks more like % = (rating – 17.8)/4.44.

  • master of wizard 101

    in some ways this has a big change to the game. now if you are going for a crit build you can figure out the exact chance you have to critical. Tough now that i think about it i can’t believe how many expensive pieces of gear i bought at lvl 50 to brag to my friends that i had critical and now i realize they were worthless

  • I guess that makes sense, but since vengeance is described as a percentage and you divide your regular critical by 4.5, does that mean that vengeance adds 90 critical rating? And that conviction gives 21.5% (22%) block rating?

  • Dylan

    So, if I have 360 critical, I have a higher chance of landing a critical on someone with 200 block than if I had 200 critical?

    • Yes. And actually 200 crit should never land a crit on 200 block, except maybe with vengeance. Even then it’s iffy.

      • mmailliw

        The crazy thing about this formula is that at Level 90, 200 critical can actually correspond to a higher percentage than 200 block if the critical comes from only two items and the block comes from five! (The numbers will be 37% and 35% respectively.)

  • nameless noob

    *brainfizzle*

  • Talon iceshield

    The block works base on ur block and the other person crit rate. For example, If u have 100 block and the other has 200 crit rate, the chance to block is 50%.

  • master of wizard 101

    my question is can’t KI just release a note giving the formula i mean how much trouble would it be?

  • Frostyflame

    actually vengeance is place with the percent value, vengeance on his pet would give roughly (25 x 40/9) = 111 critical rate. so it is safe to assume that his critical, with the pet, was much higher.

  • Stormbringer

    if you ask me best critical and block comes from lvl 80 hawkrider attire checked video and with the attire you would have 225 block and 175 critical something like that i would buy bundle for my storm wizard because if you can’t block critical as a storm wizard your in trouble

  • Blaze MeOut

    mmailliw is right … I did another test of my own using four pieces of gear that total gave me a critical of 192 … if I rounded and added all the percentages together it would be 31% critical but if Kingsisle calculates total and rounded it, it would have been 39% … I went to Cyclops lane in realm wu and spammed and recorded how many times I critical on a fire cat .. I did not count fizzles because I remember kingisisle said they calculate critical and block rating only if the spell works … it first I thought mmailliw was wrong because I was criticalling 40% of the time but as I spammed over 50 fire cats its gradually dropped to 31% after I spammed 150 fire cats mmailliw is right critical number is false the best way to get critical is getting critical on one piece of gear rather than spreading it out on several pieces of gear …

    • Blaze MeOut

      Kingsisle probably did this system as a way to force people to get better critical gear as they lvl up … because it is more affective to reduce the percentage of critical as you lvl up this way instead of taking the total and gradually reducing it

    • Blaze MeOut

      eventually they would want people to get off waterworks gear because eventually waterworks gear will be useless when there is actually way better gear at higher lvl

  • I calculated it and:

    -The critical rating decimal is 0.225
    -444.4444….. or 445 critical rating means you will literally critical 100% of the time. All. The. Time.
    -A normal vengeance increases your numeric critical rating by 88.8888… or basically 89
    -The vengeance treasure card(25% version) will increase your numeric critical rating by 111.11111… or 112
    -The Vengeance item card(30% version) will increase your numeric critical rating by 133.33333…. or 133. DANG!

    So if you had about 350 critical, and you put on a normal vengeance(here comes may cast vengeance!) then you are guaranteed a critical on your next hit, or you will have around 5% chance of not hitting a critical. This will be rare. If you had 300 critical you would hit a critical about 70% of the time. 350 critical is about 80% and 400 is exactly 90%. If you have an expansive mind and your good with numbers, then your going to add about 90 critical to your ratings with a vengeance on, your going to increase your stats so you have a fair percentage of critical(around the base accuracy of a spell πŸ˜› I always compare percentage of critical to how often you would fizzle with that much accuracy. That’s how much your spell will NOT critical.) Hope this really helped! πŸ˜€

  • Empiso

    Mind=Blown!

  • Wait does the number differ depending on the info highlighted in the critical intel article? Or is the percentage same with the formula no matter what?

  • Aaron S.

    i still find myself returning here, especially since hades gear HAPPENED. lol

    • I use this article often, myself. lol

      • Aaron S.

        It’s so useful πŸ˜› Especially when I try to access whether or not my block or critical from given gear is “sufficient” or “useable” at the least, compared to the amounting levels of critical seen in the arena.

        Also, are you certain that 270 block is enough to stop 500 + critical? I saw you write something like that multiple times, and I’d like clarification, as I’m trying to decided how much block I need (If I use one wand, I’d have 298 critical block, with less of other stats. Another wand would give 258 critical block, with higher stats in other categories, and I am conflicting on which is better)

        • This all depends on the percentage. Add up your percentages. My Fire can get about 495 crit and have around 76% critical chance. If your block amount is giving you that much block or greater, you win.

          Using a wand with 130 block and boots with 93 block, I get about 52%. Depending on how many pieces of gear the rest of the block is coming from, 270 could be close.

          Regular hades gear crit is a lot lower than that though.. I am using critical boots and a 3x crit talent pet. Without those things, I’m at around 55%.

          • Aaron S.

            Hey sorry for inconvenience, using ratings.

            with the first wand I mentioned, Teeth of the lords of night, added with rest of the gear gives me a total of 63% critical block rating (298 critical block)
            whereas the other wand, Lunar scepter of anubis, added with the rest of the gear gives me a total of 52% critical block. (258 critical block)

            Now obviously the anubis wand gives more critical, however where it seems pretty small, it’s actually an increase of 10% more critical than the lords of night wand.

            So it comes to lower yet reasonable block with higher critical, or an immense amount of block (63% is a ton, even your 76%, using the block percent/crit. percent formula, only has a 18% chance of landing) for relatively small critical. (decrease of a possible 10% critical, which is mildly high)

            Your opinion please? xD (btw with 52% block, your 76% critical has a 33% chance of landing. From the aggressor’s perspective, that may be small, but from the victim of potential critical, that seems like quite the chance of landing a critical :P)

          • Interesting. I guess the other things to consider are: (1) you’re talking about 33% of criticals landing, but not every hit will be critical so the chance of a critical attack landing is more like 24%, and (2) how much do you heal, and how much do critical heals help you?

            As for the 1st part, that’s really the problem that I see with more and more critical chance: we are now seeing MOST attacks going critical, so we are relying much more on block than ever before. If that makes sense lol.

          • Aaron S.

            1) good point πŸ˜€
            2) I am an ice wizard, running Alexander’s “frozen” build. that leaves me with 70+ damage boost, and around 30 resist. Whereas Alex has around 190 critical block, I insist on having 250+ block. Pierce rating is around 12% from gear, however pet has may cast infallible.

            Point is, I never heal. No healing. so critical heals are useless. critical attacks, however, may be accounted for, seeing how the “aggressors” have relatively low block (on average only 50 rating)

            And as mentioned, From the “victim of potential critical”‘s perspective, even 33% chance of a land seems rather big, assuming all opponent hits go critical ( and for some reason, they always seem to do exactly so!) especially seeing how the average technique is spamming low pip spells, all the more reason for criticals to trigger.

  • zphil123

    They need to just make it so gear gives a percent, and that is always what it gives, no matter what the level