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Holy Shield on a scepter probability?

Discussion in 'Theorycrafting and Statistics' started by purplelocust, Nov 15, 2006.

  1. purplelocust

    purplelocust Diabloii.Net Member

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    Holy Shield on a scepter probability?

    I tried to estimate the probability of generating a scepter with Holy Shield spawning on it, but I'm no expert and am wondering if the following computation is in the right range or if I'm way off:

    My understanding is that the only way that a scepter can spawn with Holy Shield is for it to be rolled with skills that cannot spawn on a scepter normally (Holy Shield and Smite) six times in a row, and then a seventh time it must be Holy Shield at which point the algorithm gives up and assigns Holy Shield anyway.


    So at the start, when a scepter spawns, there is a 30% chance of no skills, 40% chance of 1 skill, 20% chance of 2 skills and 10% chance of 3 skills.

    So let's start with the 3 skills case, which would have the greatest chance of spawning Holy Shield. I am assuming that once 3 skills is selected, the algorithm keeps trying to allocate the 3 skills until successful- if not, the probability would be significantly less.

    Suppose a scepter with ilvl greater than 36 is dropped/shopped, giving the 5th tier of skills to chose from. There is a 50% total chance that the skill tier could change- go up to 6th or down to 4th or 3rd. The chance of getting the first tier skill Smite on such a scepter is 0 (which also causes the reroll) so we can ignore that. The five 5th tier skills are Conversion, Holy Shield, Holy Shock, Sanctuary and Meditation. In order to get Holy Shield to spawn, it must be chosen each of the first 7 times.

    For each skill choice, the chance of getting HS is:
    50% chance of staying in the 5th tier * 20% chance of choosing Holy Shield amoung the 5th tier skills = 10%

    So for 3 skill choices, the chance of getting HS at least once is 10% + (90%*10%) + (81%*10%)= 27.1%.

    So the probability of getting HS seven times in a row is .271^7=.000107346

    And that is assuming we are amoung the 10% of the scepters that get 3 staffmods. For two staffmods and one staffmod, the chance of getting HS seven times in a row is considerably less:

    for two: (10%+(90%*10%))^7= .00000893872
    for one: 10%^7 = 10^-7 = .0000001

    Totalling, the expected values we get

    10% * .000107346 +20% * .00000893872 +40% * 10^-7

    which gives the probability of 0.0000125623, about 1 in 80,000. That seems pretty small, but since you can generate scepters by shopping and can look at a bunch for free, it doesn't seem as incredibly tiny as I would have thought. I don't know how long it would take to inspect 80,000 scepters in the shops, but that doesn't seem as hard as doing 10,000 Pindleruns and many people apparently have the patience for that!

    For other ilvls less than 37, there is also a chance of HS spawning but those chances would be much lower. For example, a scepter ilvl between 24 and 36 would start with tier 4 staffmods with a 20% chance to boost the tier by one to tier 5, so the chance of getting HS on such a scepter would be 4% for each roll instead of 10%. So when iterated seven times, this is far less likely.
     
  2. krischan

    krischan Europe Trade Moderator

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    The difference between 10,000 Pindle runs and examining 80,000 scepters is that Pindle will drop perhaps 1000 uniques during that while not much will happen with respect to the scepters.

    Edit: Of course, after 10,000 Pindle runs, your sorc will also be L95-96 or so. :wink3:
     
  3. ispankpigeons

    ispankpigeons Diabloii.Net Member

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    but wouldn't it be 1 in 80,000 scepters of that certain item level that happen to generate to have 3 staff mods?

    thats alot harder to find than say, a normal staff with one socket and one staffmod, or something.

    for instance; maybe 1 out of every 5 staffs you find fits the critera for being able to get holy shield.

    so wouldnt the odds really be something like 1 in 80,000x5?

    which is getting to the point of being astronomical...

    or am i doing that completely wrong? i've never been good with math, just trying to fire up the old common sense haha
     
  4. purplelocust

    purplelocust Diabloii.Net Member

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    The computation above (if it's correct...) includes the 0, 1, 2 and 3 staffmods possibilities, and ilvl is set by the character shopping in the case of merchants. So shopping with any character in the 37+ range should work, although you may want to use a higher level character for the chance for +2 all pally or +3 combat skills (LoD only) to spawn as gravy (or you may also be looking for a good Hammerdin +2 pally/+3 BH +3 Conc FCR scepter.) A quick check seemed to show that Akara, Drognan and Jamella seem to have four or five scepters each visit, Ormus about 8, and Malah about 3. Even though Ormus has a broader selection, probably the quickest thing to do is make a red cow portal next to Akara and pop and check until your vision gets blurry- perhaps after 20,000 pops and checks you'd have a decent shot at seeing one for sale.

    What's so great about a Holy Shield spawning on a scepter? Well, with other +skills gear Holy Shield is a one-point wonder with a lot of prerequites which aren't used for many builds. So in LoD it would be great to have it on switch and spend the skill points elsewhere, and in Classic it would be great as levels (and skill points) are so much harder to come by there.



     
  5. oneBlast

    oneBlast Diabloii.Net Member

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    I'd rather look for grey +3hs scepter and make a cta in it.
     
  6. Sgraffite

    Sgraffite Diabloii.Net Member

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    Is it possible for Holy Shield to spawn on a scepter at one of the merchants, only only as a drop?
     
  7. purplelocust

    purplelocust Diabloii.Net Member

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    That would be a fanatastic weapon to have on switch, that is for sure, but you don't see nearly as many scepters dropping in the wild as you do shopping, and it would have to be a white or already 5-socketed war, divine or cadaceus which cuts down the chances from extremely unlikely to infinitessimal.

    I'm assuming it can spawn at a shop, since I think the item generation process at shops follows the same routine as from monsters.



     
  8. hydrahydra

    hydrahydra Diabloii.Net Member

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    i thought you can only make cta in flail, knout etc.



     
  9. krischan

    krischan Europe Trade Moderator

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    You can make CtA in any nonmagical weapon with 5 sockets, even bows or whatever. Flails and crystal swords are common choices because of their low reqs.
     
  10. hydrahydra

    hydrahydra Diabloii.Net Member

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    eh u sure it even says only flails etc. on battle.net...



     
  11. PhatTrumpet

    PhatTrumpet Diabloii.Net Member

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    What battle.net are you looking at?
     
  12. purplelocust

    purplelocust Diabloii.Net Member

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    Probably what was in mind was Heart of the Oak, which requires a 4-socket mace = Mace, Morning Star or Flail. And since maces and morningstars can't have 4 sockets, the choice is flail (or Knout or Scourge, but HotO is really a caster runeword so 4-socket flail is the typical choice.)



     
  13. chubz

    chubz Diabloii.Net Member

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    it can also be made in staves, though a hoto staff would be quite useless



     
  14. Paladingo

    Paladingo Diabloii.Net Member

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    Just to get (sort of) back on topic. I have a few holy shield scepter from 1.09 where they are common. Recently I spent a couple of intense weeks (lots of hours) in 1.07 and picked up about 10 more scepters with holy shield. It would have been 50 scepters but I only collected those with +3 to HS or +2 HS and some other good mod.
     
  15. helvete

    helvete Diabloii.Net Member

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    I am so going back to earlier patches to get myself a 5s +3HS +Xsalvation +Xconviction scepter! Omg the skillpoints saved and the added party value of that hammerdin...



     
  16. pongie

    pongie Diabloii.Net Member

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    Re: Holy Shield on a scepter probability?

    Are these scepters still available in 1.12?
     
  17. Corrupted

    Corrupted Diabloii.Net Member

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    Re: Holy Shield on a scepter probability?

    I checked quite a few before landing this one:

    War Scepter
    One-Hand Damage: 10 to 17
    Durability: 61 of 70
    Required Strength: 55
    Required Level: 24
    Mace Class - Fast Attack Speed
    Item Version: 1.10+ Expansion
    Item Level: 85
    Fingerprint: 0xdec665b
    +1 to Holy Shield (Paladin Only)
    +3 to Sanctuary (Paladin Only)
    +1 to Zeal (Paladin Only)
    150% Damage to Undead

    Obviously it's much easier to get a better scepter in previous versions.

    helvete: added party value? Since when do you MP with your SP chars :p
    The only paladin that truly benefits is an Avenger I guess.
     
  18. rickster

    rickster Diabloii.Net Member

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    Re: Holy Shield on a scepter probability?

    Yes, there's actually multiple copies of a +3 holy shield cta scepter on west ladder :rolleyes:



     
  19. BobCox2

    BobCox2 Diabloii.Net Member

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    Re: Holy Shield on a scepter probability?

    Viper Bludger or whatever the name was on west, During a early years dup lag fest week on realms I got offered one for free.
    Traded it.
     
  20. pongie

    pongie Diabloii.Net Member

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    Re: Holy Shield on a scepter probability?

    That's why I asked. My avenger doesn't have the 5 points to invest for the pre-req skills. The vendors haven't been very kind to me so far, so if anyone has one to spare on USWest then pm me please.


     

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