Frozen Orb vs. Blizzard - some research with .gifs and math!

TestyFish

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Sorceress Cold Skill Investment - Doin it with smarts

Cold has always been the skill tree of choice for discerning sorceresses who needed a second element of damage. Lightning and Fire really shine with 40+ points, although Fireball makes a good case for a 41 pt backup skill. The two skills that I've seen in contention most often for the "ohcraptheyarelightningimmunewhatdoIdoAHHHH!" are Frozen Orb and Blizzard.

Comparing these two skills is problematic because of a number of things:
1) The problem with both of these skills is that they fire off a large number of bolts/shards
2) Not all of those bolts/shards will hit an enemy (I call FO shots "bolts" and blizzard shots "shards")
3) The nature of Cold Mastery is that it has a different effect on mobs of different resistances, and FO generally makes a larger investment into CM than Blizz

Let talk about Frozen Orb first:

FO.gif

- Frozen orb sends out a total of 44 bolts
- Bolts are sent out uniformly in a 360 degree spread from the Orb
- The first second of the cast sends 1-2 bolts per frame
- There is a "burst" of 16 bolts at the end of the orb's path
- It is possible (but sometimes difficult) to hit a mob with all 16 bolts
- The final burst accounts for 16/44 of the damage, or 37% or so.
- FO has a maximum synergy of 40% if 20 hard points are invested in Ice Bolt (usually ignored)

The Down Low on Blizzard:


Blizzard 01.gif


- Blizzard sends out 28 shards
- The shards land in three diagonal rows (pictured above)
- The specific pattern is not constant, but there are approx. 1 shard per "spot" in the array
- Some spots can be hit twice, some can possibly be missed entirely
- Each hit has a small area of effect
- The even distribution prevents any "sweetspot" mechanic like for FO

Blizzard 01.png

Damage Comparison - Everyone loves math, right?

Blizz vs FO Math.png

It's commonly acknowledged that Blizzard is a better choice than Frozen Orb if more than 40 points are available. Since the introduction of synergies, Blizzard has 5% bonus on three different skills, while Frozen Orb has only a single 2% synergy. Blizzard sorcs in Ancient Tunnels are the gold standard of non-Barbarian Magic Finding characters in Diablo 2 in the modern patches, and this is in a large part to Blizzard's synergies, high damage, and Area of Effect.

To make the comparison more interesting, I limited the calculations to what can be achieved with the following limitations:
1) Only 35 hard points can be spent in the Cold Tree
2) Mobs with both 0% and 50% cold resist would be considered
3) We assume that a second element will be used to kill any mobs with a very high cold resist or broken immunity
4) The math above assumes that all shards and/or bolts hit an enemy

The caveats that must be considered:
1) Not all shards/bolts hit an enemy
2) We ignored the fact that FO bolts hit a single enemy, while blizzard has a small AOE

If we assume that a similar number of Blizzard and FO shots miss, and that we are not concerned with killing cold immune monsters with cold skills, Blizzard will out-damage FO on any mob with less than or equal to 50% cold resist. This is a fair assumption, but there is one thing that needs to be taken into account. That is "sweet-spotting" a FO explosion.

In Practice:
FO bolts are largely sent out in one of the 8 cardinal directions. Over the course of the first part of the spell about 3 bolts are sent in each of the 8 cardinal directions. The final burst sends out 16 bolts. If we assume a "perfect" sweetspot where all 16 bolts hit a single enemy, you can also assume that an additional 3 bolts are sent straight forward and also hit the enemy. This means that 19/44 bolts or about 40% of the total damage is the best we can hope to deal to a single enemy. If the sweetspot is missed by one tile, 8 of the final burst will likely miss and only 11 of 44 or 25% will hit the enemy.

With Blizzard's arrangement of hits, small enemies will not be hit by 25% of the shards, but large enemies (3x3 tile-sized enemies) will likely be hit by about 10 or so "slots" or 40% ish of the shards. Exceptionally large enemies like act bosses (that don't move outside the area of blizzard) will be hit by well over 60% of the shards. If Blizzard is hitting 40% or so of its shards, and FO hits 40% of the time when sweetspotted, why not be lazy and click near the enemy instead of have to perfectly sweet spot the FO cast and pray the enemy doesn't miss?

Subjective Recommendations:
Because of this analysis, I have settled in my mind that Blizzard as a timered spell with Fireball as a non-timered spell is the strongest build for a Fire/Cold hybrid.
1) It allows for flexibility, investing additional points in Fireball or Blizzard Synergies
2) There is only one timered spell, allowing for Blizzard casts followed up by Fireballs during the 2-3 seconds blizzard is doing damage
3) It's a more relaxed playstyle, allowing for more flexibility in positioning and needing less teleport repositioning (allowing the merc to do work)

So my personal goal for my next sorc is that I throw 41 points at Fireball and 35 points at Blizzard...and then based on whichever I find myself using I will then invest heavily in the spell that makes a bigger difference in clearspeed. Others are calling it a Blizzballer, but I'm going to slightly edit a recent name for the sorc and call mine a Fizzysorc.

Hope this was helpful, I wanted to make sure we posted .gifs, counted shards, etc. Let me know if there are things you think I've missed!
 
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Mar 19, 2020
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Very cool comparison and great work, always nice to see the math backup what we've felt about the difference between the two.

Do you have any other similar comparisons planned?
 

Albatross

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Love the gifs and math :) There are two more blizzard advantages worth mentioning.

Shards actually do damage as soon as they spawn, not when reaching the monster/ground. This makes near-instant kills possible with enough damage (mages in AT).

A single shard can normally hit a target only once due to next delay. However, large clustered monsters can be hit by the same shard more than once. This is due to shard AoE and "next delay" which will reset when it hits a different target, making the first monster a valid target again. Shards can alternate between two or more monsters before they expire and blizzard shredding minions of destruction is a good example of this mechanic.
 

TestyFish

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Is that nextdelay behavior similar to Fissure's, then? I know that fissure has a "missile" of sorts that's spawned and can rapidly alternate between two mobs on the same vent. What's the curation of each blizzard shard? I hadn't heard that info before.

Another thing I'd considered but didn't include is damage per cast. It's much higher for blizzard, so casting a blizzard on a pack and then spamming FB will do more damage than throwing a single FO and then spamming FB. You get an extra FB every second or so when using blizz over FO.
 

saracen85

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^^do people actually cast fireballs in between FO?

I find the cooldown to be too fast for any spam spells to be used effectively.
 
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Swamigoon

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@TestyFish , how difficult would it be to create a gif that counts the vents opened by a druid's Fissure spell? I speculated about comparing Blizzard with Fissure in my post yesterday, and I think it would be educational to verify whether Fissure has a similar "three diagonal rows of vents" pattern, like you observed with Blizzard's shards. (Please forgive me if you judge this query as off-topic.)
 

Albatross

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@TestyFish re-read my DMs with Fruit. I mixed up the naming, that should have been lastcollide, not nextdelay.

next delay - time in frames before a target can be hit again by the same attack or spell
last collide - should prevent a target from being hit repeatedly, but is bugged (vipers in nihl's temple, dark soul lightning, etc.)

According to Fruit's research a blizzard shard lives for 9 frames, but can damage only during 8. If two large monsters are close to each other and standing still a single shard will alternate between them every frame, hitting both 4 times before it expires.

Fissure has a next delay of 5 frames, but each vent also has last collide. Therefore the same bug applies which makes Fissure so strong against clustered monsters. Edit: next delay is still taken into account. Targets alternate every 6 frames unlike every other frame in the blizzard shards case.

Detailed explanation by onderduiker.
 
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maxicek

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Love the gifs.

How do the rows stack up against the size of the monsters? Are the rows big enough that a size 2 monster can stand between them and not get hit?
I always though this was the case as in PvP I have stood in a Blizz and not been hit. But then I may have been playing an assassin and claw blocked too.
 

TestyFish

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@TestyFish , how difficult would it be to create a gif that counts the vents opened by a druid's Fissure spell? I speculated about comparing Blizzard with Fissure in my post yesterday, and I think it would be educational to verify whether Fissure has a similar "three diagonal rows of vents" pattern, like you observed with Blizzard's shards. (Please forgive me if you judge this query as off-topic.)
It's a pain, but once you asked I had to do it. I actually record the video, convert to a gif, then go frame-by-frame to label them all. =D

Fissure Vents 1.gif

@TestyFish re-read my DMs with Fruit. I mixed up the naming, that should have been lastcollide, not nextdelay.

next delay - time in frames before a target can be hit again by the same attack or spell
last collide - should prevent a target from being hit repeatedly, but is bugged (vipers in nihl's temple, dark soul lightning, etc.)

According to Fruit's research a blizzard shard lives for 9 frames, but can damage only during 8. If two large monsters are close to each other and standing still a single shard will alternate between them every frame, hitting both 4 times before it expires.

Fissure has a next delay of 5 frames, but each vent also has last collide. Therefore the same bug applies which makes Fissure so strong against clustered monsters. Edit: next delay is still taken into account. Targets alternate every 6 frames unlike every other frame in the blizzard shards case.

Detailed explanation by onderduiker.

This info is great, and I love anyone who ever links to onderduiker's posts. They're fantastic, and you're fantastic.

Love the gifs.

How do the rows stack up against the size of the monsters? Are the rows big enough that a size 2 monster can stand between them and not get hit?
I always though this was the case as in PvP I have stood in a Blizz and not been hit. But then I may have been playing an assassin and claw blocked too.

My working assumption was that a 3x3 monster would just barely span the center of two lines of blizzard "y-rows." I think that Blizz drops across 5 total rows, but I honestly have zero proof for that. Here's my current list of questions:

1) What's the "cross section" of a blizzard shard AOE?
2) What's the actual spacing of y-rows of blizzard?
3) What's the "cross section" of a fissure vent AOE?
 

maxicek

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According to the AB Wiki (=onderduiker mainly) shards are size 2

AB Wiki said:
  • An ice shard falls every four frames (0.16 second) within radius of the target for duration of blizzard. Although this means each blizzard rains down 25 shards in a somewhat random pattern, when a stationary size 3 target is selected only 4 of these shards will normally hit it; when a stationary size 2 target is selected only 3 of these shards will normally hit it.
  • Shards are size 2, so a single shard can hit multiple targets.

But he doesn't mention the diagonal rows, so you are ahead there :)
 

TestyFish

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According to the AB Wiki (=onderduiker mainly) shards are size 2



But he doesn't mention the diagonal rows, so you are ahead there :)
I want to clarify the details of how "size" relates to "tile."
1) Is a size 1 item/chest/monster the smallest unit of measurement in the game? Can everything be matched to a grid?
1a) If I move my mouse to a different spot on the same size 1 tile, will the spell cast in the same location?
2) Does size 1 mean a square with a side length of 1 tile?
2a) Does size 2 mean a square with a size length of 2 tiles?
3) Are blizzard shards spaced 2 tiles apart on the "Y axis?" If so, does this mean that each blizzard shard (size 2 aoe) hits to one side of the row, but not the other?
3a) Does this mean that blizzard hits one row above or below the graphic, but not one row in the opposite direction?

Blizzard Size.png

Blizz Size 2.png

For instance, if a size 2 monster is in those locations...would it be hit by all the light yellow shard locations?

Does row 1 hit its own row, row -1 **and** row +1? Or does a size two projectile mean it hits its row, row +1, and **not** row -1?
 
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Jamie

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I haven't scrolled through yet, but from going to the standard 1.09 Frozen Orb and finally learning in 1.10 and on, I've found Blizzard is FAR superior or Frozen Orb. The range, intense damage, glacial spike and ice blast to aid and using a Might Merc to kill everything immune that you static and telekinesis the crap out of. I quickly learned a Blizzard Sorceress is by far the best "starting over character" to amass gear, moat Mephisto, etc and can run nearly every area of the game on Players 8, outside of The Pits, some A5 areas and Countess unless you want to get frustrated, but doable.

I've made probably 40-70 Blizzard Sorceress since 1.10 began. I can solo Baal on P8, Mephisto drops like a fly, Pindleskin runs are super fast and can pay off in quick succession(once found 2x CoA in 30 minutes on B.net during 1.10), I also run the Halls directly beneath Pindleskin and find it to be the most underrated area in the game. I have found unique Sacred Armors, my current Death's Fathom on my Blizz Sorc when I was still sporting Peasant Crown and half-ass gear, found my current Griffon's on my Javazon, tons of other nice uniques and rares and lots of socket bases there. You can also continue on to the next Halls and to Nithalaak if you want. AT is barely more difficult than running the Blood Moor and can drop tons and sports a golden chest, CS/Diablo is a little more difficult but doable. You can basically go anywhere in the game, even on Players 8 often, and have success with a Blizzard Sorceress that has a viable Might Merc with her. Bosses also drop like flies from Blizzard.

If you can't tell, I love Blizzard Sorceresses and through every ladder or single player restart, I start with a Blizzard Sorc 99% of the time. People like the Lightning Sorceress with an Infinity Merc, but give me Blizzard any day of the week. I know where to go with them and I don't need any extra areas like The Pits to make her an item finding Goddess.

Orb, on the other hand, has range issues and doesn't deal out the pure damage you can lay on large groups of enemies, supported with glacial spike crowd control and ice blast damage support. Orb needs practice with aiming and Blizzard seems to just drop monsters as soon as it falls from the sky. I know some people prefer Orb still, and I am sure it is more viable in a few situations (I have Orb now that I set my Sorceress up for LK Runs only, mainly to quickly throw a few when moving around with high FCR and because it allows me to mess with other skills like cheap teleport, warmth, telekinesis and others. But I cannot support Orb over Blizzard when actually fighting enemies and item hunting.

I think PvP would be the only place that Orb could be used to outplay certain characters, as opposed to blindly throwing Blizzards all over and hoping someone falls into one and dies from the quick damage blast. Orb seems more strategical and fun in the PvP arena, but it might not mathematically add up. It might just make it more exciting and fun, which is usually more my style anyway lol.

I hope the math supported my post I made without reading any of the numbers or replies :p
 

Klonki

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Interesting! i always used FO back in 1.09 until i realised blizzard was the big puncher,

but a sorceress with max FO is really something!