Elemental Spell Simulator for the Pit and Ancient Tunnels

Luhkoh

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LINK TO SHEET (must download to use)

Alright I'm pretty excited for this one. Buckle up for lots of discussion of results from this simulator in the posts following this one. Read at your own pace, because there will be a good bit to digest :D. This was a simulator I had in the back of my mind for quite a while, and as someone whose favorite character is the sorc, I'm very excited about the results. This simulator can be used for any spell which does cold, fire, lightning, magic, or physical damage, and isn't influenced by factors such as chance to hit, deadly strike, crushing blow, etc for all those melee considerations. So I will present some results and data for some sorceress spells (including blizzard, ice blast, fireball, nova, and lightning), but know that it could be used to simulate blessed hammer, bone spear, tornado, etc.

You can input your minus enemy res from conviction or lower res as well as any additional minus res you have, and you can choose a maximum enemy resistance beyond which the simulator ignores the enemy. For instance, I set my ancient tunnels fireball sorc simulator to ignore enemies with resistances (before conviction) of 100 or greater. So that no invaders or broken immunes were counted for that data.

Also I have the simulator set up to run only for monsters in AT and pits, but it could be adapted to work for any area. Would take about an hour or two to set it up for a new area. Would involve running my resistances calculator, and editing the monster mods in the simulator sheet.

There are some tools below the main input area to more easily compare relative adjeff's of different dmg and mf combinations. And below that there is a way to generate "batch results". Where you put in multiple values of spell dmg's and it will generate you a graph of how the casts per run changes based on dmg. This type of graph provides most of the results I will be discussing.

All the discussion following this post is for players1 mf running, as that is what I'm most interested in. However I did set up the simulator to work for other psettings as well. So if you want to see how much skills vs mf is worth it for a p5 nova sorc or something, that should be doable too.
 
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Luhkoh

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Simulator Result Discussion 1: Ancient Tunnels Blizzard Sorc

Conventional wisdom from the blizz sorc gurus like @Albatross tells us that somewhere around 5400 minimum blizzard dmg, there is a "breakpoint" hit, where stacking extra damage offers little return? Is this true? Yes!
jRHUrUR.png


Here is more zoomed in version of the same graph above. Note that the y axis is on a much smaller scale, so toward the right of the graph, very small improvements on shards/run are being made
Xagipsn.png

I was very impressed to see the clear damage falloff. Somewhere around the mid 5k's in minimum blizz dmg, more dmg offers very little. Next I simmed ice blast to see if it had similar breakpoints. It provided a much smoother dimishing return on dmg investment. So not quite as interesting as the blizzard graph.
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Luhkoh

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Simulator Result Discussion 2: Ancient Tunnels Fizz Sorc

I also used this simulator to generate some results on the fb/blizz sorc (fizz sorc) ancient tunnels runner that I am so fond of. What this cannot do is compare the spirit setup that I have mostly run to the phoenix setup that ffs theorycrafted and ran. Because the two setups kill invaders in different ways that are not captured by this simulator, and which is faster or preferred will just need to be tested. What we CAN do however is make some graphs of fireball dmg vs casts per run for each setup to see if there are any dmg "breakpoints" to shoot for.

In the past I've seen these breakpoints estimated by using minimum spell dmg and maximum monster hp, and I felt that left a lot to be desired. I expected the actual return on investment for dmg was a fairly smooth line, resulting in no real damage breakpoints. Well now we can calculate and optimize. Here are the damage graphs for the fizz sorc spirit setup and phoenix setup

Spirit setup
clvGmt1.png


Phoenix setup
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So we can see that at least in the practically achievable damage ranges, the return on investment is fairly linear. This leads me to conclude there are no real breakpoints to shoot for, though the beginnings of flatter portions on the graph may reasonably be thought of as good ranges to shoot for. However, with the sim, we don't have to guess. We can see the actual time theoretically saved per run from casting less fireballs, figure out how much time that saves, calc how much mf you lose to achieve that higher dmg, and see if it is worth it.

I tackled this issue, by using my latest spirit setup, which uses zero skillers and has 542 mf, and simmed adding one skiller at a time, going down by 21 mf each time a skiller is added. I know my rough runtime/efficiency for the zero skiller case, so I started there, and got the following results.
b7dBvKY.png

So we can see, adding skillers is not worth it. I did the same type of analysis on the phoenix setup and came to the same conclusion.
SIulfMP.png

That is good information to know in my opinion! What I have still not calc'd yet that I think is an interesting avenue of investigation, is whether dropping dmg even further to get more mf will be worth it. I ran some preliminary numbers on a 6ist CS setup, but am not sure exactly what mf I would end up with when I need to stack a lot more resistances on my charms and jewelry. But the results do look promising. To be tested/calc'd in the future :).
 
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Luhkoh

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Simulator Result Discussion 3: Pit Fova Sorc

Now onto a pits runner. This fireball/nova (fova) sorc is a character I haven't yet tested, but plan to in the future. The idea is the same as the fizz sorc: fireball what you can, use a backup spell on what you cant. But nova is thought be a bit better for cleaning up the devilkins than blizzard. And interestingly, since nova is a spammable spell, rather than blizzard where the shard hit at an unpredictable rate (not to mention wont be using static and fireball on the devilkins like one will likely do on invaders), this character is completely simmable.

So my thought was, that all sounds good, but how many points is optimal to put into lightning mastery? What is the best ratio of fireball dmg to nova dmg that we can get? I took my similar setup to the fizz sorc with spirit and hoto (or more likely eschutas in pits, but the minor increase in % lightning or fire dmg was not accounted for from eschutas), which has 12 plus skills, and I got to simming.

First I generated graphs of dmg vs casts per run for both fireballs on everything but devilkins, and for nova on devilkins only.
H3sKSwq.png

CAfVMvE.png

I then used macro that generated my maximum fireball dmg for various amounts of leftover points after putting points in lightning mastery at various amounts. Then the value of nova casts and fb casts per run was linearly interpolated from the graphs shown above, and the combination that resulted in the fewest total casts (which turned out to be 12 hard points into lightning mastery) was discovered.
wFtI49z.png


The only other question I had was whether phoenix is better than spirit. And unlike the fizz sorc, we CAN calc that here. And I figured since it was pits rather than AT, we only need to drop 2 skills to use phoenix (not so desperate as to use wizzy). I figured it was not worth it even so, as nova benefits more from the extra skills than blizzard does, and more importantly, you don't get the huge fireball dmg increase from not needing to put as many points in the backup spell's tree. Turns out my guess was correct and phoenix is worse from a pure casts per run standpoint, as judged from the higher value for "min casts" (but in a +10 skills phoenix setup, 11 hard points in mastery should be best).
v3oHEns.png
 
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Luhkoh

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Simulator Result Discussion 4: Pit Lightning and Nova

Ok last one (for now :p). The last few sims I ran were for a pure lightning and a pure nova sorc in pits. I did not do a detailed analysis of mf and dmg combinations, but just generated the dmg vs casts per run graphs to see if there was any interesting behavior or dmg breakpoints to shoot for. There weren't really on either. Both just had decreasing casts per run with diminishing returns. I may do a more detailed mf vs dmg analysis on them if I actually get around to running them, but more likely ill just stack 500ish mf and high dmg and run them. Had some issues with the nova sim though, which I will discuss below

Lightning Sorc
72CZ0Cv.png


Nova Sorc
ZUzPLWN.png

I put the nova graph in a spoiler because I'm not sure it's useful. It was generating extremely high casts per run when I simmed it without crescent moon. I looked at it and it was taking >30 casts to kill unmodified archers and other broken immunes. So I simmed it with crescent moon to get more fathomable casts per run. But they're still way too high I think. It obviously doesn't actually take this long to do the runs when @ffs is doing them quickly on p7 without crescent moon. You have any advice here @ffs? What am I missing? Is it static and merc that actually takes care of the archers and other broken LI's or what?

Anyways that's it for now. Much interesting things to learn and discuss from this sim. If anyone else uses it or finds something interesting, definitely post about it here! I may update in the future if I get any more interesting results, but that's it for now. Hope everyone is doing well! Cheers :coffee:.
 
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ffs

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Fantastic stuff. I do have spreadsheets for most classes/spells/builds by now, but actually simulating runs is really nice. Especially for hybrid builds it's tough to draw definite conclusions as to how approaches compare overall. Thanks a lot! Not really playing casters much atm, but I'm sure I'll have a look at this often.

Re broken LIs with Nova Sorc in the Pit, it's indeed mostly Merc and SF that make this work. Depends on damage of course but without SF, but it does take a lot of Nova casts to kill the boss. For example in case of my most recent Pit Nova setup, my spreadsheet spits out 24 casts for Dark Archer boss, this goes down to 11 after two SF casts and 8 for minions. But that doesn't slow you down as much as it may seem because you do have the Merc and SF after all, and when using both properly (read: spamming SF and teleporting the merc on the boss) they go down quickly. Merc will kill those guys extremely fast after SF, so doesn't really matter tbh. I have a few Nova Sorc vids on YouTube, but I guess you've seen them.

Re Blizzard Sorc it's worth mentioning that Cold Mastery level is an important factor regarding that "sweet spot" for Blizzard dmg. As in, 5.4k dmg with -160 ECR from CM and 5.4k dmg with -180 ECR are not the same. My go-to AT Blizzy uses 6-Ist sword with skillers in inventory, with 5.2-5.5k Blizzard range. With Fathom, displayed damage is higher ofc but CM level is lower, which affects dmg needed to kill bosses with certain modifiers, and in many scenarios in fact results in slightly worse performance. Here's the overview I put together some time ago (no detailed numbers, but Albatross' AT guide includes the related discussion).

Your sim considers all of that of course :) just saying one shouldn't solely focus on hitting a specific Blizzard dmg number, but take ECR into account as well.
 

Albatross

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Awesome stuff, thank you for your hard work on these. I've no doubt I'll be using the sims next time I'll be tweaking my sorcs.
 
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frozzzen

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This sure came long way from "Let's go to AT and see what we get!" we had 20 years ago. Great job on this one.
 
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Luhkoh

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@ffs nice, thanks for the feedback. As to the spreadsheets, one thing I'm trying to demonstrate is that non-simulator dmg "breakpoint" calculations can give misleading conclusions. For instance, I hope I've at least convinced you to drop the two skillers on the fizz sorc. Or how gripphon was pushing for various minimum damage values or chance to hit values on the pitzerker that make very little difference in practice. I did start some casual runs with your phoenix setup btw and like it a lot, so will likely be diving into that sorc again sometime when I'm not focused on my hdin.

With regard to blizzard, I actually did run a sim and dmg graph with more levels on CM thinking of your build, and the graph was visually identical so I didn't include it. Obviously more CM will only help, but it doesn't seem to affect the "breakpoint" substantially at all, and the shards per run are only changed marginally. Actually I'll just include one. Here's a graph for -180 CM. Again note that for blizzard specifically, casts per run is really shard hitting the enemy per run.
yogd3PE.png

I think I actually should have run the blizz sims for the conventional setup at -160 (9 plus skills), but oh well. Shouldn't make any difference at all. So it looks like at ~5500 minimum dmg the extra CM shaves off a tiny, but noticeable amount of shards per run, compared to the -155 case i ran originally (EDIT: I looked, at 5450 min dmg, its 13.92 shards/run for -160 CM, and 13.86 shards per run for -180 CM). You can see where I ended this sim at a higher dmg range that you start seeing returns again in the mid 6k's. Maybe you can leverage that without sacrificing too much mf on your enigma fathom setup? Anyways, I will be interested to see what you come up with if/when you revisit the blizzy and optimize the small details.

On nova sorc, makes sense ofc on static plus merc, I figured that had to be the case. Probably just should've run the sim ignoring broken immunes for better dmg vs mf data. I'm impressed that the static field plus merc stuff still keeps runs fast on p5 though. I have seen your video so i know they do, but if I had been just looking at the number here, I wouldn't have expected it.

@Albatross thanks a lot! I'm pleased enough by many of the practical takeaways I've already gotten, but if anyone actually uses the simulator or finds something interesting with it, I'll love that!

@frozzzen haha thanks a lot! All this calculating hasn't helped me compete with you or nagisa in AT... yet ;).
 
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