Bolt spell mana efficiency

[lordsmo]

Sometimes I bolt hunt for fun, but being a war mage I'm not too good leeching, so I decided to do a quantitative analysis of which bolt spell is the most mana efficient against each armor type. Other people have probably done this, but I couldn't find anything using the search function so I figured I'd post mine.

NOTES ON METHODOLOGY
The endrolls shown on the graph are calibrated to minor shock for ease of comparison. When doing the damage calculations for other spells the endrolls are adjusted to account for AvD differences. For example, for a given AS, DS, and d100, a 140 endroll against robes with 901 would have been a 135 endroll with 903, and a 145 endroll with 904. The damage values on the graphs are what would have occurred had the endrolls been adjusted in this manner.

Average total damage is calculated using raw damage plus average crit damage, taking critical randomization into account. Chest hits are assumed. For most crit tables hits to the chest, abdomen, and back have identical damage values, and these are also the three most likely targets to be hit.

COMMENTS
While 901 appears to be generally the most mana-efficient bolt spell, quantifying the mana-saving effects of death crits was beyond the scope of this analysis. Qualitatively speaking, the greater chance of death-critting afforded by more powerful spells increases their mana efficiency somewhat. Suffice it to say that if the damage/mana of two spells is close, the more powerful spell is probably the best choice.

As far as applicability is concerned, pure mana efficiency is not the only factor in spell selection (unless you are rapid firing). It is my hope that these results can be used, in conjunction with experimentation on specific creature vulnerabilities, to help strike an appropriate balance between mana-efficiency and killing quickly.

[Rimalon]

Very interesting. Thanks for sharing!

Dan and I were just talking about this the other day.

Would there be a way to adjust for DF inflation gained via lore training?

i.e does 901 still beat 906 if I have 252 ranks of Fire Lore via my enhancives?

[Izzy]

Cool info. However, I would argue that TIME efficiency is more important than MANA efficiency for a good majority of people. People don't want to cast 901 38 times per mob.

[lordsmo]

Cool info. However, I would argue that TIME efficiency is more important than MANA efficiency for a good majority of people. People don't want to cast 901 38 times per mob.

Like I said, pure mana efficiency is probably only important when you're young and short on mana, or if you're rapid firing.

For me, I was trying to decide whether 903 or 904 should be my go-to spell, and ended up getting carried away. At least now I know: 903 for robes, leather and brig, 904 for chain.

And although casting 510/910 against plate is a fairly obvious choice already, I was surprised to learn that none of the weaker spells (except 901) really exceeds their mana efficiency against plate either.

[lordsmo]

Very interesting. Thanks for sharing!

Dan and I were just talking about this the other day.

Would there be a way to adjust for DF inflation gained via lore training?

i.e does 901 still beat 906 if I have 252 ranks of Fire Lore via my enhancives?

I could add another line for 906 with maxed fire lore. The bonus caps at +0.075 at 100 ranks right?

I may not get around to it for a few days though.

[Celephais]

Like I said, pure mana efficiency is probably only important when you're young and short on mana, or if you're rapid firing.

For me, I was trying to decide whether 903 or 904 should be my go-to spell, and ended up getting carried away. At least now I know: 903 for robes, leather and brig, 904 for chain.

And although casting 510/910 against plate is a fairly obvious choice already, I was surprised to learn that none of the weaker spells (except 901) really exceeds their mana efficiency against plate either.

My goto was 904 over 903 ... 903 if you're fighting fire creatures, but the crits anecdotally seemed a lot better with 904 for most creatures, enough so to warrant the extra mana point.

[Celephais]

I could add another line for 906 with maxed fire lore. The bonus caps at +0.075 at 100 ranks right?

I may not get around to it for a few days though.

It's +0.001 per rank until 50, then +0.0005 per rank after. The lore chart didn't mention a cap, but I think 252 ranks = +0.151 DF

[droit]

It's +0.001 per rank until 50, then +0.0005 per rank after. The lore chart didn't mention a cap, but I think 252 ranks = +0.151 DF

Wow. That's actually a huge DF bonus. You're essentially adding an extra composite bow arrow shot (vs plate) to your bolts. Hell, a falchion only has a .175 vs plate.

[lordsmo]

It's +0.001 per rank until 50, then +0.0005 per rank after. The lore chart didn't mention a cap, but I think 252 ranks = +0.151 DF

The only information I have for this is from krakiipedia.

From the 906 page: "After the 50th rank, it increases by .0005 per rank until the 100th rank."

But from the fire lore page: "Training in Fire Lore increases the damage factor by .001 up to 50 ranks, whereupon it changes to a .0005 increase."

This leaves me unclear as to whether there is a cap or not. Does anyone know for certain?

[lordsmo]

My goto was 904 over 903 ... 903 if you're fighting fire creatures, but the crits anecdotally seemed a lot better with 904 for most creatures, enough so to warrant the extra mana point.

In terms of (raw damage + crit damage)/mana expended, 903 outperforms 904 against the lighter armors through most of the envelope.

However, getting a death crit can potentially save quite a bit of mana. For much of the envelope, it's close enough between 904 and 903 that an increased chance of death critting could easily tilt the scale. This effect is difficult to quantify.

Strangely enough, although 904 obviously generates a higher average crit rank, my own anecdotal experience has 903 producing a higher incidence of death crits. If true, this could only be due to the lower fatal threshold for head/neck impact crits, compared to acid. I'm sure I bolt much less than Celephais though, so his anecdotal experience should be given greater consideration than mine.

[droit]

Fatal crit thresholds for acid and impact:

Acid
Eye: 6
Eye: 6
Head: 6
Neck: 6
Abdomen: 8
Chest: 8
Back: 8

Impact
Eye: 7 or 8
Eye: 7 or 8
Head: 5
Neck: 5
Abdomen: 8
Chest: 9
Back: 8

Where did Dan post those body location hit frequencies? It should be pretty easy to figure out which has the highest fatality chance.

[TheLastShamurai]

Game Design Discussions - Research and Investigation

[lordsmo]

Fatal crit thresholds for acid and impact:

Acid
Eye: 6
Eye: 6
Head: 6
Neck: 6
Abdomen: 8
Chest: 8
Back: 8

Impact
Eye: 7 or 8
Eye: 7 or 8
Head: 5
Neck: 5
Abdomen: 8
Chest: 9
Back: 8

Where did Dan post those body location hit frequencies? It should be pretty easy to figure out which has the highest fatality chance.

Yeah I had access to those threshold values, but I couldn't find the target frequencies. I would guess that, all else equal, impact is more likely to get a fatal crit, but I'd rather quantify than guess if possible. Also, in the 903 vs. 904 debate all else isn't equal. 904 will generate higher average crit ranks throughout the endroll envelope.

If someone can post the target frequencies, figuring out which spell is most likely to generate a death crit will still be a fairly quick calculation, as droit says.

Comparing mana efficiency between 903 and 904 when adjusted for fatal crit frequency will be more difficult, as the mana saved by a fatal crit is dependent on target hitpoints. It's doable though. Maybe I could do a few graphs of "average required casts to kill vs. target hitpoints" for a few different endroll envelopes.

EDIT: "average required mana to kill vs. target hitpoints" might be more useful, now that I think of it.

[droit]

Okay, assuming that each hit has an equal chance of being anywhere from 0 to 9 crit ranks, here's what I've come up with (I'm sure there's a more mathematically elegant way to calculate this, but it's literally a back-of-the-envelope calculation). I just took the percent chance of a hit to each location being fatal and multiplied it by the percent chance of that body part getting hit, according to Dan's research. Then I added them up to get the percent chance that any given unaimed attack (i.e. a bolt) is fatal (assuming, again, that it could result in anywhere from 0 to 9 crit ranks).

Acid|Rank|% Fatal|Body Loc. %|Result
Eye|6|40|5.3|2.12
Head|6|40|5.2|2.08
Neck|6|40|7.4|2.96
Abdomen|8|20|12.1|2.42
Chest|8|20|14.7|2.94
Back|8|20|10.1|2.02
Total||||14.54


Impact|Rank|% Fatal|Body Loc. %|Result
Eye|7 or 8|30 or 20|5.3|1.59 or 1.06
Head|5|50|5.2|2.6
Neck|5|50|7.4|3.7
Abdomen|8|20|12.1|2.42
Chest|9|10|14.7|1.47
Back|8|20|10.1|2.02
Total||||13.8 or 13.27


Looks like acid has a slight edge over impact.

[lordsmo]

Okay, assuming that each hit has an equal chance of being anywhere from 0 to 9 crit ranks, here's what I've come up with (I'm sure there's a more mathematically elegant way to calculate this, but it's literally a back-of-the-envelope calculation). I just took the percent chance of a hit to each location being fatal and multiplied it by the percent chance of that body part getting hit, according to Dan's research. Then I added them up to get the percent chance that any given unaimed attack (i.e. a bolt) is fatal (assuming, again, that it could result in anywhere from 0 to 9 crit ranks).

Acid|Rank|% Fatal|Body Loc. %|Result
Eye|6|40|5.3|2.12
Head|6|40|5.2|2.08
Neck|6|40|7.4|2.96
Abdomen|8|20|12.1|2.42
Chest|8|20|14.7|2.94
Back|8|20|10.1|2.02
Total||||14.54


Impact|Rank|% Fatal|Body Loc. %|Result
Eye|7 or 8|30 or 20|5.3|1.59 or 1.06
Head|5|50|5.2|2.6
Neck|5|50|7.4|3.7
Abdomen|8|20|12.1|2.42
Chest|9|10|14.7|1.47
Back|8|20|10.1|2.02
Total||||13.8 or 13.27


Looks like acid has a slight edge over impact.

The only problem is that the high-end crits are less likely to occur than the mid-range ones. You need a high endroll and favorable crit randomization to get a rank 8 or 9 crit, but a high endroll alone is enough to guarantee a rank 5. Rank 5's could also be generated by a lower endroll with favorable crit randomization.

[lordsmo]

I'm getting started assuming that the combined target frequency for both eyes is 5.3% (i.e. left eye is 2.65%, right eye is 2.65%). If this is wrong, someone please let me know before I get too deep into this....

[droit]

I'm getting started assuming that the combined target frequency for both eyes is 5.3% (i.e. left eye is 2.65%, right eye is 2.65%). If this is wrong, someone please let me know before I get too deep into this....

That's correct.

[Riltus]

Fatal crit thresholds for acid and impact:

Acid
Eye: 6
Eye: 6
Head: 6
Neck: 6
Abdomen: 8
Chest: 8
Back: 8

Impact
Eye: 7 or 8
Eye: 7 or 8
Head: 5
Neck: 5
Abdomen: 8
Chest: 9
Back: 8

Where did Dan post those body location hit frequencies? It should be pretty easy to figure out which has the highest fatality chance.

The rank 7 (impact) eye crit is fatal. I finally found the elusive crit but forgot to post it on Krakiipedia. The messaging and damage I had listed for the rank 8 crit is actually rank 7. KP has been updated with the new rank 8 crit messaging.

Mark

[lordsmo]

I've plotted fatal crit probability vs. endroll for 903 and 904 against all armors. Endrolls are calibrated to 903's AvD. I may add the other spells at some point. I've included plate for completeness, even though neither of these spells can produce a fatal crit against plate in the endroll range examined (<400).

904 produces more fatal crits at comparable endrolls. What remains is to determine under what conditions this leads to better mana efficiency than 903.



This is not to say that the acid table by itself is more lethal than the impact table. For two bolt spells with identical DFs and AvDs, one using the acid table and the other using the impact table, the impact spell would have a higher incidence of fatal crits in the lower/middle portion of the endroll range, with the acid spell's fatal crit probability surpassing it once raw damage was sufficient to produce rank 8 crits. As for comparing acid flaring weapons vs. earth flaring weapons, we'd need to know the crit rank frequency for weapon flares, and I can't think of any way to get that, short of a massive amount of field research. My inclination is that the impact table would have a small edge in lethality, but I've already guessed wrong in this thread.

[Rimalon]

There is no cap to DF gain via lore.

Get to calculating!

[Askip]

I have been using 505 for my low-end and setup spell due to the stun. The damage is fairly decent too.

:D

[DaCapn]

I've plotted fatal crit probability vs. endroll for 903 and 904 against all armors. Endrolls are calibrated to 903's AvD. I may add the other spells at some point. I've included plate for completeness, even though neither of these spells can produce a fatal crit against plate in the endroll range examined (<400).

904 produces more fatal crits at comparable endrolls. What remains is to determine under what conditions this leads to better mana efficiency than 903.



This is not to say that the acid table by itself is more lethal than the impact table. For two bolt spells with identical DFs and AvDs, one using the acid table and the other using the impact table, the impact spell would have a higher incidence of fatal crits in the lower/middle portion of the endroll range, with the acid spell's fatal crit probability surpassing it once raw damage was sufficient to produce rank 8 crits. As for comparing acid flaring weapons vs. earth flaring weapons, we'd need to know the crit rank frequency for weapon flares, and I can't think of any way to get that, short of a massive amount of field research. My inclination is that the impact table would have a small edge in lethality, but I've already guessed wrong in this thread.

For your crit-kill probability, what body part are you shooting for? Or are you looking at some aggregate of all body parts?

[lordsmo]

Aggregate. The crit-kill probability for each endroll is the sum of the probabilities of each possible fatal outcome for that endroll.

For example, with a 180 endroll with 903 against robes, the max crit rank achievable is 7, so the fatal crits that are possible are rank 5 head/neck, rank 6 head/neck, rank 7 head/neck/eye. At this endroll crit ranks 4, 5, 6 and 7 each have probability 0.25, hitting the head has probability 0.052, so a rank 5 crit to the head has probability 0.25(0.052) = 0.013. Repeat for all fatal outcomes and add to get the crit-kill probability for that endroll.

At some point, maybe later this week, I'm gonna do "average mana expended per kill vs. target hitpoints" graphs that take crit-kills into account. Since the x-axis will be target hitpoints, I'm gonna do three graphs for each armor, using three different 100 point endroll spreads. I'm thinking 100-200, 150-250, and 200-300. Unless of course anyone has any suggestions for a better way to set it up. Also if you see anything wrong with what I've done so far, please let me know. Also, Rimalon, don't worry, I'll have at least one extra line on the graphs for 906 with fire lore.

[lordsmo]

Also, for anyone looking to duplicate these results, remember to adjust for AvD. Like for the 180 endroll point on the robes graph, the 904 crit-kill probability is calculated using an endroll of 190 to account for it's AvD advantage over 903.

[Daragon]

Also, for anyone looking to duplicate these results, remember to adjust for AvD. Like for the 180 endroll point on the robes graph, the 904 crit-kill probability is calculated using an endroll of 190 to account for it's AvD advantage over 903.

Hmm, I'm gonna say there are other things that go into bolts. Like something wearing plate armors, like, reivers are affected more by Electrical bolts. Orcs and Trolls, fire. Acid is more of a catch all, which I primarily use because I never had a problem critting with it. Water and Ice affect fire based critters more etc..
So really it also comes down to the type of creatures. This is why I never really looked at the numbers, because I don't believe the numbers are accurate because it is more then just the bolt, its also the creature and what they wear.

[Celephais]

Hmm, I'm gonna say there are other things that go into bolts. Like something wearing plate armors, like, reivers are affected more by Electrical bolts. Orcs and Trolls, fire. Acid is more of a catch all, which I primarily use because I never had a problem critting with it. Water and Ice affect fire based critters more etc..
So really it also comes down to the type of creatures. This is why I never really looked at the numbers, because I don't believe the numbers are accurate because it is more then just the bolt, its also the creature and what they wear.

/facepalm

Good point, nothing like facts and evidence to ruin perfectly good assumptions about how things work.

Most creatures do not have specific vulerabilities/resistances, and if you are fighting one that does, then it's pretty obvious how to address it. He's making multiple graphs for armor types, so what they wear is being accounted for.

Things that "wear plate armor and are affected more by Electrical bolts", are not. That's factored into the DF, which is exactly what this thread is using to produce info.

[phantasm]

So if I'm wearing double leather, critters can start getting crits at 180 end rolls, but in scale they gotta get 220 endrolls?

[Celephais]

So if I'm wearing double leather, critters can start getting crits at 180 end rolls, but in scale they gotta get 220 endrolls?

Death crits ... with these particular attacks.

[phantasm]

Yah no big deal, just 40 points of endroll death crit prevention.

[Celephais]

Yah no big deal, just 40 points of endroll death crit prevention.

It shouldn't be news to you that higher AGs provide vastly superior defense. From a mechanical perspective every person should be in the highest AsG they can without otherwise crippling themselves.

[Jace Solo]

Get'em

[droit]

It shouldn't be news to you that higher AGs provide vastly superior defense. From a mechanical perspective every person should be in the highest AsG they can without otherwise crippling themselves.

Fucking armor groups...how do they work?!?