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Let's talk about Effective Crit

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10 hours ago, Cysx said:

Wait, no, my argument never was that deathblow is indispensable, I was asking for a good reason to skip it. Though to be frank, guaranteeing kills on roughly half the maps, that doesn't sound awful, but then again, ch 20 has a lot of low def enemies.
 

23 hours ago, Owns said:

You're not factoring in all the extra Wexp you could be getting from class weapon proficiency being in the right class as opposed to sidetracking to Brigand for Deathblow. I don't think it'll make up the gap, but I wouldn't think it insignificant either, I don't have those numbers to crunch either way.

That's fair, though this is easy to calculate. It takes 50 rounds of combat to master Brigand, and Archer gets +2 bow exp per fight, so that amounts to a clean 100 Wexp loss. Added to the 180 *1.5(because boon) from earlier, that's 370 bow Wexp. Which isn't nothing, but still not that significant.
Also, crit builds usually don't need S+ rank in the first place, as they deal enough damage already. Well, if they have Deathblow, anyway, but foregoing a +6 damage boost for most of the game in order to get a +5 one at the end... that just doesn't make much sense. Which I wish I brought up earlier.

Fair enough, and you're right to point out that deathblow gives you an early +6 to +12 damage which is very valuable. Just to be clear though what I said was "i wouldn't go out of my way for it", which I admit is vague. I guess the way I see it is this: if a character doesn't have a boon in Axes, and I'm building them as an archer, there's no overlap whatsoever with axes. That means I need to spend time training axes and fighting as a Brigand (sacrificing +1 range of archer) for an ability that is useful but might not be that important. There's two things I usually consider with something like this: 1) What else could I be doing with  my time? 2) How many total skills do I want to train for that character's final build?

If I'm building someone as say a sniper or swordmaster (essentially a route that requires fewer weapons in its certifications) then I consider that a low investment character. Stick with Bows / Swords, Auth, done. This means I can spend more time on other characters and that's valuable. Someone training to be a warmaster on the other hand needs an A in both Axes and Brawling, on top of Auth, and might want to pickup Heavy Armor for Armored Blow as well, or a Weight -3. So being able to train one character less, means I can train someone else more. Similarly if I'm going Bow Knight or any riding class really, you need the main weapon at A, Riding at A (eventually), Auth, and lances at C. (I usually shoot for at least B Auth on all characters, with maybe a few reaching A and a couple remaining on C). This is not to mention that by training others less (in other words spending less activity points or money to boost their motivation, means I can train Byleth more as well).

Edit: Admittedly my "crit build" characters do tend to fall off in the early-mid game before become useful again once their crit improves with Killer weapons and stats. So it helps if they have support skills too for that period of very low damage.

That about sums up how I look at things, I might be exaggerating how much investment getting actually Deathblow is, admittedly it isn't a whole lot but still getting it on every physical unit is not only a pain to me, is also unnecessary. If I'm sticking with Sniper, that's a very low investment build, I guess might as well pick it up (especially on someone like Ashe who has a boon in Axes), but then again maybe I won't (just so I can reduce that character's training) and they'll still be useful.

10 hours ago, Cysx said:

but in my head a 50% chance to crit 5 times amounts to 2.5 crits, not 3.

Not sure what you're doing here but the way I calculated it is following the probability of getting "at least" X number of crits out of 5 total attempts. This is very different from asking for example 3 crits in a row (which for a 50% chance would be 0.5^3 = 12.5%), actually this is the calculation for getting all 5 hits to crit. I do appreciate people checking my math as I'm not particularly great at it either and am prone to errors so if anyone spots anything or is able to check my work then by all means let me know.

And yes, as @haarhaarhaar also pointed out, you have to actually Hit first before Critical Hit is even considered. Everything above assumes a Hit of 100. While this is unreasonable for sure, having a variable Hit analysis would 1) be a nightmare, 2) not too relevant from the point of view of comparison anyway since Hit always applies whether you're considering Crit or not. There is a point to be made that Astra does have a -10 Hit which is bad though.

Surely there's a lot that can be criticized and debated about my analysis and thoughts, the least of which is that I randomly picked Ignatz and GD Ch. 20 enemy units as my sample case and the results might be very different on another map or character. I'd say the most takeaways are probably the Effective Crit graphs (ie the first one in OP) and the Astra chance to crit graph too since they can be used as a reference. And then also, I hope that by exploring the mechanics of how these probabilities work, it shows that crits can be a lot better than they look based on the displayed Crit since that doesn't factor in the number of hits you will be dealing in attack (what I call effective crit).

10 hours ago, haarhaarhaar said:

Isn't there only one Cursed Ashiya Sword available per run?

Oh you're right, I thought i remembered having 2 in my last run, but that must've been the 2 dropped Wo Daos. My bad.

10 hours ago, haarhaarhaar said:

Another potential solution to the lack of late-game killing power is to try and find a better unit for this build - Felix is an obvious candidate, and will have better Dex/Luck than Catherine, but I doubt it would be enough to make a real difference. The only people I can think of who might really make a difference would be Ingrid and Sylvain, whose Crests have 40% percent activation rate to raise CA Mt by 5 (which means you can probably rely on them triggering twice per Astra). Ingrid in particular will need Strength help to be of real use, but it's not impossible to achieve.

These are interesting considerations. For what it's worth, if I simply change the average stats calculator to Felix, he'd have 9 more str than Ignatz at lv 35, which is huge, similar if you do this with Byleth. Doesn't Felix's crest also activate with combat arts? I thought that was the case.

And yes, Astra Lethality would be an interesting gamble to use, a 1/4 to 1/3 chance when using Astra isn't so bad tbh. If I didn't expect to get the kill any other way, I'd probably attempt Astra with a training sword and just test my luck with Lethality (assuming I can survive a counter or have good chances to evade, there's always divine pulse to fall back on too).

Edited by Owns

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Hey, first of all let me just say that this is an interesting topic and I’ll be reading through it all later.

15 minutes ago, Owns said:

This means I can spend more time on other characters and that's valuable.

Or being able to go out of your way with this characters build. It’s easier for lower investment characters to go out of their way for skills like Death Blow or Hit+20. If you give them the same amount of investment as a higher investment character, then the lower investment character can get extra skills or higher ranks in their primary skills. It just depends on what you want.

18 minutes ago, Owns said:

the way I calculated it is following the probability of getting "at least" X number of crits out of 5 total attempts.

I don’t have a graph for it but I do have excel file that calculates the chance of Astra killing an enemy compared to other options, if you’re interested. All I need to do is input the enemy’s HP, and your unit’s damage and Hit and Crit rates against them.

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44 minutes ago, Whisky said:

Or being able to go out of your way with this characters build. It’s easier for lower investment characters to go out of their way for skills like Death Blow or Hit+20.

Sure. This is a fair point, it's just a choice in the end, that might be very important sometimes, less so others. I just don't think that "Get Deathblow on every physical character" should be the requirement it's made out to be. Not only do I find that bland, like I showed earlier with the Ignatz example, in some cases it doesn't even make a difference. Edit: Although, it is a good rule of thumb as general advice, I'll give it that much.

Quote

I don’t have a graph for it but I do have excel file that calculates the chance of Astra killing an enemy compared to other options, if you’re interested. All I need to do is input the enemy’s HP, and your unit’s damage and Hit and Crit rates against them.

If you want to, and you're sure you know what you're doing, then sure.

6 hours ago, Cysx said:

That's fair, though this is easy to calculate. It takes 50 rounds of combat to master Brigand, and Archer gets +2 bow exp per fight, so that amounts to a clean 100 Wexp loss. Added to the 180 *1.5(because boon) from earlier, that's 370 bow Wexp. Which isn't nothing, but still not that significant.
Also, crit builds usually don't need S+ rank in the first place, as they deal enough damage already. Well, if they have Deathblow, anyway, but foregoing a +6 damage boost for most of the game in order to get a +5 one at the end... that just doesn't make much sense. Which I wish I brought up earlier.

Oh and I forgot to thank you for these numbers. 370 Wexp, isn't a whole lot sure, but it is 1/3 of the way from S to S+ rank. What would that mean, maybe getting S+ a whole month earlier, or is that too big of a stretch? Not to mention it's that much progress towards whatever your next rank at the time was, depending on the build/character you're pursuing that can be important. Take my Leonie for example, reaching rank A gets her PBV for x2 damage, delaying that by 1-2 months for Deathblow? Admittedly, I'm finding that occasions where she's just 3 or 5 damage shy of a ORKO without Deathblow, so one could argue that it is worth it. So I got to ORKO some enemies sooner, in exchange for not being able to ORKO as many enemies later. Alternatively, a couple of str boosters could also fix this, and it isn't like she isn't ORKO'ing a decent number of enemies without. In the end, I don't see ORKO as the be all and end all anyway, and am fine with not always getting kills, others might be a bit more demanding in that sense and that's okay. It's a preference.

Edited by Owns

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31 minutes ago, Owns said:

If you want to, and you're sure you know what you're doing, then sure.

If I want to do what? I’m just saying that if you give me a scenario that includes Enemy HP, your unit’s damage, Hit and Crit rates I can tell you the exact chance of Astra killing the enemy and compare that to the chance of killing the enemy with other options.

I don’t know know how to share the file. Can files be attached on here? If I was going to share the file I’d have to update it to make sure it’s easy to use first. I know how to use it because I made it but it might not be user friendly yet.

As for knowing what I’m doing. I just cross multiplied binomial distribution tables for Hit and Crit rates. It’s accurate as long as there aren’t other factors like Crests or something.

If you do want me to send you the file, then give me some time to fix it up and make it easy to use and understand and then I’ll send to you. I’d be happy to help however I can, especially since I already put in the work of making the file and don’t want it to go to waste lol. It can’t really be made into a graph because there are too many variables.

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2 hours ago, Owns said:

Death blow

Brigand doesn't have range +1, but it does has a +2 str mod. That's also why people don't mind spending time in it.
Beyond that, I'm not going to tell you how you should play the game(or at least not that directly, I like to hide that I'm actually a douche). It's more when it comes to a general discussion about how things work, that I couldn't really give you that it's cool to skip Deathblow. It's one of the best skills in the game for a very reasonable amount of investment, I mean it when I say it's pretty much universally expected for physical units to go for it. Does that make the earlygame a bit dull, arguably, yeah. Since people can use any weapon they want still, it's usually fine, though.
Going back to your table, Ignatz does also have:
+1 base strength if he went through brigand
A Raphael damage support for +3
Hilda's passive to take advantage of, since he has flexible range; obviously that's if she's around
Technically, access to the Failnaught on routes where it's available.

So he can get by. It's just that the next two chapters get rough... and that not everyone is Ignatz.

2 hours ago, Owns said:

Not sure what you're doing here but the way I calculated it is following the probability of getting "at least" X number of crits out of 5 total attempts. This is very different from asking for example 3 crits in a row (which for a 50% chance would be 0.5^3 = 12.5%), actually this is the calculation for getting all 5 hits to crit. I do appreciate people checking my math as I'm not particularly great at it either and am prone to errors so if anyone spots anything or is able to check my work then by all means let me know.

Honestly, I wish I could demonstrate but I kinda can't. In my head, if you have precisely a 1/2 chance for something to happen, on average it will happen half of the time, and in that case, half of 5 is 2.5. Maybe you took 3 as the center value as a result of it being precisely the middle between 1 and 5... but there's also 0 to consider? Idk.

2 hours ago, Owns said:

While this is unreasonable for sure, having a variable Hit analysis would 1) be a nightmare, 2) not too relevant from the point of view of comparison anyway since Hit always applies whether you're considering Crit or not.

It's not impossible to have near perfect hit rates and it's 2 rn, so it doesn't always have to be a problem really... but yeah this would take a ton of work for sure.
 

2 hours ago, Owns said:

Surely there's a lot that can be criticized and debated about my analysis and thoughts, the least of which is that I randomly picked Ignatz and GD Ch. 20 enemy units as my sample case and the results might be very different on another map or character. I'd say the most takeaways are probably the Effective Crit graphs (ie the first one in OP) and the Astra chance to crit graph too since they can be used as a reference. And then also, I hope that by exploring the mechanics of how these probabilities work, it shows that crits can be a lot better than they look based on the displayed Crit since that doesn't factor in the number of hits you will be dealing in attack (what I call effective crit).

I mean, being a critic is the easier route, that's no secret. You put in the work and there's no taking that away, and yes, I'd definitely say those are valuable resources.

2 hours ago, Owns said:

Doesn't Felix's crest also activate with combat arts? I thought that was the case.

Nope. That's a common question since the in-game description is unclear, but it doesn't.

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Edits
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1 hour ago, Owns said:

Oh and I forgot to thank you for these numbers. 370 Wexp, isn't a whole lot sure, but it is 1/3 of the way from S to S+ rank. What would that mean, maybe getting S+ a whole month earlier, or is that too big of a stretch? Not to mention it's that much progress towards whatever your next rank at the time was, depending on the build/character you're pursuing that can be important. Take my Leonie for example, reaching rank A gets her PBV for x2 damage, delaying that by 1-2 months for Deathblow? Admittedly, I'm finding that occasions where she's just 3 or 5 damage shy of a ORKO without Deathblow, so one could argue that it is worth it. So I got to ORKO some enemies sooner, in exchange for not being able to ORKO as many enemies later. Alternatively, a couple of str boosters could also fix this, and it isn't like she isn't ORKO'ing a decent number of enemies without. In the end, I don't see ORKO as the be all and end all anyway, and am fine with not always getting kills, others might be a bit more demanding in that sense and that's okay. It's a preference.

But again, why would you want S+ rank if you don't want Death blow?

Also, do you really make such a difference between Deathblow HV Ignatz, which you don't care much for, and Deathblow-less PBV Leonie, which you're defending? I just don't get your reasoning on that. But yes, as you said, Leonie's primary role is killing with PBV, so Deathblow solidifying that makes it an acceptable detour in general; you're also on a class with bowfaire, many people put her on a wyvern instead to get flight, which has a bit less damage and makes going through brigand a more... natural part of her growth. Either way, obviously one'd need to math it out(which is not my way of asking you to do it, please don't bother), but Im all but convinced that early PBV doesn't beat what Deathblow brings. For what it's worth.
Finally, it's... it's not really a matter of preference(sorry, this is going to sound patronizing), I mean as I said, absolutely play however you like and screw me if I ever tell you not to. But the ability to kill more, it isn't advantageous in a subjective way; if one unit can kill more than another, and there's no other difference... the first one is better. This is true in easy FE games, but even more so in a context where not killing can easily mean dying.

As for boosters, from my understanding we typically ignore them because it can't be assumed that any given unit will get them(outside of cases like Conquest!Xander or early FE5 Leif) and it's a genuine advantage not to need them in the first place; regardless of that, they do exist. If I'm not mistaken, people primarily fix the speed of a lot of characters so they remain competitive, and focus on maxing out the strength of one or two key units to take care of problematic enemies(such as endgame bosses), rather than spread them around.
But full disclosure, I wouldn't know, I don't use them.

Edited by Cysx

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3 hours ago, Whisky said:

If I want to do what? I’m just saying that if you give me a scenario that includes Enemy HP, your unit’s damage, Hit and Crit rates I can tell you the exact chance of Astra killing the enemy and compare that to the chance of killing the enemy with other options.

Oh, I misunderstood what you mean, sorry. That's pretty neat actually and I've been working on something similar myself actually, a battle predictor basically. One that's user friendly and can automatically get stats of enemies, weapons, equipment, etc. that one would select from a drop down menu. I'm hoping to share at least a working version soon even if incomplete to see if anyone wanted to help populate the statistics to be used (mainly enemy stats). Anyway, yes, I'd like to see your sheet. that would be helpful both to test out some stuff with Astra but also to maybe get some ideas / formulae from your sheet if you don't mind (I'd definitely credit you). Could you share it as a google sheet link? Edit: Heck depending on how your sheet is currently designed, I might even be able to use it as the basis and just make an UI sheet to go with it.

3 hours ago, Cysx said:

Honestly, I wish I could demonstrate but I kinda can't. In my head, if you have precisely a 1/2 chance for something to happen, on average it will happen half of the time, and in that case, half of 5 is 2.5. Maybe you took 3 as the center value as a result of it being precisely the middle between 1 and 5... but there's also 0 to consider? Idk.

I'm no expert but my best explanation is that while you're not wrong by looking at it this way, you're also not asking the same question I am. I think the way I did it is more accurate though (or at least more meaningful) and here's why: Sure, on average you expect 2.5 crits, but there's no half crits so what do you do with the 0.5, round up or down? (I don't think there's a correct answer by the way). The calculation I did asks a more specific question, ie. odds of getting at least X crits, the "at least" part is important here. So if X is 3, that includes the odds of getting 4 or 5 crits (small as they might be, still a possibility) as well as the odds of getting 3 crits, and that's probably why 50% lies higher than at 2.5 crits.

Edit: I didn't take any "center value" here, I just calculated the odds and the plot is what came up. Edit2: I do consider the odds of getting 0 crits in the calculation, it would be wrong otherwise. Anyway the 0 crit case is basically 1-P(at least 1), which would just look like the curve of P(at least 1) flipped upside down.

3 hours ago, Cysx said:

But again, why would you want S+ rank if you don't want Death blow?

Well there are significant enemy stat spikes in the end game, so there's that.

3 hours ago, Cysx said:

Finally, it's... it's not really a matter of preference(sorry, this is going to sound patronizing), I mean as I said, absolutely play however you like and screw me if I ever tell you not to. But the ability to kill more, it isn't advantageous in a subjective way; if one unit can kill more than another, and there's no other difference... the first one is better. This is true in easy FE games, but even more so in a context where not killing can easily mean dying.

Okay, I admit there is an objective claim to be made about whether getting Deathblow is better or not, beyond it being a matter of preference. And again, I agree that generally speaking Deathblow is desirable. I guess the way I'm thinking is like this, if someone asks "Should I get Deathblow on a physical character?", to which I'd comfortably answer yes. Then a follow-up question, "Okay but do I really have to?" and it's this question that I'm exploring and trying to see in which cases will it make a huge difference versus others where maybe not so much. I don't have a concrete answer by the way, and frankly if I had to bet on it, I'd say you're right. I'm probably just being a bit hard-headed, I have a bad habit of learning things the hard way.

Edited by Owns

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43 minutes ago, Owns said:

I'm no expert but my best explanation is that while you're not wrong by looking at it this way, you're also not asking the same question I am. I think the way I did it is more accurate though and here's why: Sure, on average you expect 2.5 crits, but there's no half crits so what do you do with the 0.5, round up or down? (I don't think there's a correct answer by the way). The calculation I did asks a more specific question, ie. odds of getting at least X crits, the "at least" part is important here. So if X is 3, that includes the odds of getting 4 or 5 crits (small as they might be, still a possibility) as well as the odds of getting 3 crits, and that's probably why 50% lies at "at least" 3 crits as opposed to 2.5 crits.

Alternative way to look at the maths: if it's 50% chance to crit, that means that crit and not-crit have the same probability. So, the chance to get 5 crits is the same as the chance to get 5 not-crits, so the same as 0 crits. Similarly, the chance at 4 crits is the same as 1 crit and the chance of 3 crits is the same as 2 crits. Everything is symmetric. So, the chance to get 0, 1, or 2 crits is the same as the chance to get 3, 4, or 5 crits. So, exactly 50% chance of getting 3 or more crits.

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4 hours ago, Owns said:

2) not too relevant from the point of view of comparison anyway since Hit always applies whether you're considering Crit or not. There is a point to be made that Astra does have a -10 Hit which is bad though.

I get what you're trying to say; physical avoid can get a bit ridiculous with some Maddening enemies, and crit builds will always be in a bit more danger than normal OHKO builds with high-avo enemies, that's just inevitable. But it's relevant at least for your comparison with HV (which suffers no hit penalty from 2 spaces, but the CA itself gives a hit and crit boost). 

It also means the likes of Ignatz will be (somewhat) more reliably critting compared to Catherine/Felix, especially against Swordmasters/Falcon Knights and the like. Since you don't really want to spend a skill slot or change battalion to something which lowers your crit, this is a relatively serious issue which has to be addressed from the beginning - whether to prioritise damage or accuracy when setting up this build.

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1 hour ago, Owns said:

Well there are significant enemy stat spikes in the end game, so there's that.

Weaponfaire gives +5 damage from weapon.

Death Blow gives +6 damage, when initiating, with a physical weapon.

If you're talking player-phase damage with a physical weapon, then Death Blow is always doing more for you than Weaponfaire. Plus, you can access Death Blow much earlier, so it's helping you for more of the game.

An Iron Bow with Death Blow does the same damage per-strike as a Silver Bow without.

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Extra considerations for Astra (very important). TL;DR; As a Sword Master, it's practically almost always better to choose a regular double attack over Astra, with 1 (potentially rare?) exception.

Now that we've looked at how Astra works, and it's damage compared to single hits, the question remains, what about double hits? Sword Masters are pretty fast after all and will be able to double a lot of enemies. Well, double attacks can deal x4 damage if one of them crits (which Astra only beats if all 5 hits are crits), and x6 damage if both hits happen to crit which is more than Astra's maximum damage. It seems obvious then that a normal double attack should be favorable over Astra, but let's look at the odds and damage values together on 1 plot to see:

Astra-v-x2Hits.jpg.8985332d3ea32fac02146dea706d40d1.jpg

Okay so in terms of reliability, we want the "highest" curves, of which in order are Astra's at least 1 crit, Astra's at least 2 crits, followed by Double Hits (at least 1 crit). Since the only way to deal more damage than Double Hits (at least 1 crit) is to get Astra's all 5 crits, but that line is never higher, then that automatically takes out of consideration P(at least 3), P(at least 4), and P(at least 5). In fact even getting 2 of 2 crits with Double Hits for x6 damage, always has better odds than Astra's (all 5 crits). What remains is just the "highest" 3 curves. Among those curves, Astra (at least 1 crit) at only x2.1 damage practically deals the same amount of damage as a double hit with 0 crits, so let's forget about that.

Now we're only left with 2 options to choose from, do we prefer the odds of Astra (at least 2 crits) over the odds of Double hits (at least 1 crit)? Between these two, Astra is more reliable when crit >35 (which should practically always be the case) so one could argue to go with Astra in that case. But what are we really gaining? x2.7 damage vs x2.0 damage if you fail to crit with a normal Double Attack at the cost of an extra 7 durability. IMO this gain is not worth it for the cost, especially since the actual difference is pretty small between the odds of getting x2.7 dmg with Astra versus x4 damage with a normal double attack. With Double Hits (at least 1 crit) you have an effective crit >90 when displayed crit is >68. The only time I think it might actually be worth preferring Astra over a regular double attack is if the following are all true: 1) my displayed crit is <75, ie Double Hits (at least 1 crit) is less than 95% chance. 2) Astra's P(at least 2) (ie x2.7 damage) deals enough damage to get the kill, and 3) It is crucial to get this kill with this attack (ie. it's life or death). Any other time, I'm going with a regular double attack over Astra. Not to mention that Astra also has -10 Hit penalty to consider.

Edit: Okay, I overlooked one important point which is that you have to take a counter when going with Double Hits. This could get you killed for sure, so it's something to consider as well. How good is your evade? Will the enemy OHKO you? Etc. Ultimately this still falls under the 3rd condition above though, that "3) It is crucial to get this kill with this attack". If you can use Battalion Desperation (or even Desperation technically, but how/why), then you might not have to worry about this in the first place.

This might sound like it makes Astra look worse, but I don't think that's the case, in fact this just makes Sword Master look better since it gives you more good options. Meaning, since it's easy to reach high Crit values with sword master, you can relatively easily get x4 damage and to a lesser extent, x6 damage through double attacks (higher than what you're getting with Astra). While Astra is there to boost your damage to x3.3 up to x4.5 damage when you otherwise could've only got x1 or x3 damage with a single attack.

Side note: It's pretty late, apologies if I'm not responding to previous comments at the moment but I'll get to them.

Edited by Owns
Modified conditions when I'd favor Astra over x2 hits.

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7 hours ago, Owns said:

Now we're only left with 2 options to choose from, do we prefer the odds of Astra (at least 2 crits) over the odds of Double hits (at least 1 crit)?

TL;DR doubling doesn't happen often on Maddening, and hit rates need to be taken into account more. As a result, Astra is still a useful option.

(Skip to the bottom for conclusions)

Firstly, it's worth bearing in mind that without significant stat boosting or a brave weapon, your sword master is at most going to double 1/3 of enemies in a given map in the 2nd half of Part 2. And doubling becomes really hard to do for a lot of enemies the closer and closer you get to the end of the game (even enemy Warlocks need 39 AS to be doubled in VW endgame, which is about the highest AS I could expect from anyone in normal circumstances). Which helps the case of Astra, anyway.

Doubling with high-crit weapons may not always be possible, but you can always double with a brave weapon. Stacking crit for a brave weapon user does sound like a great idea (even if Brave Sword has weight and maintenance issues). Any sword user can get to 45 base crit with a good set-up (and Brave Sword) from Ch. 14, with that number climbing to up to potentially the low 60s by the end of the game. Enemy luck doesn't regularly or significantly break 20, except for Gronder (lots of named characters with luck reaching 30+) and endgames (18-28 for almost all enemies in AM endgame, but 28-33 for grunts in SS endgame, the Elites/Nemesis get late 30s to early 40s, Rhea can get above 50). Prowess crit avo is also a thing, meaning you can only assume about 20 displayed crit with a Brave Sword for most of Part 2. 

We also need to remember that hit plays a part in these discussions. Brave Sword+ has 85 hit, CAS+ has 70, and Wo Dao+ has 90. Given Goneril/Leicester battalions, a sword master will probably hit Ch 14 with around 45 base Hit, climbing up to 55 Hit by endgame. By the time they get Astra (around Ch 17 at the earliest) they'll have about 50 Hit. That's pretty good odds for hitting with a Brave Sword (it'll only start struggling against units with 55+ Avo, but a fair few of those do crop up even from Ch. 17) and Wo Dao+ is a bit better for normal attacks. That changes a bit with Astra. With 80 displayed Astra hit there's a 67% chance of hitting 5 times - not bad, but a little iffy. However, you aren't often going to get 80 displayed hit with CAS+ Astra, as the average enemy's Avo climbs above 30 before Ch. 17. Wo Dao+ will regularly dip into the 65-75 hit range as the game progresses, and CAS+ will fall below 60 displayed hit well before endgame. 

With all that in mind, here's some numbers against an enemy with 55 Avo:

Brave Sword+ with 80 displayed hit, 20 crit: 33% chance of at least 1 crit, 3% chance of 2 crits.

Wo Dao+ (normal) with 85 displayed hit, 60 crit: 57% chance of 1 crit if hitting once. 82% chance of at least 1 crit if hitting twice, 33% chance of 2 crits if hitting twice.

CAS+ (normal) with 65 displayed hit, 70 crit: 53% chance of 1 crit if hitting once. 78% chance of at least 1 crit if hitting twice, 28% chance of 2 crits if hitting twice.

Wo Dao+ (Astra) with 75 displayed hit, 60 crit: 78% chance of 3 crits, 4% chance of 5 crits.

CAS+ (Astra) with 55 displayed hit, 70 crit: 66% chance of 3 crits, 1% chance of 5 crits.

As you can see, the 'best damage' scenario is a toss-up between doubling with Wo Dao+ and CAS+. CAS+ is more powerful and can get kills that Wo Dao+ might not, but the more reliable 4*damage for Wo Dao+, especially running Death Blow etc, will be enough damage to kill things that aren't axe infantry... in theory.

The big problem is that you'll almost never double anybody with 55 Avo. Hell, on average you'll need 35+ AS to double anyone with 40 Avo, and there are lots of those units before Ch. 20 (Ch. 19 is the earliest I could even imagine reaching 35 AS, even with Wo Dao+). In general, mages are the only units with decent avo who are potentially slow enough to get doubled by your swordmaster (and even then they remain competitive, expecting at least 35-6 AS and with 40+ Avo by endgame, and not significantly slower before). 

It's also worth saying that Brave Sword+ is still very competitive - you have a 33% chance of dealing 4*damage, which is better odds than trying to deal the same kind of damage on the same enemy with Wo Dao+ Astra. 4*damage with a Brave Sword+ will also exceed 3.3*damage from CAS+ as well. Brave Sword+ 4*damage won't exceed CAS+ 3.9*damage, but CAS+ is only 9% likely to get 4 crits with the above numbers. So if you need 4*damage in the above scenario, Brave Sword+ has the highest odds of getting it (though those odds still aren't very high). 

Brave Sword+ might come out better in the above, but you can do other things (adjutants/linked attacks/gambiting enemies) to increase your hit rates and thus odds of CAS+ success, while there are no ways outside of your normal set-up (except triggering a personal like Petra's) to increase crit rates for a Brave Sword. If you can increase CAS+ hit rates to 100 TH (which often means adjutant and 3 linked attacks), then you have 36% chance of CAS+ 3.9*damage, and still a 36% likelihood of Brave Sword+ 4*damage with 100 TH. CAS+ 3.9*damage should normally be 11-12 more damage than Brave Sword+ 4*damage, so CAS+ Astra is now the better choice.

Conclusions

Astra is a more reliable way of reaching 3*damage on a weapon than a single attack. 

Doubling is the best choice where you can get it/assuming you can survive the counter, but not common enough to be expected.

CAS+ Astra is the best combination listed here of reliable and powerful damage on Maddening.

If a normal crit isn't able to kill, and you can't engineer 99+ TH, then a Brave Sword+ on a crit build Swordmaster has more solid odds of dealing high damage than Astra.

 

Also, side question: Does Hilda's personal/Sacred Power etc stack its damage boosts onto individual Astra attacks, or just onto the total damage number that gets fed into the Astra calculations? If the former, then having those skills handy would be great for Astra (and it adds credence to the idea of Sylvain doing this), but if the latter, then you'd have to set up multiple skills of this kind to see even small effects.

Edited by haarhaarhaar

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17 hours ago, Owns said:

Oh, I misunderstood what you mean, sorry. That's pretty neat actually and I've been working on something similar myself actually, a battle predictor basically. One that's user friendly and can automatically get stats of enemies, weapons, equipment, etc. that one would select from a drop down menu. I'm hoping to share at least a working version soon even if incomplete to see if anyone wanted to help populate the statistics to be used (mainly enemy stats). Anyway, yes, I'd like to see your sheet. that would be helpful both to test out some stuff with Astra but also to maybe get some ideas / formulae from your sheet if you don't mind (I'd definitely credit you). Could you share it as a google sheet link? Edit: Heck depending on how your sheet is currently designed, I might even be able to use it as the basis and just make an UI sheet to go with it.

Oh wow, that sounds pretty cool, though a lot of work to collect all of the data on the enemies. I’ll try to send you the file I have after I get off of work. It would be cool to add a drop down bar for different weapons and combat arts in order for easy comparisons between them.

-

To comment on the above analysis of Astra vs double attacks. Double attacking is almost always better than Astra if you are using the same weapons and if you are able to double, which is of course hard to do on Maddening. Astra can be more effective than a Brave Sword if you use it with a Wo Dao or a CAS but you have to consider that you will be using about half of the weapon’s durability with each use of Astra. The Rapier+ can be pretty good with Astra as well, especially when it’s effective, but even if it’s not, it has a lot more durability than those other options and still has a decent Crit boost and high accuracy.

But while Astra can be useful for a Swordmaster, I have to ask, why make the character a Swordmaster in the first place? There is a guaranteed way to always double every enemy with a Killer weapon; Hunter’s Volley. Hunter’s Volley is more effective than Astra in almost every situation and can be used at range and costs less durability. There’s also Fierce Iron Fist and Swift Strikes.

Another thing to consider with Astra is that if you use it with Seteth, or to a lesser extent Ferdinand, it will have a pretty high chance to prevent the enemy’s counter attack. 

Edited by Whisky

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1 hour ago, Whisky said:

But while Astra can be useful for a Swordmaster, I have to ask, why make the character a Swordmaster in the first place? There is a guaranteed way to always double every enemy with a Killer weapon; Hunter’s Volley. Hunter’s Volley is more effective than Astra in almost every situation and can be used at range and costs less durability. There’s also Fierce Iron Fist and Swift Strikes.

I mean yeah, HV and other brave arts just are better, and Sniper in general is more optimal than Swordmaster. I think the point of the thread, or at least the OP, is to attempt to find the good in other, overlooked Crit builds, particularly Astra Swordmaster. 

1 hour ago, Whisky said:

Another thing to consider with Astra is that if you use it with Seteth, or to a lesser extent Ferdinand, it will have a pretty high chance to prevent the enemy’s counter attack. 

This is interesting - do you know how it works in more detail? As in, if the crest triggers once, will that prevent both enemy counterattacks if the enemy can attack twice?

Hmm - a sword build Ferdinand will hopefully be getting enough avoid to dodge counters, so this could be a nice boost. Then again, this feels a little like we're preparing for Astra not to KO, rather than doing everything we can to make sure it does (i.e. using Ingrid/Sylvain). I guess no version of this Astra build will be so reliable that it always kills what it sets out to, so it's definitely worth considering though. 

Edited by haarhaarhaar

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19 hours ago, Owns said:

That's pretty neat actually and I've been working on something similar myself actually, a battle predictor basically. One that's user friendly and can automatically get stats of enemies, weapons, equipment, etc. that one would select from a drop down menu. I'm hoping to share at least a working version soon even if incomplete to see if anyone wanted to help populate the statistics to be used (mainly enemy stats).

I don't know if it would be useful for you, but there are these available if you want them:

Black Eagles Enemy Stats Spreadsheet

Azure Moon Enemy Stats Spreadsheet

Imgur Gallery for enemy stats on all maps (barring DLC)

Edited by LoneRecon400

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2 hours ago, haarhaarhaar said:

I mean yeah, HV and other brave arts just are better, and Sniper in general is more optimal than Swordmaster. I think the point of the thread, or at least the OP, is to attempt to find the good in other, overlooked Crit builds, particularly Astra Swordmaster. 

That’s fair enough.

2 hours ago, haarhaarhaar said:

This is interesting - do you know how it works in more detail? As in, if the crest triggers once, will that prevent both enemy counterattacks if the enemy can attack twice?

 

Oh um. I was thinking that each hit of Astra would be a chance for Seteth’s Crest to proc, and that it would only need to proc on any one of those hits to prevent the counter attack completely, but I could be wrong. I’m not sure how it works exactly.

-

On 8/12/2020 at 5:26 PM, Owns said:

Dmg = RoundDown{ [total.mt. - target.prot]* 0.3 * 3 } * n.crit + RoundDown{ [total.mt. - target.prot]* 0.3 } * (5 - n.crit)

Wait, I don’t think that’s quite right. If Crits multiplied the damage before rounding down then the decimal would be multiplied by 3 and could go over 1 and add an extra point of damage. I could be wrong but I think it rounds the damage down before Crits multiply the damage.

Edited by Whisky

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21 hours ago, lenticular said:

Alternative way to look at the maths: if it's 50% chance to crit, that means that crit and not-crit have the same probability. So, the chance to get 5 crits is the same as the chance to get 5 not-crits, so the same as 0 crits. Similarly, the chance at 4 crits is the same as 1 crit and the chance of 3 crits is the same as 2 crits. Everything is symmetric. So, the chance to get 0, 1, or 2 crits is the same as the chance to get 3, 4, or 5 crits. So, exactly 50% chance of getting 3 or more crits.

This is great! Took me a couple of rereads to correctly understand what you're saying, but you're right, and great way of looking at it. Thanks for the explanation.

21 hours ago, Shanty Pete's 1st Mate said:

If you're talking player-phase damage with a physical weapon, then Death Blow is always doing more for you than Weaponfaire. Plus, you can access Death Blow much earlier, so it's helping you for more of the game.

Sure, but for a character who might be doing both phases (for me that includes Leonie and Cyril since PBV is 1-range and they can actually take a hit) Bowfaire is much more valuable. But of course getting Deathblow so early in the game can't be undervalued.

@haarhaarhaar Thanks for that very grounding post. These types of considerations and perspectives are a very important compliment to my mostly 'theoretical' analysis. In the end, it's these considerations that set the more realistic expectations. Not sure why I didn't consider Brave Sword before, or even Rapier+ ( @Whisky), these are very good weapons and a big oversight on my part.

3 hours ago, LoneRecon400 said:

I don't know if it would be useful for you, but there are these available if you want them:

Black Eagles Enemy Stats Spreadsheet

Azure Moon Enemy Stats Spreadsheet

Imgur Gallery for enemy stats on all maps (barring DLC)

Yes, this type of spreadsheet is actually a tremendous help. I'd come across the screenshots before but didn't know someone (you? I can never figure out who created these sheets) had already tabulated them too. The Azure Moon sheet doesn't grant me permission btw, looks like it isn't open to public, can you share a public version? I only looked briefly at the format of the sheets, do you know if their information is complete with all enemy stats? Would save me the hassle of confirming everything if someone knew.

Also that Imgur link isn't working, probably just moved, this is the one I found that was shared on another thread recently: https://imgur.com/a/dSnk6C9

 

5 hours ago, Whisky said:

I’ll try to send you the file I have after I get off of work.

Appreciate it.

2 hours ago, Whisky said:
3 hours ago, haarhaarhaar said:

I mean yeah, HV and other brave arts just are better, and Sniper in general is more optimal than Swordmaster. I think the point of the thread, or at least the OP, is to attempt to find the good in other, overlooked Crit builds, particularly Astra Swordmaster. 

That’s fair enough.

This is basically it. Originally starting this thread I wasn't really thinking about swordmaster specifically, it was more to get into the details of how crit works and the effect that no. of hits has on your "effective" crit. Astra having the highest n hits just naturally led the conversation in this direction. While I agree that yea other brave classes / skills are generally better than swordmaster, after having looked in more detail at what sword master can potentially do it's looking better than it used to for me. It can reach an impressive amount of damage, certainly more than Hunter's Volley, albeit inconsistently.

At this point, I'd say that for a select few characters (let's say Byleth, Felix, and maybe Ferdinand), i wouldn't take for granted that Sword Master is necessarily an inferior choice. I'm not arguing it isn't, I'm just saying it isn't obvious (to me) and maybe is worth reconsidering under a new light. For some of you more experienced players it might indeed be obvious though and I'd like to hear your thoughts. But these characters I think have the potential to reach SM's maximum potency (which again, is pretty impressive) given that they 1) are able to survive a hit or two, 2) Have good str and dex allowing them to maximize both normal and crit damage, and 3) have good speed as well, allowing them again to maximize damage from potential double hits, but also Avo for survivability. Not to mention of course they all have sword boons, and no Axe/bow weakness opening up optimum progression paths with ease.

2 hours ago, Whisky said:

Wait, I don’t think that’s quite right. If Crits multiplied the damage before rounding down then the decimal would be multiplied by 3 and could go over 1 and add an extra point of damage. I could be wrong but I think it rounds the damage down before Crits multiply the damage.

Yea I'm not sure either and it does make a small difference. I don't think it'll affect this thread's previous damage considerations by much but something I'll definitely want to get right for any calculator.

 

On 8/13/2020 at 4:00 PM, Cysx said:

you're also on a class with bowfaire, many people put her on a wyvern instead to get flight, which has a bit less damage and makes going through brigand a more... natural part of her growth.

was just thinking about this a little more. Even in this case, wouldn't it be better to rush PBV first, only then to backtrack to Brigand into Wyvern Rider? That way you get x2 damage sooner which is a lot more than Deathblow, before getting Deathblow to maximize your damage. Or would you disagree? I wouldn't say the optimum answer is obvious tbh. As you say, one might need to "math it out".

 

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44 minutes ago, Owns said:

Yes, this type of spreadsheet is actually a tremendous help. I'd come across the screenshots before but didn't know someone (you? I can never figure out who created these sheets) had already tabulated them too. The Azure Moon sheet doesn't grant me permission btw, looks like it isn't open to public, can you share a public version? I only looked briefly at the format of the sheets, do you know if their information is complete with all enemy stats? Would save me the hassle of confirming everything if someone knew.

Yeah, I'm the person who made both the spreadsheets and the Imgur Gallery.

Looking at it, the AM one is actually incomplete so I'll just withhold it for now. The Black Eagles one (which include SS and CF) is pretty in depth and includes all of an enemies stats, how their stats change with different weapons, battalions, and even benchmarks such as how much speed to double or the amount attack to kill with a crit in one hit.

Only thing it's missing really is the paralogues from potential recruits. Other than that, it should have everything you need.

Edited by LoneRecon400

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On 8/14/2020 at 10:12 PM, Owns said:

Thanks for that very grounding post. These types of considerations and perspectives are a very important compliment to my mostly 'theoretical' analysis. In the end, it's these considerations that set the more realistic expectations.

I just realised I was using completely the wrong formula for some of my calculations, and I've undersold things a lot as a result. Like, a lot. What I said previously was:

On 8/14/2020 at 2:11 PM, haarhaarhaar said:

Brave Sword+ with 80 displayed hit, 20 crit: 33% chance of at least 1 crit, 3% chance of 2 crits.

Wo Dao+ (normal) with 85 displayed hit, 60 crit: 57% chance of 1 crit if hitting once. 82% chance of at least 1 crit if hitting twice, 33% chance of 2 crits if hitting twice.

CAS+ (normal) with 65 displayed hit, 70 crit: 53% chance of 1 crit if hitting once. 78% chance of at least 1 crit if hitting twice, 28% chance of 2 crits if hitting twice.

Wo Dao+ (Astra) with 75 displayed hit, 60 crit: 78% chance of 3 crits, 4% chance of 5 crits.

CAS+ (Astra) with 55 displayed hit, 70 crit: 66% chance of 3 crits, 1% chance of 5 crits.

The chances are still the same for the extremes, but the other numbers are off. I made several mistakes with the Astra ones - the first was that I should have been figuring out the odds on 3*damage or greater (3 Astra crits is only 2.7*damage, so those odds aren't useful for comparison with normal attacks). So what I actually needed to work out were the odds of {all combinations where 3 crits happen and at least one of the remaining 2 attacks connects}. In general, I didn't account for permutations at all, and with Astra that significantly affects your odds in a good way. My second mistake was that I used the wrong formula for calculating probability anyway - 78%/66% in my original post was in fact an incorrect attempt to calculate the chance of not critting twice in an Astra attack, which isn't even the same as critting three times, let alone 3*damage. 

Huge apologies (I make stupid maths mistakes like this all the time, where I look back on my calculations and they're just garbage) - let me try and fix it now.

Brave Sword+ with 80 displayed hit, 20 crit: 37% chance of at least 3*damage, 34% chance of at least 4*damage, 3% chance of 6*damage.

Wo Dao+ (normal) with 85 displayed hit, 60 crit: 57% chance of 3*damage if hitting once. 82% chance of at least 3*damage if hitting twice, 55% chance of at least 4*damage if hitting twice, 33% chance of 6*damage if hitting twice.

CAS+ (normal) with 65 displayed hit, 70 crit: 53% chance of 3*damage if hitting once. 78% chance of at least 3* damage if hitting twice, 40% chance of at least 4*damage if hitting twice, 28% chance of 6*damage if hitting twice.

EDIT: Don't use the crossed-out calculations, they're incorrect. @Whisky's spreadsheet will give you accurate numbers.

Wo Dao+ (Astra) with 75 displayed hit, 60 crit: 100% chance of at least 3*damage, 100% chance of at least 3.3*damage, 38% chance of at least 3.6*damage, 34% chance of 3.9*damage, 4% chance of 4.5*damage

CAS+ (Astra) with 55 displayed hit, 70 crit: 89% chance of at least 3*damage, 27% chance of at least 3.3*damage, 16% chance of at least 3.6*damage, 2% chance of 3.9*damage, 1% chance of 4.5*damage

A third thing that I hadn't previously accounted for was that the 30% damage shown in the battle window is always a rounded down number. Which means, for example, that there's no difference in an Astra damage output between a build that normally deals 17 damage and a build that deals 19 damage - that difference isn't marginal when talking about a crit build. This is why I have written out a more detailed breakdown of the odds - because unless your original battle window has a damage output ending in 3 (13 damage, 23 damage, etc.), then it's 3.3*damage in Astra that will at least equal, if not exceed, a normal crit attack - 3*damage in Astra will only do that occasionally.

Now our conclusions are hugely different. Astra is in most scenarios the most reliable choice, if you can afford it (and that -9 cost is beginning to make sense now). Marks against Astra still include its lower damage cap compared to doubling normally, and its potentially lower odds of reaching high damage compared to Brave Sword crits. But the huge boost in reliability I think vastly overshadows that.

It's now also very clear that to do this build best, you want to have linked attack/adjutants for hit help. Here's the forecast:

Wo Dao+, 85 displayed hit (i.e. one linked attack/an adjutant), 60 crit: 100% chance of at least 3.3*damage, 54% chance of at least 3.6*damage, 52% chance to deal 3.9*damage, 6% chance of 4.5*damage

Wo Dao+, 95 displayed hit, 60 crit: 100% chance of at least 3.3*damage, 64% chance of at least 3.6*damage, 63% chance to deal 3.9*damage, 8% chance of 4.5*damage

Wo Dao+, 100 displayed hit, 60 crit: 100% chance of at least 3.3*damage, 65% chance to deal 3.9*damage, 8% chance of 4.5*damage

CAS+ (Astra), 65 displayed hit, 70 crit: 100% chance of at least 3*damage, 86% chance of at least 3.3*damage, 40% chance of at least 3.6*damage, 30% chance to deal 3.9*damage, 4% chance of 4.5*damage

CAS+ (Astra), 75 displayed hit, 70 crit: 100% chance of at least 3.3*damage, 71% chance of at least 3.6*damage, 62% chance of 3.9*damage, 9% chance of 4.5*damage

CAS+ (Astra), 85 displayed hit, 70 crit: 100% chance of at least 3.6*damage, 96% chance of 3.9*damage, 13% chance of 4.5*damage

CAS+ (Astra), 95 displayed hit, 70 crit: 100% chance of 3.9*damage, 16% chance of 4.5*damage

Note that CAS+ benefits far more from hit boosting than Wo Dao+. This is because the higher your displayed hit already is, the less a +10 boost to displayed hit will do to your true hit percentage. Of course, CAS+ also has 10 crit on Wo Dao+, which helps too. Given that CAS+ Astra can only be used twice per map, it should really be saved for when hit rates can be raised to the 80s for best results.

Note also that unless your original damage output with CAS+ ends in a 3, 3.6*damage with CAS+ will exceed 4*damage with Brave Sword+.

 

Just to see how this works out, let's transplant your Ignatz from earlier in the thread into this build. 24 Str, Death Blow, class Faire, Goneril Valkyries +8 and CAS+ comes to 57 Atk. Let's assume (Dex + Lck)/2 comes out at 20, which is low for Ignatz but whatever. With a Crit Ring and S Swords, we get to 110 base crit. Ignatz has his personal to help, so we're gonna pretend he can't use adjutants/linked attacks for the time being. His base hit against VW endgame enemies with Astra will be 75 - about 1/3 to 1/2 of the map has avo >55, so that number will go lower. Most enemies in VW endgame have 37 Prt or less (a few have 38 which is annoying, Fraldarius and Nemesis get above 40/50 respectively). We'll also assume 40 crit avo (only the snipers and a few of the elites/Nemesis get above that anyway). Which means that the modal damage window for CAS+ Astra will be roughly 20 damage, 75 hit, 70 crit. That means you have a 62% chance to deal 72 damage, which will OHKO between 40-50% of the map (quite a few people are on or just over the threshold - some strength boosters/hit help/a better character will fix that). Of course there's only 2 hits of CAS+ Astra per map, so you'll have to use Wo Dao+ sooner or later. And even though you still have decent odds of dealing 3.9*damage, this is a fair bit worse (with the round-down and drop in Mt, you're losing 20 points of damage here compared to CAS+). So not only will your swordmaster need to be able to survive counters, but they'll be consigned to chip and mopping up mages for much of the endgame. Of course, all the additional help previously mentioned in this thread will make things much better, and this is also with endgame stats in mind - this build will do extremely well before this point. 

I'm way too tired to compared this to Sniper Ignatz and the like - I'm sure Sniper Ignatz is overall better, but I don't know by how much. Anyway, what you have here is a very solid crit build, that will get kills for much of Part 2, and with a bit more effort than the above will be competing with your best OHKO units.

Edited by haarhaarhaar

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Just to finish off what I started last night, here's what the same Ignatz, but now as an HV Sniper, looks like.

24 Str, Death Blow, class Faire, Goneril Valkyries +8 and Killer Bow+ comes to 53 Atk. With Failnaught, that's 61 Atk.

Since Ignatz is a Sniper as opposed to a Swordmaster, he should have at least 5 points more of base Crit, so (Dex + Luck)/2 = 25. Again, this is low for Ignatz/Sniper, but fine for comparison to the earlier Swordmaster build. With a Crit Ring and S Bows, we get to 90 base crit.

Ignatz has his personal to help his hit rate, but we're going to assume 2 range only for now. His base hit against VW endgame enemies will be 85 with a Killer Bow+, 80 with Failnaught - about 1/3 to 1/2 of the map has avo >55, so that number will go lower. Prt and Crit Avo will be the same as above.

This means Ignatz's modal damage window for HV will be around 17x2 damage, 100 hit, 60 crit with a Killer Bow+, 25x2 damage, 95 hit, 45 crit with Failnaught. 

With a Killer Bow+, that's an 84% chance of getting at least 4*damage, and 36% chance of 6*damage.

With Failnaught that's a 70% chance of getting at least 4*damage, and 20% chance of getting 6*damage.

4*damage with a Killer Bow+ is, in most scenarios, less than 3.6*damage (4 crits) from CAS+ Astra (and will get some but not all of the KOs SM Ignatz was getting in our VW endgame scenario). Of course, Failnaught is more damage, as is Parthia (hard to obtain) and Bow of Zoltan+ (only available for endgame in Church routes), and the latter two have lower crit, meaning less reliable chance of 4*damage.

So, as was assumed, HV Ignatz is better than SM Ignatz. Range is the big difference, of course. And the fact that HV has a significantly higher damage cap (as well as being more likely to reach that cap) means it's more suited to the endgame. But a HV crit build isn't guaranteed Failnaught (Claude in VW is a big contender, or Bow Knight Felix in AM), and CAS+ Astra is a combination of reliable and powerful that exceeds Killer Bow+ HV, which is the most likely second best for a Sniper.

Astra SM is going to be worse than most other builds with brave CAs, but by stacking crit you can still make a build that hits hard very reliably, and is keeping up with those other builds in terms of KOs available.

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(I'm pretty sure this thread has reached overkill status, but I'm having fun so why not. Respect to anyone who's still following this thread haha 😁)

Okay, here's some reference 'tables' for the actual expected crit taking into consideration your hit value as well.

In the calculation I use the true-hit values, not displayed hit. 

  • At least 1 crit (of 2 hits); at least 3*damage:
Spoiler

at-least-1-of-2.thumb.jpeg.2a68d0d7ec94eb9c798977a6489ae5ca.jpeg

  • All 2 of 2 are crits; 6*damage:
Spoiler

at-least-2-of-2.thumb.jpeg.d82508e7ceec2e251fb46f51e700f4f4.jpeg

 

  • Astra - at least 1 crit; at least 0.9*damage:
Spoiler

astra-at-least-1-crits-hit-contour.thumb.jpeg.781b54619ae1121758430f7e249504ac.jpeg

  • Astra - at least 2 crits; at least 1.8*damage:
Spoiler

astra-at-least-2-crits-hit-contour.thumb.jpeg.21098c82df08c1a69a8f038a817647be.jpeg

  • Astra - at least 3 crits; at least 2.7*damage:
Spoiler

astra-at-least-3-crits-hit-contour.thumb.jpeg.61e39b789d7bdd58bba4ba28241c67fa.jpeg

  • Astra - at least 4 crits; at least 3.6*damage:
Spoiler

astra-at-least-4-crits-hit-contour.thumb.jpeg.4d2f4ecdbb9153a4b57957c6d6fd3ab6.jpeg

  • Astra - all 5 are crits; 4.5*damage:
Spoiler

astra-at-least-5-crits-hit-contour.thumb.jpeg.9b6598374fc39228560d4e2e08781b20.jpeg

 

I didn't bother with x3 or x4 hits because I don't see think they're as relevant for crit builds but if anyone really wants them for some reason I can make them with relatively little effort now that the template's in place.

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On 8/14/2020 at 11:25 PM, Whisky said:

Hey, here's my Excel file. I made sure that it is user friendly and I added the drop down lists for Weapons and Combat Arts.

Battle Forecast Calculator.xlsx 30.52 kB · 3 downloads

Thanks for that. Nice and neat calculator. Not to nitpick (my brain tends to flag anything that says 100% or 0% if the base itself wasn't so) but I noticed that the boxes with "at least" values off to the side use rounded percentages, does the game calculates things this way as well?

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On 8/14/2020 at 10:27 PM, haarhaarhaar said:

(3 Astra crits is only 2.7*damage, so those odds aren't useful for comparison with normal attacks)

3 Astra crits are 3.3*damage! Edit: Oh, you mean 3 Astra crits + 2 misses, just got it. I need to reread what you were saying now, with this understanding heh.

On 8/14/2020 at 10:27 PM, haarhaarhaar said:

Brave Sword+ with 80 displayed hit, 20 crit: 37% chance of at least 3*damage, 34% chance of at least 4*damage, 3% chance of 6*damage.

Wo Dao+ (normal) with 85 displayed hit, 60 crit: 57% chance of 3*damage if hitting once. 82% chance of at least 3*damage if hitting twice, 55% chance of at least 4*damage if hitting twice, 33% chance of 6*damage if hitting twice.

CAS+ (normal) with 65 displayed hit, 70 crit: 53% chance of 3*damage if hitting once. 78% chance of at least 3* damage if hitting twice, 40% chance of at least 4*damage if hitting twice, 28% chance of 6*damage if hitting twice.

Wo Dao+ (Astra) with 75 displayed hit, 60 crit: 100% chance of at least 3*damage, 100% chance of at least 3.3*damage, 38% chance of at least 3.6*damage, 34% chance of 3.9*damage, 4% chance of 4.5*damage

CAS+ (Astra) with 55 displayed hit, 70 crit: 89% chance of at least 3*damage, 27% chance of at least 3.3*damage, 16% chance of at least 3.6*damage, 2% chance of 3.9*damage, 1% chance of 4.5*damage

Okay, these look good until I get to the Wo Dao+ (Astra). What's with the 100% chance? Is that a typo or maybe I'm misunderstanding what you're doing here? The only way to ever get 100% anything is if both hit and crit are 100. After all no matter how good you're odds, it's still technically possible to miss all 5 hits (unless 100/100). Also, you're probably over complicating things with the Astra calculation since 3 Astra crits are indeed 3.3*damage (I tabulated these above, but again here I might just be misunderstanding your meaning).

On 8/14/2020 at 10:27 PM, haarhaarhaar said:

because unless your original battle window has a damage output ending in 3 (13 damage, 23 damage, etc.), then it's 3.3*damage in Astra that will at least equal, if not exceed, a normal crit attack - 3*damage in Astra will only do that occasionally

Didn't fully understand this because again I'm not understanding how you can get 3*damage with Astra. I like the way you went through the rest of the analysis and your later comparison to HV, but I'm not sure about how you're getting those numbers for Astra so I can't comment on or take in your conclusions yet.

Edit: again here, I now get what you're saying: 3 Astra crits + 1 normal astra hit. But I still don't understand the 100% chance stuff you listed.

Edited by Owns
correctedd plots for (2 of 2), and Astra (all 5 crits), the first versions weren't using true-hit

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15 minutes ago, Owns said:

Thanks for that. Nice and neat calculator. Not to nitpick (my brain tends to flag anything that says 100% or 0% if the base itself wasn't so) but I noticed that the boxes with "at least" values off to the side use rounded percentages, does the game calculates things this way as well?

No, by all means, nitpick it. At first, I only offered because I already had the file, but now I’m interested in helping out however I can. Please let me know any suggestions or requests for how to improve the file and I’ll do what I can.

No, those aren’t actually 100s, they’re just rounded up to save space so that it’s easier to read. That can easily be formatted to show the actual exact percentage.

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9 hours ago, Owns said:

What's with the 100% chance? Is that a typo or maybe I'm misunderstanding what you're doing here? The only way to ever get 100% anything is if both hit and crit are 100. After all no matter how good you're odds, it's still technically possible to miss all 5 hits (unless 100/100).

Hmm, when you say it out loud, it is very strange. I did those calculations quite late at night, so there is a very real chance that even those corrections are flawed somewhere. Anyway, will leave my working here, and perhaps you can figure out where I messed up. 

So for Astra, I calculated the odds with the following formula:

(crit chance^no. of required crits)*(hit chance^no. of required hits)*(number of available permutations in 5 attacks)

So to calculate minimum 3*damage for Wo Dao+, 75 displayed hit (87.75 true hit), 60 crit, I needed all the permutations of 3 crits and 1 hit in 5 attacks - there are 20 of those.

The numbers were thus (0.5265^3)*(0.8775)*(20), which is greater than 1.

For minimum 3.3*damage with the same, (0.5265^3)*(0.8775^2)*(10) also exceeds 1. So actually you can probably expect 3.3*damage from Wo Dao+ with those odds, I had thought. 

Minimum 3.6*damage: (0.5265^4)*(1)*(5) = 0.3842, rounded down to 38%

Minimum 3.9*damage: (0.5265^4)*(0.8775)*(5) = 0.3371, rounded up to 34%

Minimum 4.5*damage: (0.5265^5)*(1)*(1) = 0.0404, rounded down to 4%

 

I went through the same process for all my Astra calculations - I'm sure I went wrong again somewhere, because 100% does feel weird, but I'm beginning to doubt my double-checking ability as well, so I'm gonna let someone else point out my (probably obvious) mistake.

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25 minutes ago, haarhaarhaar said:

So for Astra, I calculated the odds with the following formula:

(crit chance^no. of required crits)*(hit chance^no. of required hits)*(number of available permutations in 5 attacks)

So to calculate minimum 3*damage for Wo Dao+, 75 displayed hit (87.75 true hit), 60 crit, I needed all the permutations of 3 crits and 1 hit in 5 attacks - there are 20 of those.

The numbers were thus (0.5265^3)*(0.8775)*(20), which is greater than 1.

You need to also include the probability of a miss. The probability of getting exactly 4 hits out of 5, when each has an 87.75% chance is 0.8775^4 * (1-0.8775)^(5-4) * 5choose4. And the probability of at least 4 hits is 0.8775^4 * (1-0.8775)^(5-4) * 5choose4 + 0.8775^5. Basically, you're including all the different ways of getting the result, but not fully accounting for how unlikely each specific outcome is, which is over-inflating your numbers.

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I’ve studied statistics and probability a little bit but I’ve never been good with permutations. I prefer to do my calculations with binomial distributions.

The file I attached earlier has two tables on the right side of the ‘Main Sheet’, one for Hits, and one for Crits (and one for Crests but that’s not important).

The Hits table uses binomial distribution to calculate the probability of Hitting y number of times out of x number of Attacks, and is dependent on the number of Attacks, which for Astra will be 5 so we will only be using the ‘5 Attacks’ column.

For the Crits table, the column we use will vary depending on the probability of getting x number of Hits calculated back in the Hits table. The Crits table again uses binomial distribution to calculate the probability of getting y number of Crits out of x number of Hits. We will need to use every column of this table for our calculations.

We can multiply across the two tables to get our calculations. For example, there is only one way to get a 3.0x multiplier; by Hitting 4 times with 3 of those being Crits. So I multiply the ‘4 Hits’ underneath of the ‘5 Attacks’ column of the Hits table, with the ‘3 Crits’ underneath the ‘4 Hits’ column in the Crits table. 36.32% * 34.56% = 12.55%.

I went through this process for every possible multiplier of Astra with 0x being the minimum and 4.5x being the maximum. Then I Summed all of the results from 3.0x and above. The final calculation for doing at least 3.0x damage with 87.75% true Hit and 60% Crit is 52.77%.

Hopefully that helps. Let me know you have any questions.

edit:

P(4.5x) = 4.05%
p(at least 3.9x) = 17.53%
p(at least 3.6x) = 22.24%
p(at least 3.3x) = 40.22%
p(at least 3.0x) = 52.77%
p(at least 2.7x) = 66.95%
p(at least 2.4x) = 79.50%
p(at least 2.1x) = 87.87%
p(at least 1.8x) = 93.96%
p(at least 1.5x) = 97.41%
p(at least 1.2x) = 99.02%
p(at least 0.9x) = 99.73%
p(at least 0.6x) = 99.96%
p(at least 0.3x) = 99.99%
p(at least 0x) = 100%
 

Make sure to remember though that each hit of Astra deals (30% of a normal attack) rounded down. So if it rounds down, then the multipliers above won’t be accurate in relation to a normal attack. It might be better to use multipliers for a single attack of Astra. For example 3.0x would become 10x.

Edited by Whisky

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