How does Critical Strike work?

[Ziggurat]

Skip this long one if don't care to hear more about math, etc...

I agree a model is crucial, although many models can be tested.

What would need to be done to simplify this process is make a party of identical characters. Say 5 samurai, same race (and sex?) with same armor and weapons. Add a bishop perhaps to help keep them alive. Then track the number of hits against identical enemies, along with all relevant stats including all those mentioned above in previous posts. This could be alot of parameters to track!! But write them all down for each battle. Keep it simple. Total crits and TS may be enough to count, but you will need the other params, too.

There will be differences in how many hits each sam gets based on the randomness and the inevitable changing enemies in the same battle, so there is an inherent fuzziness to the data. Some of this may be averaged out over the long run. Position in the party must be rotated evenly. And these strikes really don't emerge regularly til mid game. This project would be time-consuming.

On leveling, make each develop differently, one trait at a time. Say, keep piety or intelligence the same for all three. (That is why I choose 5 instead of 4 sams.) Each one pushes one trait, with the other trait always being piety (or intelligence). As some traits lead to better fighters, or more attacks, etc., the number of total attack attempts and penetrations should probably be tracked as well. You perhaps see how this is getting ridulous...

Then you have five equations in five unknowns and need to find a correlation between these 5 factors and the quantity which is the outcome, critical strike average or tigerstrike average. These will have small correlative "slopes" which give how fast the CS or TS skill rises with each of the five abilites (assuming they are linear equations! If not, this would show up on a graphic display of each). It may be assumed something like piety or intelligence would have a low correlation coefficient (statisticaly saying no cause or effect of the quantity on CS or TS) although the description of intelligence in the game says it effects close combat (maybe just the rate of increase in leveling it up during combat?). If so, it makes the equation even easier to solve if there are less parameters. And it would give you a double check. This might also be useful to help reduce the inevitable noise since there are not a large number of battles.

This is one way to do it, multiple models can be tried with the same data to determine the best fit (highest correlation). Another technique called the simplex method can zero in on the solution so you don't need a computer if you know the technique or have a good linear algebra book. Non-linear equations probably aren't used, but any of these parameters are multiplied instead of added it adds more difficulty and the model would have to be changed.

Once it is discovered how these four or five character traits effect the strikes, then you can start your real work!

You can start looking at how enemy armor class, weapon damage, initiative or number of attacks, to penetrate, close combat, martial arts, carrying capacity load, bow skills, range skills, special bonuses from weapons, and the critical strike skill itself effect the CS and TS rate. (I probably left a few out...)

You also may want to use CS or TS per swing instead of the total per battle (but only count the first swing if it is a Tiger Strike).

For the data to be meaningful, it would better to cut out as much extraneous noise as possible. This is my first thoughts on determining the equations. As I said, it wouldn't be easy.

I wouldn't even attempt to do something on this scale with a group effort using different parties and characters, too many variables. A good math program COULD be used to solve this, say twenty equations with twenty unknowns, but the data would have to be pretty good for it to be meaningful. And a large data set that would be! And how would you be sure if a factor was 0.02 (relating, say, CS probabilty of occurence to critical strike skill) when it was really 0.023? Remember, these factors are tweaked during game testing and may even differ between races. My two cents...Zig

[ 08-19-2003, 04:46 PM: Message edited by: Ziggurat ]

[Ziggurat]

Thinking about this, I wonder how fast identical members of a party would diverge, even with everything kept the same? And how would you keep them the same? I guess you don't upgrade armor, rings or weapons until you enough for everyone! Unlikely to be able to do this and survive. But if you could, it would be a measure of the randomness of battle. Otherwise, it's back to the many param problem again.

[ 08-19-2003, 05:24 PM: Message edited by: Ziggurat ]

[EEWorzelle]

Well, Zig, if it is that difficult I would just throw up my arms and say no way (I may anyway)!

There are three simplifying factors.

1) We do not have to set this up as a mathematical problem with full generality. We already know some of the things that affect it. Well, maybe we can't be certain, but we can simpify the problem by making educated guesses (like Scott's above).

2) We do not need to run a long, tedious, huge experiment. A series of simple experiments will do the trick. Something like: "If you have one or more characters with Critical Strike capability, record combat info, including opponents, (for as long as you can stand it), summarize it and post it." Just that. I bet, with lots of people looking at that and follow-up data, that we could zero in on a pretty good answer... fairly soon.

3) The end result is qualitative, more than it is quantitative. For example, Scott speculated above that weight is not a factor unless it is too much. I believe he is probably right, but several players about nine months back had a strong theory they say is backed up with results. That was that if your encumberance was very low (a lot lower than 50%) you would get a lot more Critical Hits and Lightning Strikes. I think most players ended up not believing it but... The point is that we only need to know if that does anything or not and, if so, a general idea of how much difference it makes. It is not a messy answer like 2.4729872, or something like that.

Right now I have an IM party where I am measuring the impact of Piety on magic casters (by making it as low as possible). It's a different question, but a pretty simple experiment and I'm having a blast doing it! If it's not fun, it will get old fast.

P.S. - Isn't great that same characters diverge in this game. The variety adds to the replayability. Makes it more difficult to measure stuff, though, I agree.

[ 08-19-2003, 08:00 PM: Message edited by: EEWorzelle ]

[ScottG]

Ironmaster your right on about the lack of data for the game. As for the critical thing vs. the weapons - there really are not that many weapons that have 10% in critical (and VERY few that have more than this amount), so it is not as bad as it seems. The real problem with criticals is that your critical ability not only depends on your critical kill number (or the rangers ranged attack number), but it also seems to depend heavily on the attribute Senses. When I said that criticals "felt" like they were achieving 10% this is ONLY in conjunciton with a 100 in Senses. (You didn't bring it up before so I didn't.) In fact it feels like Senses determines your upper limit on your critical capability (i.e. 50 in Senses and your max is 5%, 60 and your max is 6%, etc. provided you have 100 in Critical Strike). This then means that you have to "plow in" points to Senses which results in having fewer points to distribute to your hit attributes (str. and dex.) - and if you can't hit then you won't get a chance for a Critical!

Critical hits are a cool gimmick, in most instances you should never rely on them. Lets say however that you have not only a maxed senses and critical skill, but also a weapon with additional critical capability. For a ranged attack this works quite well because damage is less than melee and presumably your ranged character is not in a position to be attacked via melee (they are protected from massive damage and you have spent your attribute points on senses instead of vitality). Alternativly your critical attack character is a melee attacker but again you have spent no additional points on vitality (so they are weak in melee) - HOWEVER this can work if your (using weapon(s) with additional critical capability) AND this character is a stealth class character (with maxed stealth), AND at least one other character exposed to melee attack and has no stealth capability. For this melee type of character then you are ruling out a Samurai unless they have taken a level in Rogue for the Stealth skill. (Hmmm, roleplaying-wise that Samurai sounds like a Kensai.) Otherwise you essentially have a Monk to consider with the Staff of Doom or a Ninja with dual stilletos. Alternativly because of the enhanced number of attacks you could have a Ninja with two double-strike daggers and achieve similar results to a Ninja wielding dual stilletos.

EE's:
"Sultan and ScottG - We, like many others, have an urge to advise new and experienced players of the game, in order to enhance their fun. Those players do not want to be given complex mathematical formulas. They want to know things like, "What weapon should I use with my Valkyrie?" The formulas help those who would advise others to give correct advice not based on speculation, guesses, or only their own, limited playing experience. Not every new player wants advice, but if they do, those who give it have a natural urge to want to do it with... quality."


I really only added that extra because of Sultan's response and because it would give at least some basis for my conclusions to Ironmasters questions. Additionaly of course I think I made it very easy for Ironmaster to get specific answers to his specific questions without a lot of verbosity, (could be wrong though...was I Ironmaster?).

Hmmm, your right EE - I didn't differentiate swings vs. attacks. Like you I believe this occurs imeadiatly after the attack calculation and it would make sense that lightning strike would precede this calculation to determine the number of swings that attack.

I don't think though that there is a specific "penetration" calculation after your chance to hit - otherwise you are simply re-rolling for a chance to hit. As to wether this is a modifier or a scale deviation (or both), I don't know. Your impression seems to suggest that it is actually "tipping" the scale in that character's attack which would mean that it is a scale deviation. This view point (at least for expert skills) does make sense if indeed there is a character level vs. monster level scale deviation (and I'd say there is based on magic's ability to hit monsters higher in level). (In otherwords it doesn't make sense to change the basic structure of the rounds calculation for magic vs. physical attacks.) For the ninja's auto-penatrate (at least from the book description) it simply suggests that it is an over-ride to the hit calculation - meaning that if a thrown weapon, (not simply ranged), is used then it will always hit. Logically in this instance then during the hit calculation the engine will first check to see if its an auto-penetration and then overide all other calculations within the hit calculation, ending of course with a hit and progressing on to a critical or damage calculation for that hit.

[ 08-20-2003, 12:20 AM: Message edited by: ScottG ]

[Ziggurat]

You guys make sense, more than I do. Yet it still verges on speculation. Build up your speed, strength, senses and critical kill stats...(maybe dexterity as well) get some weapons that enhance this, don't carry too much weight and hope for the best!

[ 08-20-2003, 01:08 AM: Message edited by: Ziggurat ]

[Scatter]

Level is indeed a huge factor. In my party of three plus a dead L1, the mobs' levels were usually 3/4 of mine. I got at least twice as many crits as with an otherwise equally developed party of only three, for whom the mobs were mostly on the same level. (Ninja, Monk, Sam--with a rogue level for the Sam) I made this test by keeping them parallel through the game, staying within a zone of each other in 'real' time so i could keep the developments in step.

[Wereboar]

Originally posted by EEWorzelle: For each swing, there is a chance to hit. The AC of the foe is involved in this one. Level of the character may matter.

In my experience, level does matter a lot. I just cleared most of Rapax Rift/Castel with a party that stopped levelling at level 11/12 (but with high skills), and my fighter had a hard time hitting them. I think the difference was much bigger than what i would expect for the lower fighting stats. In fact, he rarely did hit in berserk mode (but quite often without).

Another point to your math model:
After calculating the number of swings, roll up for an attack mode if several are available (swing, thrust, berserk, bash ...). I'm quite sure that the attack mode influences the chance to hit, and the damage done. This is clearly true for berserk.
Back in Wiz7, there was a table which attack mode has what modifier. And there was an attack form called melee, which worked much like berserk nowadays: double damage, but -6 to hit IIRC. In Wiz7, you could choose the attack form from the ones that were supplied by your weapon. I think Light Sword was about the only one which could be used to melee.

[EEWorzelle]

Wereboar, excellent points as always!

Some work by Morlac earlier, using an editor, also showed that the number of attacks depends upon both level and the type of character.

The point about attack mode is also a good one. I remember the table in W7. It explains why the Diamond Epee, with decent damage and excellent bonuses to both initiative and "to hit" is such a mediocre weapon. It only has a "thrust" attack. Perhaps against some foes it would be excellent.

Scott, I honestly was only able to understand part of what you wrote about my posts. It was not clear specifically what you were referring to. Several of the things you said in our respective discussions above are speculations, of course, but you clearly labeled them as such, and I have no criticisms of anything you said in those posts. I think many of your ideas were very insightful and several of your arguments solid. We need speculations as the hypotheses we then measure against. It is only when it becomes advice that it ought to be fact, or, if not, at least labeled as the way things "might" work.

Regarding penetration, my evidence is observing combats in my game, after turning on verbose combat messages. I often see where an attack hits the foe, but then does not penetrate. The only evidence here is that the game does define and recognize a "hit but does not penetrate" event. It does not prove there is a second calculation for it. Of course it could be like one of the alternatives Sultan pointed out, where one range in the roll might be "hit but not penetrate", and the other "hit and penetrate", but then the percentages would need to change for each different foe. In many other games there is this dual aspect of an attack being effective, where one part is whether the attack connects and the other whether it does anything. There are generally very different things that determine success or failure for each aspect. It is possible that these two calculations were combined in W8, but more likely there are two, separate calculations. made. In many games the same roll is used for both calculations, as I suggested. Both possible explanations (yours, mine, or other ones) are speculation and not fact. The speculations are good on the way toward getting the facts, but let's not jump the gun. We should be compiling evidence, like the observation I just spoke of, the evidence from several players that Diamond Epee is a mediocre weapon (although that could be measured better), and, for the level impact thing, the evidence Wereboar and Scatter spoke of from their games.

[ 08-20-2003, 08:16 PM: Message edited by: EEWorzelle ]

[ScottG]

I just had a nice explanation all written out and the browser craped-out on me.

Well the short of it is this....

Sorry about the format - my writing can be somewhat obtuse at times.

you (EE) wrote: "It is only when it becomes advice that it ought to be fact, or, if not, at least labeled as the way things "might" work."

I'd have to strongly disagree with this statement. This is an informal gaming forum, and as such the overwhelming emphasis is opinion through persuasive writing. There really is no need for me, you, or others to apply a caveat or state: "this is my opinion, it is not fact" or some derivation thereof. Opinion here is implied. Only things that are intended to be stated as facts, should be stated as such....(or it should be obvious from what is written, like a detailed accounting of events, or a quote, etc.).

That said...

I'm fairly certain what you are seeing is not penetration with regard to a hit calculation, instead it is penetration with regard to damage. For instance, assume you have a Ninja attacking a Granite Golem with a simple throwing dagger. Now the Ninja is using a "thrown weapon" and the manual states:

"The Ninja can also kill from a distance, throwing objects with such accuracy that they always penetrate the opponent's armor.."

The words "accuracy" and "opponents armor" clearly suggest that the "auto-penetration" feature is referencing the ability to hit an opponent. Furthermore the word "always" strongly suggests that it is an over-ride to a hit calculation. In otherwords a Ninja throwing a weapon will not have to determine if it hits the opponent or not - it automatically hits the opponent. So continuing on with our example the Ninja will hit the Granite Golem despite its enormous AC, (regardless of level or skills such as throwing weapons and ranged combat). (No doubt however that this is a class specific feature - meaning that the character's present class must be a Ninja for this automatic hit.) HOWEVER, the Ninja will in all probability fail to "penetrate" (as stated in the verbose messages) the Granite Golem because the Golem has a damage reduction feature and because in all probability the simple throwing dagger will not provide enough damage to overcome the damage reduction. Functionally then on that "swing" it would work out something like: hit; damage = 5 vs. damage resist of 10 = "no penetration". The interesting thing here is that while the Ninja (or any critcal skill character or device) may not be able to penetrate a target for the sake of damage, it can still critical a target (and yup, I've seen it happen).

[ 08-21-2003, 03:40 AM: Message edited by: ScottG ]

[TINKER_TINKERMAN]

Originally posted by ScottG: "The Ninja can also kill from a distance, throwing objects with such accuracy that they always penetrate the opponent's armor.." The words "accuracy" and "opponents armor" clearly suggest that the "auto-penetration" feature is referencing the ability to hit an opponent. Furthermore the word "always" strongly suggests that it is an over-ride to a hit calculation. In otherwords a Ninja throwing a weapon will not have to determine if it hits the opponent or not - it automatically hits the opponent.

Sorry to tell you but this statement is not correct. The ninja's auto-penetration ability does not mean he/she will hit the enemy. The Auto-penetration means that IF you hit, you will do damage and possibly a critical.

For example in my current pansy party i have a ninja. At Thrown range at least half of her weapons go flying off into the wild blue yonder. If she scores a hit it always does damage.

Another thing if the enemy has missle shield up, it will deflect the thrown weapons just as much as it deflects arrows or other missles.