How does Critical Strike work?

[Ironmaster]

Hi all,
i hope this question is not asked every week, but i couldn't find any post relating exactly to this.
When CS is about 100, what does this mean? Is it perhaps about 10%? Is a highlevel enemy you trying to critically hit decreasing your chances, when you hit?
Is your critical Strike skill added to your weapon kill ratio?
Is Lightning Strike or Critical Strike influenced by your armor?
I really like the idea of both Strikes, but Sirtech should really explain how it works.

[TINKER_TINKERMAN]

Originally posted by Ironmaster: When CS is about 100, what does this mean? Is it perhaps about 10%? Is a highlevel enemy you trying to critically hit decreasing your chances, when you hit? Is your critical Strike skill added to your weapon kill ratio? Is Lightning Strike or Critical Strike influenced by your armor? I really like the idea of both Strikes, but Sirtech should really explain how it works.

I'm not sure about how it all works but i can give you some observations from playing the game.
1. When CS is near 100, I get a ton of criticals on lower level monsters. I've never gotten criticals on some of the high level monseters so IMO it depends on what the monster is as to whether or not you will score a critical.
2. I'm not sure what you mean by Weapon kill ratio?
3. Regarding Lightning Strike IMO it has to do with how much weight your carrying. For example if my samurai is carrying less than 25% of his C/C I have a lot more lightning strikes than if he's say at 40% of his C/C. So is it influenced by your armor? I'd say it depends on how much your armors weighs.

There is some very useful info in the Thread "Just got it" page 3.

I really don't know how CS works, but the higher the better. I think it also adds to your weapons instant kill percent.

I don't think CS or LS has to do with Weight, but I could test it out. And no, not everyone has asked this question, in fact i haven't seen the question ever.

One last thing...

Welcome to IW IronMaster [img]graemlins/happywave.gif[/img] [img]graemlins/happywave.gif[/img] [img]smile.gif[/img]

[Halsey]

It would appear that lightening strike has more to do with the number of times one strikes, rather than the effect of it....more like the bezerk option. I've seen Samurai's hit six or seven times in one phase with it.
Critical Strike is always about the kill. Since a number of factors influence a critical hit (intelligence, senses, inherent weapons factors and character type) it is difficult to give any precise numbers. Suffice to say, that if your critical strike number is at or over 100, you have a greater chance of a critical, but certainly not a 100% chance.

[EEWorzelle]

For the last two years players really interested in understanding have been frustrated by questions like this.

There are lots of questions. The level of monster you face is definitely a facter, but it is not certain whether that is direct or indirect (like dependent upon the monsters AC). The level of the character striking might matter too, but again we have no idea exactly how.

This is information that the writer of the strategy guide should have gotten directly from the developers prior to the game's release. Due to an accounting error at CompUSA, my strategy guide only cost 88 cents. When, honest fool that I am, I brought this up to the manager, he insisted that he could charge me no more or it would mess up their accounting. So giddy and happy I took it home, little realizing that it was just another case of a fool and his 88 cents soon being parted! Mostly it was just a diary walkthrough of that one player's game, but the real tragedy of it was the lost opportunity to get the information from the developers when they were still there and working on the project. While uninformative, the only real problem with it was that it filled a slot that should have been occupied by a real strategy guide emphasizing facts, such as this about critical strike, affecting strategic choice, rather than answers based upon opinion, or just no strategic information at all.

Determining it experimentally is possible, but very time consumming, recording lots of battle details from at least one or a few games, then crunching all the data, then verifying it in even more games. And that's just one question. This should not have to be reverse-engineered, interested players should simply be told what affects what and how much, based upon and backed up by precise numbers in an appendix somewhere.

What I would be even more interested in, strategically, was how much damage Critical Strike gives, i.e. the average amount of HP the monster has left when critically struck, minus the amount of damage, on the average, that would have taken place during the rest of that attack (since the rest of the swings in a specific attack (not the whole round, just that attack) are "lost" when death takes place). Another factor, if one wants to go deeper, would be a minus for the average number of additional attacks lost due to no other enemy in range. This is all pretty ugly stuff, but what matters is choice, for example when deciding to give a great sword to a Bard (with higher damage) or Samurai (with Critical and Lightning Strike).

Sorry, maybe only mathematicians such as Sultan and others would want to go there, you just want a simple answer and I can almost guarantee you that the answer, once obtained, is simple... but nobody who's talking, knows what it is. Maybe if we all contribute a little to the measurement of this sort of thing, we will have it all in time, but it will take some actual, careful measurement beyond identifying what it seems to depend upon. Obtaining this would have been so easy at the time the strategy guide was being written, but is more work now. Maybe if the Wizardry 9 development actually gets going, one of the developers, responsible for the formulas used in the new game will give us the Wizardry 8 ones that he or she would also have to become familiar with.

[ 08-18-2003, 05:27 PM: Message edited by: EEWorzelle ]

[Ziggurat]

Some of these game developers don't want to release their formulas or even give a hint of all the parameters involved. It's a competitive thing in the business. Once, in an interview, D.W. Bradley said he would never reveal how the "Luck" attribute affected other stats.

Rediscovering the equations for Critical Strike or Lightning Strike would be difficult, as EEW suggested. Not sure if it would be worth it. Take your best guess on how they work and go with your instincts while developing your characters.

There is likely a random probability factor with every hit as well, further complicating this determination. This would require a statistical analysis of the data. I'm decent with statistics but wouldn't want to try this multi-dimensional problem. Not for a game.

yes, my maths and stats background craves to know more! there was a fascinating thread at another board i lurk at (sorry, cant remember which or find the thread) where they came up with two main hypotheses:

(before i get into this, i must mention this is going to be a bit tedious, and perhaps a bit frustrating since we cant really know as the others have pointed out. furthermore, my examples are really hypothetical as i'm not certain of all the modifiers for the various skills and outcomes.)


a) to determine the result of an attack, the game calculates a series of random values tested against you skills/abilities vs. your opponents skills/abilities, with each subsequent random value potentially resulting in an even better outcome. so, for example, your samurai swings.

i) first, the game *rolls* to see if you hit, based on the cumulative modifiers of relevant skills/abilities (eg sword, close combat, dex) vs. opponent's armour class
ii) if you hit, the game *rolls* to see if you penetrate, again based on relevant modifiers (eg strength, sword, close combat) vs. opponent's armour class
iii) if you penetrate, the game *rolls* to see if the result is a) normal damage, b) lightning strike, or c) critical strike, where, again, all your modifiers apply
iv) if you do normal damage (or lightning strike) the game *rolls* for damage and ammortises down according to damage resistance.

this implies that you have to surpass numerous tests to get to the best results. statistically, that would mean it is exponentially more difficult to get the better results, particularly against opponents with high armour classes.

b) the other hypothesis is that there is a single roll to determine the outcome, and that the likelihood of each outcome is represented, based on your skills/abilities and your opponent's skills/abilities, as a proportion from this single table. so, taking the same samurai swing:

i) as an example, let's say the roll for the outcome goes from 01-100. for a given samurai and given opponent, 01-30 might result in a miss, 31-50 in a no penetrate, 51-80 normal damage, 81-90 enhanced damage (eg head hit), 91-95 lightning strike, 96+ critical strike.
ii) but for a different samurai, with lower skills, the results may be distributed as: 01-50 miss, 51-75 no penetrate, 76-90 normal damage, 91-95 enhanced damage, 96-99 lightning strike, 100 critical strike

in this scenario the distribution of strikes is determined directly from attack and defense stats, and because the result stems from a single "random" event, your ability to get better results wouldnt be exponentially penalised by the need to achieve numerous previous events.


furthermore, each of the above calculation scenarios would apply to each strike, meaning that the more strikes you get, the more chances there are of each outcome. given that many battles will run for a long time, with multiple strikes per round, it may actually be reasonable for the exponential event model (hypothesis A) to be true.

anyway, it's fascinating to me.

in practice, i find that items with high critical strikes (eg staff of doom, fang, stilleto) perform as well or better than classes with high critical strike skill and low critical strike weapon bonuses, given the same number of swings. this would seem to imply that, for comparison purposes, your critical strike skill divided by 10 is on the same scale as the listed instant kill percentage for an item.

[ScottG]

I'd say it works something like this:

First determine number of attacks in a round which is soley based on the character making (or not making) an attack that round, (no monster modifiers). Factors include things like attributes (dex. and speed), weapons skill level, class type (and class level?), and modifiers (i.e. weight problems). Lightning strike would either be part of the calculation here or would be a seperate calculation per attack imeadiatly afterwards. I think I remember having additional normal attacks effectivly eliminated after having 1 lightning strike in a round. If so then this would confirm the former, if not (somebody needs to pipe-in here) then it would be the latter.

Second determine chance to hit per attack.
1. compare character level vs. monster level for a deviation scale (the mean if both character level and monster level were the same).
2. determine hit rate via attributes (str. and dex.), weapon skill, and modifiers (i.e. weight problems), (possibly class type and class level here as well). Who knows what the scale is here...
3. compare #2 with monster's AC. Who knows how the AC interacts with the scale, though it doesn't work as well as it should/(isn't as realistic as it should be).
4. alter #3 if there is a deviation from the mean, (#1), and determine if there is a hit or not.

Third determine the chance of a critical OR damage per successful hit, (in otherwords if you can critical then that is rolled first - if unsuccessful then roll for damage). Chance of critical or damage amount "should" have a deviation similar to #1, in the hit calculation, based on the type of monster - NOT on the level of that monster (though in practice higher level monsters typically will have greater deviations from the mean, i.e. they will be harder to damage or critical).

To answer your questions Ironmaster:
1. it feels to me as if 100 in critical is indeed a 10% chance of achieving a critical (and it follows similarly to all the non-magical skills 1-100 scale and skills like Stealth that give an extra 10 in AC...i.e they have a 10 of 100 theme going on.)
2. again effectivly most of the higher level monsters will be more difficult to critical, but I think it has to do with the specific monster - not the monster's level vs.s your critical characters level.
3. YES a weapons critical is "added" to the critical skill level, however how it is computed is unknown. It could be that the two are added together to achieve an increased percentage (i.e. critical skill is 100 and it equals 10% PLUS the weapon's critical equals 10% = a value of 20%). Alternativly it could be that, (following the bases above), it rolls for a 10% chance based on your critical skill (determining a critical or not) and then rolls again another time for your weapon's 10% (which I believe statistically is superior to the prior method).
4. Both lightning strike and critical strike are not directly influenced by weight. Of course if you have a reduced number of attacks per round because of weight then you have fewer chances to roll for a lightning strike. Additionally if you have a reduced number of attacks per round and/or a reduced likelyhood of hiting the monster then you will have a reduced chance of a critical.
5. No, lightning strike is in no way related to a monster's AC. Indirectly critical strike is related to a monsters AC (in otherwords it isn't directly related but it affects a chance of landing a hit which affects your chance to even roll for a critical).

Of course this is all speculation on my part, but I have observed several repeatable occurences within the game that lead heavily to these conclusions.

[ 08-19-2003, 04:05 AM: Message edited by: ScottG ]

[Ironmaster]

Thank you all for your answers. [img]smile.gif[/img] I am kind of suprised that this information is held back, because a part of the fun is to fully understand the game and to build the party accordingly. Especially the critical classes are very difficult to develop, when you do not know how often the character will critical hit in the future. Two thoughts come to my mind: first: i do not feel contented that some weapons have the same or an higher skill as a fully developed character, this should be different. Secondly: strength is much more important for this classes, because the amount of critical hits is too low to rely on it.

[EEWorzelle]

Ironmaster, I sure agree with you that this information should be available. It is sort of sick and disturbing that developers (thanks for the info, Ziggurat) would consider something as elementary as the formulas they use as their "secret sauce". That's like revealing that your secret, advance car design is going to have tires. Formulas are the kinds of things developers should share as a community, with other, much more subtle, aspects such as balance, separating the mediocre from the excellent. Players are only interested in the results of what affects what and how much, not what the programmer did to get there.

D.W. Bradley did a great job with puzzles and complexity in the Wizardry games he worked on, particularly the unparalleled Wizardry 7. I have to admit, however, that the Wizardry 8 team, building upon his earlier good work, went well beyond it and did much better in the strategic aspects of the game. They removed the ridiculous twitch skill needed in the player for locks and traps, made expert skills centrally strategic, rather than based upon finding them in the game, and made character creation and increases at level up strategic rather than random. The smaller (but not small), less complex, Wizardry 8 design may have had more to do with shrinking financial budgets rather than intentionally giving us less game. I suspect that the more strategy-orientated developers of this game would have been more forthcoming if the strategy guide writer thought to ask. I could be wrong about that.

Personally, I enjoy a RPG game much more if I take some time, up front, to study non-spoiling strategic information (like formulas and what effects what), so I can make an attempt to create a great party even the first time I play. If available, I will play on whatever expert mode is available, to compensate for the advantage that gives. I find it desirable to do that the first time I play because usually I would play RPGs once, or the really good ones twice. The incredible replay fun of Wizardry 8, even after many times through the game, is new to me.

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.

We as players who would advise, even informally as one player to another, have a right, or even duty to determine the actual formulas, as well as possible, to publish our results so others can attack their veracity, and to remove as much of the speculation as possible. This shouldn't be necessary. The developers should simply do this, but in the meantime, it is important to not make advice "too strong" before it can be based upon fact.

Regarding the specific points about Critical Strike and other key capabilities affected by many things, you are both correct that a model is needed, before measurements can be meaningfully taken.

Concerning specific speculations, arguments such as the 10 to 1 ratio are very effective, because we are trying to get inside the designer's heads, in a sense, and assumptions of simplicity make for higher quality guesses.

Okay, so here's my take -

There are several decisions or rolls involved, as you both said. Of course it is not exponential (low order polynomial) but the gist of that word (exponential) is commonly known and so it's use is a good way to communicate the behavior. Actually, the most fun games have the characteristic that excellent, or "optomized." is much, much more powerful than the nearly excellent or "optomized". That makes it worthwhile and fun to really go for excellent! I put "optomized" in quotes because it is always relative to the party and combat style, to some degree.

The evidence is that the maximum number of attacks in a round is determined at the very beginning of the round, before any actions take place. For example casting Haste does not increase one attack, in the round it is cast, to the two that a particular Hasted character might get in the next round and thereafter, for example. Attacks might be lost during the round, however, if the character is struck enough. They might also be lost due to "good" reasons, as you suggested, Scott. I think I remember attacks after an attack that gave a Lightning Strike, in the same round of combat, but I don't remember for certain (I will watch for this one). Speed, dexterity and weapon initiative clearly affect this. I'm not certain if weapon skill does... probably. Stamina and encumberance can clearly affect it negatively.

At the beginning of an attack, the maximum number of swings in that attack is determined. I'm not certain if Lightning Strike is determined per attack or per swing, but it might be the former, and that it gives x extra swings in that attack. A number of factors are involved in the determination. If the target dies, I believe the rest of the swings in that attack are lost, Lightning Strike or not. I can recall killing one target and attacking another in the next attack in the same round as very common, but not moving to a new target within the same attack.

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. When Dexterity is maxed and senses are high, this can, in my experience, become a near certainty. In the case of Lightning Strike, each swing is determined here, as to whether it hits. I have seen many times where some swings in the Lightning Strike hit, and some don't.

Penetration is determined seperately, I believe, but there may or may not be an independent roll for it. Ninjas get auto-penetrate on ranged attacks and Powerstrike greatly impacts this for melee attacks, as two examples. With very high Powerstrike, this can become a near certainty, too, depending upon the foe. This is probably when Critical Strike is determined, making no damage calculation necessary.

Next is damage determination. This is affected by damage percentage increase which is based upon Strength, plus factors which double it (ex. target crippled) or half it (ex. bosses?). Chances are, by this point, weapon skill (unless 2x against those foes), and many other factors considered above don't matter.

Given a choice of model, it then becomes a matter of taking the measurements.

For example, we can try out a model that says that the Critical Strike percentage (assumming Scott is correct that it is Critical Strike Skill divided by 10 plus weapon Critical Strike), is what will apply, on the average, unless other factors reduce it. Then we (or other players who wish to particate) can measure the actual percentages (by averaging), come up with some hypothesis as to how it is affected, so players who want to get more precise, like Ironmaster, can be advised what to consider in order to maximize the Critical Strike capability of his or her character. If the model and measurements are close to correct, a pattern will appear that can be further tested and nailed down as factual.

Speculation and complexity are part of the road that needs to be taken to get there, but simplicity and facts are the destination. I doubt many players would be interested in doing this kind of... work, for a game, but many more would be interested in the simple facts, if someone does go get them.

[ 08-19-2003, 04:27 PM: Message edited by: EEWorzelle ]