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I am having a hard time wrapping my head around the math for setting difficulty levels.  Let me see if I have this right.  If my PC had say, a 90 in stealth, and my opponent had a 90 in spot hidden, that would make it an extreme difficulty level and give me only an 18% chance of success??

But if I had similar skill levels and went against a PC using opposed skill rules, it would basically be a 50/50 contest.

 

this makes no sense to me.  Why would an npc have such a better chance of succeeding against me when our skill levels are equal?

Thanks in advance for the help.

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You have it right. It was designed with ease of use prioritised above statistical balance, and some compromises were accepted. One additional factor that helps to swing things, is that the PC can choose to push their roll when making a skill roll vs an NPC, boosting their chance of success to around 33%. Whereas in an opposed roll there is no push option. Hope that helps. 

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56 minutes ago, Paul Fricker said:

You have it right. It was designed with ease of use prioritised above statistical balance, and some compromises were accepted.

Ironically, I think it actually makes the game harder to use. A Player with a 90% skill is going to expect to be able to hold their own against a similarly skilled NPC, and instead, has a one in three chances of winning in the best case scenario.

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15 minutes ago, Atgxtg said:

Ironically, I think it actually makes the game harder to use. A Player with a 90% skill is going to expect to be able to hold their own against a similarly skilled NPC, and instead, has a one in three chances of winning in the best case scenario.

Yeah, that’s what was bothering me.  In my example, even with a push, the PC is going to lose 3 out of 4 times.  
 

I understand they were trying to streamline the game, but I guess I don’t see how just doing opposed rolls for all character vs character actions whether or not they are box or pc slows the game down more than a couple seconds.  To me, those few seconds are better than having the pc feel like they have been screwed over.

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2 minutes ago, Fred said:

I meant to include the above in my reply. I believe it is better not to view opponent percentages as comparable, or the same as players make “all” the rolls here. Remember, you are dealing with some extremely formidable and supernatural opponents at times, and this system, while harsh, lives up to that in an elegant way. You can still push, you can use luck.

You have some good points there. That does make sense for many cases.

 

hmmmm.  I guess I should just judge whether certain situations should use the regular rules for difficulty, or use opposed checks.

in a case like say where 2 lawyers were competing to prove someone’s guilt or innocence, and opposed check could be used, but when sneaking past a horrific mythos creature, use the standard rules.

 

or maybe I could houserule that if both characters are in the same general skill category, such as both being 50-89, that they always use opposed checks.  

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5 hours ago, Josh777 said:

I am having a hard time wrapping my head around the math for setting difficulty levels.  Let me see if I have this right.  If my PC had say, a 90 in stealth, and my opponent had a 90 in spot hidden, that would make it an extreme difficulty level and give me only an 18% chance of success??

But if I had similar skill levels and went against a PC using opposed skill rules, it would basically be a 50/50 contest.

this makes no sense to me.  Why would an npc have such a better chance of succeeding against me when our skill levels are equal?

Thanks in advance for the help.

Dear Josh777,

this is a good point. There are some ways around (some mentioned by Fred). For example, when appropriate, I use Hard difficulty instead of Extreme difficulty for rolls where opponent has skill 90% or more. Usually my investigators do not have skills above 70%, so using Extreme difficulty would sometimes make the game just too hard for them. Lowering the difficulty level is a simple, clean and effective way of helping your players. Moreover, the philosophy of the rulebook, as I understand it, is that Extreme difficulty should be used rarely. Also, that opposed rolls should be mainly used for combat and confrontations between PCs.

In practice no NPC in any of my games has ever had any skill at 90% or above. This basically solves the problem. Monsters do have 90% skill or above, but they have unimaginable powers, so I think the rules should favor them over PCs and they do (vide your example with 90% Spot Hidden and 90% Stealth).

As it is repeatedly emphasized on this forum: rules are important, but they are mainly to serve you and your group and the narrative. I feel it is much more useful to read the rulebook as a guide on the philosophy of how to play a given game. In the case of Call of Cthulhu, the rules might make no sense if they are considered outside of this "philosophy", but when looked from the point of view of what game tries to achieve I think they make sense. In other words, this game should be hard, and PCs should perish!

Edited by Tranquillitas Ordinis
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1 hour ago, Fred said:

Instead of looking at it as comparable percentages, look at it as formidable opponents are hard to sneak by even with a very high rating.

The players usually  don't get to pick their opponents, the GM does. Not do the players have much choice about where they need to sneak into. So if the adventure requires that the PCs sneak into the temple of the evil cultists and steal the Wii of Cthulhu before the cultists use it to raise Rhy'leth from the depths and end the world as we know it, well, that's just tough luck. 

Players generally figure that thier chances to succeed in any endeavor are based heavily upon thier own skills, thats why they have them. But in this case the differewnce between a 05% skill and a 95% skill is only a 17% difference in success chance. This in a game where the players are all hopeless outclassed by 95% of the Mythos beings. 

 

1 hour ago, Fred said:

I for one like this a lot. I am sure Chaosium is well aware of this when they design creatures as well. The mess of having creatures doing opposed rolls with very high percentages with hard-to-judge-what ties mean, must be avoided in CoC at all costs, in my opinion.

Glad you like it. I don't.  I agree with you that Chaosium is aware of the situation, but that doesn't make it a good design choice for a game. As for opposed rolls, the game originally didn't have them. The D100 system used in most BRP games isn't suited to opposed rolls, as it predates it. But I think there has to be a better way to handle this that giving a NPC a two to one advatage when skill scores are the same. For instace:

What if the difficulty of the roll was tied to the relative skill of the characters rather than the absolute skill of the NPC? If this situation were, say a half skill or less roll, it would be just a simple but play out a lot better.

 

1 hour ago, Fred said:

A creature with 50% in Spot Hidden halves your chance and one with 90% crushes almost any chance. You can still use Luck or Push to get heroic results.

And still fail most of the time. 

1 hour ago, Fred said:

As a compromise, this is almost the ideal solution.

What crtiera do you use ? As a compromise this is a terrible solution. At the 90% mark it makes the player character's abilities close to irrelevant. A situation where a player has the same or greater skill than a NPC and yet is only going to win about one time out of five, one in three if he pushes it, is not anywhere near what I consider ideal. It's a marked downgrade from the way the used to do it. 

1 hour ago, Fred said:

I’m at awe of it.

I'm repulse by it. So much so that I'd play an earlier edition. 

1 hour ago, Fred said:

Think of an opponent having 50% as a very challenging creature to sneak by.

...regardless of how proficient you are at sneaking. 

1 hour ago, Fred said:

I can’t quite see why you feel it is harder to use (fewer rolls are made), rather only much harder to succeed in some quite rare circumstances.

Because player skills are now secondary to the NPCs skills. Consider a typical game session.

The players want to get into a location but there is a guard. The players discuss the situation and try to decide if they should risk sneaking past the guard or not. Based on the information available to the players, which is mostly the environment and their own skill scores they have to decide what to do. The best case scenario for the players would be if someone has maxed out their Sneak skill. 

But if the guard has a Spot of 50% or higher, the players chances of success drop by 50%, and there is no way for the players to know until they are committed. So they might as well plan to fail because, mathematically the probably will. 

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1 hour ago, Josh777 said:

Yeah, that’s what was bothering me.  In my example, even with a push, the PC is going to lose 3 out of 4 times.  
 

I understand they were trying to streamline the game, but I guess I don’t see how just doing opposed rolls for all character vs character actions whether or not they are box or pc slows the game down more than a couple seconds.  To me, those few seconds are better than having the pc feel like they have been screwed over.

Me too. Plus,there are better ways to get the same streamlining. This is like one of threshold high level  AD&D modules where some sort of magical field prevents teleport, wish and all the other high level spells from working.  

 

 

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1 hour ago, Fred said:

You seem quite frustrated and upset.

I'm not. I just believe it to be a bad method of doing things. People can dislike a rule without being upset. 

1 hour ago, Fred said:

You are obviously, for example, right the players does not choose their chances, the GM does.. So if you have a good GM, they can house rule or adjust things or play another edition.

Yes, but that doesn't make the rule any better. A good GM can house rule or adjust anything. Considering how CoC7 plays, I can't really see a reason why a GM would put someone in there with a 90% spot skill except to trip up the players.  

It would be differernt if it was something that the players were made aware of and could try to work around it, but it's just something that will pop up an ambush them. 

 

1 hour ago, Fred said:

As you have basically said the same thing throughout the the rest of your message, I would instead of responding to each of your points, sincerely encourage you to use an earlier edition of the game as indeed you are already doing. While it might be frustrating, there is simply nothing at all you can do about the core rules, which me and many others enjoy immensely.

Actually there is quite a bit people can do about core rules they don not like. FOr instance they can mention it. Much like how the OP can mention that is seems off to him, because, well it is off. 

1 hour ago, Fred said:


As mentioned by Josh777, otherwise it would be easy to house rule around things you don’t like, and view percentages are very abstract, and then the elements of Luck and Push are there to compensate for hard rolls (the Opposed ones requiring extreme success being so rare), 

Yes, it easy to house rule around, but so if everything else in an RPG. Just because something is easy to fix doesn't mean it isn't broken. 

1 hour ago, Fred said:

giving players advantages the opponents don’t have.

while still doesn't offset the advantages the opponents have. For instance, if someone with 90% sneak skill tries to get past a 50% guard, the odds favor the guard, and if the PC pushes he suffers greater consequences.

1 hour ago, Fred said:

Another thing you can do, which many GMs does, is offer disadvantage instead of Hard (so a player who has 90% has to roll the D10 twice and choose the worst).

Yes. I'm not opposed to the idea of there being hard or extreme difficulty tasks, Only that an opposed task against someone with the same or lower  someone with the same skill rating, shouldn't be extreme. Personally I think it makes more sense to set the rating by the relative difference in skills.

1 hour ago, Fred said:

For skills not opposed: A Hard roll for History or Occult and the player has 90%? Completely realistic, how can you know anywhere near everything?

I agree completely. If someone trying to decipher a 2000 year copy of the Necromicon  tome written in a  archaic Sanskrit it should be tough. 

1 hour ago, Fred said:

Also, usually, many players try, so it’s good the game mechanics cater for this. But if you dislike it, you can just use the disadvantage instead and players with 90% will almost always make it. So also in the Spot example you gave, if you want to soften it, offer disadvantage instead of halving it. Or just do opposed like Josh777. So easy.
But you don’t like the concepts. OK, OK.

I don't like the consequences of those concepts. Not only does it give the players a false sense of thier own competence, but they have no way of knowing what they are in for until it's too late. 

1 hour ago, Fred said:

I agree with everything Tranquillitas Ordinis mentioned, an especially good point about achieving the difficult feel of a game like this.

I don't agree with everything. The stark reality is that the laws of probability still continue to function at the gaming table. Players still make decisions about what they do based upon their understanding of what they believe will work and what won't. CoC is pretty bleak as it is without needing to up the ante for the players. 

1 hour ago, Fred said:

Fortunately, a lot of the material is very easily adaptable. Since I have no ambition of convincing you of anything, and listening to your arguments I already know where you are coming from and disagree, instead of debating over this, I definitely wish you the best of luck in gaming.

Okay, same to you, except then why do you put that after trying to continue on with your argument? If you are going to debate a point with someone you actually need to listen to the other side, otherwise there is no debate or discussion. 

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The nerdly cultural obsession with "canon" is an interesting aspect of our hobby.

I've gamed with a lot of people, and in that time I've met many an enthusiast that get visibly upset when they aren't "on the side of canon." They treat the RAW as a sacred thing. "If its in the RAW, it must be 'right,' and if it isn't my perspective, the RAW's wrong."  It strikes me as a need for belonging. A need for the "official authority" to jive with personal perspective. People will sometimes take derivations that don't jive with their personal beliefs of fairness personally (that is not a comment on Joshua's original question...it is never wrong to question.)

The truth is that there is nothing sacred about the RAW. It is what the human designers did with a human creation at a time when they decided they were finished with playtesting and editing. In CoC Paul et al decided to have a tiered difficulty setting system rather than strict arithmetic comparison of rolls. And it fits the setting. If you are "world-class good" at something, it should be all the harder for someone to avoid your experienced and skillful eye.

What is the real surprise to me is the continual raging that some people continue to have over 7th. Its just getting so boring. We get it. A designer took a different direction than you would have. The ship has sailed. The complaining doesn't accomplish anything other than continuing to poison the well of the fandom. Its hard to justify why someone would be so upset about something that they feel the need to ruin it for everybody else.

Edited by klecser
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1 hour ago, Atgxtg said:

I don't agree with everything. The stark reality is that the laws of probability still continue to function at the gaming table. Players still make decisions about what they do based upon their understanding of what they believe will work and what won't. CoC is pretty bleak as it is without needing to up the ante for the players. 

Dear Atgxtg, 

How can you not agree with me? This is outrageous! Anyway, you noticed an interesting thing. Players make decisions based on their understanding of what they believe will work. But what if CoC is a system where players should not believe even for a moment that what they think is correct? In some situations, even the fact that they have 90% skill means nothing. You might not like it, and I understand your position. I do not like it or dislike it, it is a rule and try to follow it due to my need of belonging.

Also, if you have players who really know the rules, they will incorporate that fact into their game and decision-making process. They will know that probabilities are low (this is the nature of the game) and will try to optimize their actions accordingly. They probably can guess that monsters are better at everything mechanics-wise, and a smart way of defeating them is needed. So I do not think this particular rule puts players in disadvantage or treats them unfairly.

57 minutes ago, klecser said:

What is the real surprise to me is the continual raging that some people continue to have over 7th. Its just getting so boring. We get it. A designer took a different direction than you would have. The ship has sailed. The complaining doesn't accomplish anything other than continuing to poison the well of the fandom. Its hard to justify why someone would be so upset about something that they feel the need to ruin it for everybody else.

Dear klecser,

I have not noticed any raging anywhere. I think that Josh777 and Atgxtg made good points, that should be considered by authors of the 7.5th or 8th edition (when it appears in 20 years time) and such critique can only help the game to be better. It is nice that Mr. Fricker took time to respond, and probably got the intention of their message. Maybe they are right, maybe they are wrong, I personally do not think it is that much of an issue, but certainly they should not be accused of "poisoning the well of the fandom" or "ruining the game for everybody else". 

14 minutes ago, Fred said:

I agree. If I disliked this edition so much I would not want it to steal time from me, posting in a forum about a game I hate. I would spend my time doing what I love instead.

Rules can’t be for everyone, of course, and I have definite sympathy for constructive suggestions or even strong opinions - I certainly share them from time to time, and debating with respect can be absolutely fine. But at some point down the line if a person hates the game, it seems for some people the whole thing  becomes an obsession where said person is bashIng a head against a brick wall in frustration. Nothing will change, and the person’s frustration won’t either. A time waste for everyone. And as you said, for some saps the interest of discussing a hobby they love.

I think some frustration comes from players being almost too used to a certain previous ruleset also. I think the choices here will win in the long run.

Dear Fred,

As I agree with you about the rules, and I think you made several great remarks, why do you assume they hate the game, or that they are too used to the previous ruleset? We can not know that. I read the messages by Atgxtg and feel like I need to defend him/her, because his/her intentions seem to be somewhat misinterpreted. There is no need to judge anyone or to discourage from expressing their (sometimes harsh) opinions.

Edited by Tranquillitas Ordinis
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And I don't mind people disagreeing at all. There are certainly aspects of CoC (any version) I liked from the beginning, grew to love, or have never liked. People hate change. That is an immutable fact. I've worked in a profession for 18 years now and no matter how logical or beneficial some changes are, there will always be people immediately opposed to any change. One of my favorite game-related quotes of the past: "If boosters were filled with hundred-dollar bills, people would complain about how they were folded."

4 minutes ago, Fred said:

In regards to the hatred: See the above comment - “so repulsed by it he plays an earlier edition.” 😉 

And that you all get to hear about that repulsion...over and over and over and over and over again...

I don't come here to be people's therapists or punching bags. Which is why I have a hefty Ignore list.

Back on topic, I'm really glad that @Josh777 posted this thread, because it gives some of us another opportunity to hear insight from a game designer ( @Paul Fricker ) about the hithertos and why-fores of the design process. Like the final decision or not, I find the discussion of the choices fascinating.  

Edited by klecser
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The game possesses two means to deal with this:

a) adjust difficulty of player roll based on skill of opponent, which is given priority in the rules as it streamlines play, with a single roll being made by the player.

b) make an opposed roll, with both player and Keeper making rolls and comparing the results. Apply bonus/penalty dice if necessary.

Option B is available to use wherever the Keeper feels it works best, and it does even the playing field where high skill values come into play. 

 

Edited by Mike M
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I dropped the "NPC skill adjusts PC skill" rule almost immediately; it's one of only two rules that I discarded for my table*. In its place, I just use opposed skill rolls for everything (as per Mike M's comment above), and couldn't be happier with that approach.

* The other is "ties go to the higher ability". Instead, I have "ties go to the contestant with the best (lowest) roll".

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8 hours ago, Tranquillitas Ordinis said:

Dear Atgxtg, 

How can you not agree with me?

 

8 hours ago, Tranquillitas Ordinis said:

 

This is outrageous!

Inconcieable!

 

8 hours ago, Tranquillitas Ordinis said:

Anyway, you noticed an interesting thing. Players make decisions based on their understanding of what they believe will work.

Of coruse. It's really the only they they can do. 

8 hours ago, Tranquillitas Ordinis said:

But what if CoC is a system where players should not believe even for a moment that what they think is correct? In some situations, even the fact that they have 90% skill means nothing.

Then it is a broken system. The whole point of a RPG is allow players to do things than have meaning, and a game where their abilities mean nothing id pointless. It's not like CoC was alwalys this way. It was changed to streamline the rules. Now, I mentioned this rule to one of my players ealier today and the resonse from her was "Why bother wring up a character and  playing?"

8 hours ago, Tranquillitas Ordinis said:

You might not like it, and I understand your position. I do not like it or dislike it, it is a rule and try to follow it due to my need of belonging.

I think it's a bad way to write up and run an RPG. I believe there were better ways to handle an opposed task.If I were to run that rule my players would all quit the campaign, and I can't say as I blame them. 

8 hours ago, Tranquillitas Ordinis said:

Also, if you have players who really know the rules, they will incorporate that fact into their game and decision-making process. They will know that probabilities are low (this is the nature of the game) and will try to optimize their actions accordingly.

Players who know the rules just say "$%^# that! Let's play something else." And yes, that is a somewhat censored quote from one of my players. 

8 hours ago, Tranquillitas Ordinis said:

They probably can guess that monsters are better at everything mechanics-wise, and a smart way of defeating them is needed. So I do not think this particular rule puts players in disadvantage or treats them unfairly.

Of course it does. Look we aren't talking about Shoogoths or some such here. We are talking about any normal NPC with a skill score past a certain threshold. 

For example, let's say that an Investigator has Chess at 90% skill and is a Master. He plays a match against a decent player who has a 50% skill and only has a 45% chance of winning. That is a textbook example of a "particular rule puts players in disadvantage or treats them unfairly."

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6 hours ago, Mike M said:

The game possesses two means to deal with this:

a) adjust difficulty of player roll based on skill of opponent, which is given priority in the rules as it streamlines play, with a single roll being made by the player.

b) make an opposed roll, with both player and Keeper making rolls and comparing the results. Apply bonus/penalty dice if necessary.

Option B is available to use wherever the Keeper feels it works best, and it does even the playing field where high skill values come into play. 

 

Sorry Mike, nothing personal but I honestly cannot not think of a single situation where I'd consider Option A to be a viable option. 

I have nothing against Fred either. I just think it's a bad rule. 

 

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5 hours ago, trystero said:

* The other is "ties go to the higher ability". Instead, I have "ties go to the contestant with the best (lowest) roll".

Thank's for mentioning that. I've been advocating that approach to handle opposed rolls in BRP for years, but people claim that it favors the lower skilled character. The math indicates that it doesn't, and that most people focus on one subset of the possible outcomes." It's kinda like if the guy with a 05% skill rolls an 01 it's unfair to the guy with a 99% skill because he has no way of winning. 

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12 hours ago, Fred said:

It’s a fair and easy change. I always house rule a few things myself. Adapting both to my taste and my players. I hope they keep both those options to handle it in later editions for flexibility. This in combination with advantage/disadvantage mechanics makes it smooth.

Flexibility is the key. Every table is different and every group of people have their own interpretations of what is fair and fun.

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9 minutes ago, Closterphobia said:

This is really the best response to all RPG rule arguments.

It is just a shame that, for some people, the idea of someone else finding fun in different ways than them is just untenable. 

Josh777 started the thread with a critical premise: That they/their players don't find as much fun in the rule of increased difficulty for high NPC skill. I hope they've found the discussion interesting, but if they ultimately decide to ditch the rule and their games are more fun, then it's a win.

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17 hours ago, Atgxtg said:

For example, let's say that an Investigator has Chess at 90% skill and is a Master. He plays a match against a decent player who has a 50% skill and only has a 45% chance of winning. That is a textbook example of a "particular rule puts players in disadvantage or treats them unfairly."

Dear Atgxtg,

This one paragraph was able to convince me. How did you know that I am a vivid chess lover? Indeed, the situation you describe does not look right—I was stupid not to think about that.

But we can not just agree which each other and stop here; the best solution to the problem needs to be found. Therefore, I decided to do some research, trying to answer several questions:

  1. What is a reasonable skill measure/ scale, that allows to compare effectively characters of different skill level?
  2. Can "difficulty level" system be corrected to give more sensible outcome? If yes, how?
  3. Does "opposed rolls" system give more sensible outcomes? If not, can it be corrected?

I have to warn potential readers: I anticipate this might be a long message, with some (rough) math involved. It will not be very rigorous, but I hope it may be interesting. There is a considerable chance it is all wrong. It was done for fun, but took me a lot of time, during which I should have done other work. Moreover, this is obviously highly original research, to which I claim authorship, and if someone knows how I could make some money on this, please let me know... because I like money.

Ad. 1: The first question is simple. Let us indeed use the Elo rating system, which is used in professional chess.

If you are not familiar with the Elo system, here is the Wikipedia page: Elo rating system and a short article: Math of Elo rating. Short story is: it tries to assign the "rating" (skill level) to players, based on the probabilities with which stronger players win against weaker players. It is exactly what we need. We want to use not only the Elo rating system, but also the data set of chess players and their ratings, to estimate how a particular "skill" is distributed in population. Why the data set of chess players? Because it is huge and mostly reliable*. It can be found here: FIDE ratings. Below is the histogram of rating vs. number of players distribution.

plot1.png.c5904a61b5a66ea7f3a8791cf9b2f7c3.png

As you can see, it is not a Gaussian (Normal) distribution. This is due to several factors: 1) the way new players are gaining their rating, which is related to FIDE rules, 2) the fact that there are two groups represented here: people who I would call "professionals" and "amateurs", 3) There is no negative ratings, so Gaussian distribution will fail to reproduce these values anyway. There is also a large number of people who play chess, and are quite decent, that are not FIDE members. There is an even larger group of people who do not know how to play chess at all. But too keep things simple, let us assume that this data set (of over 350,000 rated players) represents accurately the distribution of skill in society. Also, because we do not want to make things too complicated again, let us use double Gaussian distribution to parametrize this data set.

plot2.png.c1fda9c3ecf628af16a4923f6e7deeec.png

As can be seen from above histogram, the double Gaussian does not work perfectly, but let us not be too picky—it gives more or less a good estimate. We see that Chess (as any other specialized intellectual pursuit like: Anthropology, Biology, Library Use, Accounting etc.) has both "Professional" and "Amateur" participants. There are less Amateurs than Professionals, and they are worse on average. Now, we want to find the relation between the rating of a player and a the player's percentile. The players percentile will be used as a skill value in CoC. This way we will establish the correspondence between the Elo rating and CoC Skill value. Indeed, knowing the functional form of the "Overall fit" we can easily make the following plot and an example conversion table:

plot3.png.849be636bdbf5c6e635362a9ae0da8e3.png            table1.png.1ed3f2f59faf682075db6f4f96e7a0f5.png

Now, there may appear objections that the distribution of the "Chess Skill", or how just the "Chess Skill" works in real life, is very different e.g. from "Drive Auto Skill", so that using Elo system, and particularly a data set of chess players, as a criterion of "sensibility" that applies to every skill in a RPG is wrong. In other words: why distribution of skill among chess players should be the same as a distribution of skill among Firearms users? It is a valid point, but taking that into account (and correcting all other approximations that were made here) would take me too much time. Anyway, knowing the conversion rule we can use the Elo formula that tells you the percentage chance of winning based on the rating difference between you and your opponent. Now, there is another problem: in CoC we usually compare two different skills and not the same one. But since we already assumed that all skills are distributed in the same way, it is not really an issue. As we can already see from the table, we might expect a non-trivial conclusions. If you know something about chess, you probably expect a 2600 Elo player to win 100% times against 1900 player. That means that a character with 100% CoC skill value should almost always win against a character with 70-75% skill value. This is not how people commonly understand the skill differences in RPG, because we unconsciously assume that "skill" is distributed "uniformly" among people and not according to something like Gaussian distribution. To better illustrate this, below is a table where a chance of winning for (H)igher rated player and (L)ower rated player is compared against their rating difference (I found it here: Chess forum)

446794300_Table2.jpeg.2dddcf5851fa19dac4057ac6ad174de0.jpeg

Last point. In Chess we have three possible outcomes: Success, Failure and Draw. In chess the percentage of a draw (especially in the case of professionals) is non-negligible. In CoC ties can be ignored, and we basically have only either Success or Failure. The Elo system takes that into account, by considering a draw as a 0.5*Success. Meaning that if we look e.g. at rating difference 092-098 in the above table, the higher rated player will win on average 63 points in a match of 100 games, where a win is equal to 1 point and draw to 0.5 points. I think this represents the normal situation in CoC pretty well: since draw (meaning that nothing good/ bad happens) about 50% of the time make players happy (so it is a success) and 50% of the time unhappy (so it is a failure). Again it is a very rough estimate, more careful analysis could introduce some corrections.

Finally, let us introduce three characters: "Mr. Dumb" (skill level 10%), "Mr. Average" (skill level 50%) and "Mr. Genius" (skill level 90%) and ask a question: how would they do against an NPC with a skill level X%? In other words: what is their chance of winning? We use the master formula of the Elo rating, the conversion table given above, and we get the following plot:

plot4.png.78541243f52c6b3690a545165e441dd0.png Let us call it the "Realistic" Plot.

As can be seen, Mr. Genius should not have any problems winning with his opponent most of the time, unless the opponent has the skill 80-90% and above. For example, if your character has skill level 90%, he should win 90% of the time with 70% skill level opponent. For Mr. Average the probability looks more or less linearly, while Mr. Dumb has less than 20% chance of winning when his opponent has skill 30% and above. We see that the difficulty level is different for characters of different skills. To conclude, I think this chart looks reasonable, and more importantly—it is based on reality, in a sense that we took real data containing the distribution of skill among chess players, made several simplifying assumptions and converted these data into a skill scale used in CoC. Now we can move to other questions.

Ad. 2 Can the "difficulty level" based system reproduce the last plot?

Probably not, but maybe it could be improved easily? Let us ask the same question: using the 7ed CoC rules, what is the chance of Mr. Dumb, Mr. Average, Mr. Genius winning against their opponent, if he has skill value X%? It is not difficult to obtain the following plot:

plot5.png.ca094c043a5d8749a46c0304f734d7e0.pngLet us call this a "Difficulty level" plot.

We see that we obtain a rather big discrepancy with the "realistic plot". That means "Difficulty level" system is bad. But let us look at some interesting features more closely:

  • The "Difficulty level" system can (roughly speaking) still predict the outcome of a confrontation with a very skillful opponent pretty well. It gives numbers comparable with the realistic plot, for opponents with skills 90% and more for Mr. Dumb and Mr. Average, and for opponents with skill 95% and more for Mr. Genius. In other words, the problem mentioned at the beginning by Josh777 (opponents with skills 90% and above having too much advantage) is not as serious as one could have thought.
  • However, in the "difficulty level" system the most skillful characters are somewhat mistreated. On the realistic plot Mr. Genius has 50% chance of winning with a 90% skill opponent, while in the "difficulty level" system he has only 18%. Almost 3 times less.
  • The confrontation of Mr. Genius with much less skilled opponent, and confrontation of Mr. Dumb with more skilled opponent are predicted relatively well by the "difficulty level" model. Other cases are predicted badly. Mr. Average gets too much disadvantage when fighting with less skilled opponents, and somewhat big advantage when fighting with much more skilled opponents.

Now, can this system be improved? I seek the simplest improvement possible, so that almost no math is required from the players during the actual CoC game session. One idea would be to introduce an "Easy difficulty level". Let us say we would now had four levels: "Easy" (1-30), "Regular"(31-60), "Hard"(61-90) and "Extreme" (91-100). When a Keeper requires an "Easy success" a Player must roll below Skill + Skill/2. Such a rule would produce an outcome that looks quite promising.

plot6.png.3a8a2a25c860543c960d0360b86d4a6b.png"Improved Difficluty level" system.

It is still not perfect, but it is hard to achieve a great improvement under a constraint of simplicity. Let us then leave this point and move to the "Opposed rolls" system.

Ad. 3 Does "opposed rolls" system give more sensible outcomes?

"Opposed rolls" system is more complicated mathematically. We have two random variables: roll outcome of PC and roll outcome of NPC. Also we do not compare rolled values, but rather achieved success levels. For simplicity I ignore fumbles, criticals, this should not change the result too much. If the levels of success are the same, the person with higher skill level wins. After doing some math—it is a basic probability tree, but I do not want to describe it here—we obtain a plot:

plot7.png.d01f07143180e67fba2232499c0309d3.png"Opposed rolls" system.

Several remarks are in place:

  • "Opposed rolls" system gives generally better outcome than the "Difficulty level" system and comparable results with the "Improved Difficulty Level" system.
  • The main feature of this system is the discontinuity that happens between two regions: a) region where opponent has better skill and b) region where opponent has worse skill. This discontinuity is of the order of 80% for Mr. Dumb and 40% for Mr. Average and Genius. This implies that if we are confronted with a weaker opponent we have much better chance of winning (we have an advantage compared to the "realistic" system), but when confronted with the stronger opponent, our chances suddenly go down (Even if the opponent is just 1-2% skill above us!)
  • The main discrepancy, compared to the "realistic system", is that weak characters have much less chance of achieving success than in "real" life. "Opposed rolls" system does not seem to mistreat strong characters too much, but certainly puts characters without skills in a clear disadvantage.

Again, the question is, if above plot could be improved easily. Introducing another difficulty level does not change anything. However, there already is a rule of "Bonus" and "Penalty" dice, which allows Keeper to somewhat adjust chances. Let us focus on "Mr. Dumb" case (because he is the one who suffers the most) and see how his chances improve, if his opponent is given a penalty dice. This introduces a third random variable, and makes math slightly more complicated. See the plot below for the result:

plot8.png.e667de383354d2900d8af70630c9a0d3.pngHow giving penalty dice to his opponent changes the fate of Mr. Dumb.

It does not look much better in my opinion, which is a little suspicious. I hope I have not made any stupid mistake in my calculations. If someone could check this results I would appreciate that. Anyway, it seems that opposed skill system, in which achieving the same success level means the person with better skill value wins, seriously disadvantages weak characters, even if corrected with the penalty dice system. This is a little troubling, and I need more time to: a) check my calculations, b) see if I can come up with an improvement for the "opposed roll" system.

To conclude:

  • I hope you find this message interesting. There are severe simplifications here and there, but I think that general conclusions would still hold even if someone did more careful analysis.
  • The "difficulty level" system does not reproduce "reality" accurately. It has some weak and strong points (see above), but can be improved easily.
  • The "Opposed rolls" system works better, however it puts weak characters in disadvantage. "Penalty" dice for the opponent does improve situation, but not much.
  • Therefore, it seems that, indeed, the skill roll system in CoC 7ed fails to justly deal with some situations. Before checking that myself I had a completely different impression, but I have not really paid any serious attention to outcomes of all rolls during my games. 
  • I guess this means that either: a) GMs need to do more work to avoid harming or killing characters and still play according to rules, or b) everyone has to accept that the game is a little bit harder, c) GM has to stop paying attention to the rolls outcomes and in consequence has to break the rules of the game. It is ok, but I would be pretty upset if I was a creator of the game, where players have to forget about rules to have fun. 
  • I personally choose option b), i.e. I play according to the rules because I like when the game is hard and my players accept that. I still like CoC rules, and enjoy the game.
Edited by Tranquillitas Ordinis
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8 hours ago, Closterphobia said:

This is really the best response to all RPG rule arguments.

Dear Closterphobia,

I do not think this is true. Of course that different players and groups like different things, and RPGs are for fun, and if they have fun then everything is ok. But it does not mean that rules should not be judged based on some objective criteria or common sense. Rules should increase fun, but also should be sensible. And rules matter—we all have these rulebooks for something, don't we? If I saw a sentence in a rulebook which says: "After each critical success Keeper buys ice cream for everybody and makes 100 push-ups and then every character takes 15 HP damage" I would laugh at person who says "It is ok, there are different groups and different players". No, I would simply call such rule ridiculous. Does it mean that I criticize other people? No it does not. Does it mean that (as klecser wrote later) for me the idea of someone else finding fun in different ways than me is untenable? No, it does not. It just means that I believe there is an objective criterion for "good" and "bad" rules, and I judge them accordingly.

I enjoy immensely CoC rules, but now it seems understandable to me when someone decides to criticize them. I think it can only make the game better.

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Okay Tranquillitas Ordinis, I'll play...

4 hours ago, Tranquillitas Ordinis said:

Dear Atgxtg,

This one paragraph was able to convince me. How did you know that I am a vivid chess lover? Indeed, the situation you describe does not look right—I was stupid not to think about

First off I used chess as an example. We could just as easily pick any other tasks that could be covered by a skill in the game. Move Quietly vs. Spot, Driving vs. Driving whatever. 

Fundamentally the problem here is that the better skilled character is going to loose more often that not to a lower skilled NPC. That result doesn't just  "not look right", it isn't right. Both from a mathematical standpoint, and from a game play standpoint. Now you can jump through all sorts of hoops, try to rephase things, or deflct thing by obfuscation, but the simple fact remains that when, everything else being equally,  the higher skilled character, especially  a player characters, is at disadvantage against a lower skilled character, it's a bad game rule. 

 

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But we can not just agree which each other and stop here; the best solution to the problem needs to be found.

Nice bit a sarcasm there. We don't not need to find a best solution, but we certainly have a better solutions available, namely the task resolution method used in virtually any other RPG. Can you think of any other RPG where the higher skilled character has a lower chance of winning in a skill based contest than the lower skilled opponent?

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 Therefore, I decided to do some research, trying to answer several questions:

Good idea.

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  1. What is a reasonable skill measure/ scale, that allows to compare effectively characters of different skill level?

THat is a good question, and one which 

 

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  1. Now, we want to find the relation between the rating of a player and a the player's percentile. The players percentile will be used as a skill value in CoC. This way we will establish the correspondence between the Elo rating and CoC Skill value. Indeed, knowing the functional form of the "Overall fit" we can easily make the following plot and an example conversion table:

Is a flawed comparison percentile grading relative to other people isn't not necessary the same as success chance. If it were then half people firing a gun would miss the target half the time because they were in the lower 50% percentile, half the people taking their driver's test would fail and so on. All percentile grading does is measure a persona's ability reative to the general population.

Nor is the relative distribution of skill in chess among the populace necessarily indicative of relative ability. Since the vast majority of people in the world don't play chess, the statistical mean would put the average rating much lower than what your have on your table. THat average person doesn't have anywhere near an ELO rating of 1650, but are unrated and play that way. 

 

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Now, there may appear objections that the distribution of the "Chess Skill", or how just the "Chess Skill" works in real life, is very different e.g. from "Drive Auto Skill", so that using Elo system, and particularly a data set of chess players, as a criterion of "sensibility" that applies to every skill in a RPG is wrong. In other words: why distribution of skill among chess players should be the same as a distribution of skill among Firearms users? It is a valid point, but taking that into account (and correcting all other approximations that were made here) would take me too much time.

A pity, it might be the only useful and constructive part of your apparent attempt to prove your point by trying to belittle mine. 

Basically your whole argument is that you don't care if the odds favor the NPCs over the characters and that is it somehow silly if other people do. I respond with if these values and result aren't important, why bother having them in the first place? 

 

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Anyway, knowing the conversion rule we can use the Elo formula that tells you the percentage chance of winning based on the rating difference between you and your opponent. Now, there is another problem: in CoC we usually compare two different skills and not the same one. But since we already assumed that all skills are distributed in the same way, it is not really an issue.

Actually is is an issue. But not with the skill percentages buy with your method of linking skill percentage to ELO.  In COC and other BRP games, skills are rated on the same scale. That's why someone with Sword 60% can skill parry an Axe at 60%, as well as another Sword, mace, or spear. To some extent that is a necessary abstraction required to make a game.

 

Not quite. I don't think people expect someone with a 50% skill to win half or a third the time when facing an oppoent with 100% skill. They certinaly don't expect someone with a 90% skill to lose most of the time against a person with a 50% skill. 

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Last point. In Chess we have three possible outcomes: Success, Failure and Draw. In chess the percentage of a draw (especially in the case of professionals) is non-negligible. I

QUite true there. In Chess, getting a draw is both easier that a win, and is also better than a loss, so often players will play for a draw. 

 

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As can be seen, Mr. Genius should not have any problems winning with his opponent most of the time, unless the opponent has the skill 80-90% and above. For example, if your character has skill level 90%, he should win 90% of the time with 70% skill level opponent. For Mr. Average the probability looks more or less linearly, while Mr. Dumb has less than 20% chance of winning when his opponent has skill 30% and above. We see that the difficulty level is different for characters of different skills. This chart looks reasonable, and is based on reality, in a sense that we took real data for the distribution of skill for chess players, made several simplifying assumptions and converted these data into a skill scale used in CoC. Now we can move to other questions.

 

 

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Ad. 2 Can the "difficulty level" based system reproduce the last plot?

  • The "Difficulty level" system can (roughly speaking) predict the outcome of a confrontation with a very skillful opponent pretty well. It gives numbers comparable with the realistic plot, for opponents with skills 90% and more for Mr. Dumb and Mr. Average, and for opponents with skill 95% and more for Mr. Genius. In other words, the problem mentioned at the beginning by Josh (opponents with skills 90% and above having too much advantage) is not as serious as one could have thought.

No, it doesn't. With an opposed roll the 90% skilled PC would beat the 50% skill NPC most of the time. With the difficult scale, he doesn't. So it doesn't predict the results "pretty well" at all. In fact it does a really bad job of it. 

 

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  • However, in the "difficulty level" system the most skillful characters are somewhat mistreated. On the realistic plot Mr. Genius has 50% chance of winning with a 90% skill opponent, while in the "difficulty level" system he has only 18%. Almost 3 times less.

He also only have a 45% against a opponent with skill 50, where with an opposed roll he'd have a significant advantage and win over 75% of the time.

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  • The confrontation of Mr. Genius with less skilled opponent, and confrontation of Mr. Dumb with more skilled opponent are predicted relatively well by the "difficulty level" model. Other cases are predicted badly. Mr. Average gets too much disadvantage when fighting with less skilled opponents, and somewhat big advantage when fighting with much more skilled opponents.

No. Mr. Genius vs even a 50% are not predicted relatively well by the Difficulty level. So the difficulty level method only works well for Mr. Dumb.

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Now, can this system be improved? I seek the simplest improvement possible, so that almost no math is required from the players during the actual CoC game session.

It is still not perfect, but it is hard to achieve a great improvement under a constraint of simplicity. Let us then leave this point and move to the "Opposed rolls" system.

What if you rated the difficulty not by the absolute value of the NPCs skill, but in the relative skill ratings?

For instance, lets say that if the skills are within 20% of each other the player needs a hard (1/2 skill) roll to succeeds, and we shift the difficulty up on down one step per 20% difference in skill? I think you'd find the results to be an improvement over the current method. Then the odds would be closer to what they should be. They wouldn't be perfect, but they'd be better than what we get with the difficulty method.

 

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Ad. 3 Does "opposed rolls" system give more sensible outcomes?

Several remarks are in place:

  • "Opposed rolls" system gives generally better outcome than the "Difficulty level" system and comparable results with the "Improved Difficulty Level" system.

Which right there reveals that opposed rolls give better results than difficulty levels.Thanks for proving my point.

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  • The main feature of this system is the discontinuity that happens between two regions: a) region where opponent has better skill and b) region where opponent has worse skill. This discontinuity is of the order of 80% for Mr. Dumb and 40% for Mr. Average and Genius. This implies that if we are confronted with a weaker opponent we have much better chance of winning (we have an advantage compared to the "realistic" system), but when confronted with the stronger opponent, our chances suddenly go down (Even if the opponent is just 1-2% skill above us!)

Yes that's another result of simplification, in that the higher skilled character wins on tied success levels. This means that a 50 vs 51 results in the lower skilled character needed to roll a higher success to win, greatly reducing their chances. Frankly I'm not thrilled with that either, but at least it still favors the higher skilled players against a lower skilled NPC. Some improvement is better than none.

 

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  • The main discrepancy, compared to the "realistic system" is that weak characters have much less chance of achieving success than in "real" life. "Opposed rolls" system does not seem to mistreat strong characters too much, but certainly puts characters without skills in a clear disadvantage.

Your "realistic" system was only realistic in terms of chess. Not in terms of other conflict.  Now, yes in the game all skills are treated fairly equally, but that doesn't mean the data points between contests match up. 

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It does not look much better in my opinion, which is a little suspicious. I hope I have not made any stupid mistake in my calculations.

What do you consider to be better? You don't consider a higher skilled PC to have an advantage against a lower skilled NPC to be better?

It seems to me that you don't care what the results are, you just want to do things the simplest way possible and avoid any math. 

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If someone could check this results I would appreciate that.

While I understand why you dropped criticals and such in your calculations, it does skew the results a bit. 

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Anyway, it seems that opposed skill system, in which achieving the same success level means the person with better skill value wins, seriously disadvantages weak characters, even if corrected with the penalty dice system. I need more time to: a) check my calculations, b) see if I can come up with an improvement for the "opposed roll" system.

Yes it does, and illustrates why CoC wasn't originally designed to have opposed rolls. They don't really work well in a D100 roll low system with success levels. 

 

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To conclude:

  • I hope you find this message interesting. There are severe simplifications here and there, but I think that general conclusions would still hold even if someone did more careful analysis.

I did find it interesting, although I'm not sure what conclusions you think this proves. Does it prove that the difficulty level method gives results similar to the opposed method, or is just as good? If so then I'd say they don't.

Simpler isn't necessary better.

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  • It seems that indeed, the skill roll system in CoC 7ed fails to justly deal with some situations. Before checking that myself I had a completely different impression, but I have not really paid any serious attention to outcomes of all rolls during my games. 

Again you exaggerate. It not the outcomes of "all" roll, but the general trends that you should pick up on. If you players are failing a lot of the time, desite having good skills, well, there is a good reason right there.

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  • I guess this means that either: a) GMs need to do more work to avoid harming or killing characters and still play according to rules

Or at least give the players a fair chance. I'm not say thing the player have to be better than whatever oppostion they face. I'm saying that when they are better the rules should reflect that.

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  • , or b) everyone has to accept that the game is a little bit harder,

It's not a little harder, it's a lot harder.

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  • c) GM has to stop paying attention to the rolls outcomes and in consequence has to break the rules of the game.

In which case why roll? 

Look, when a player builds a character and puts points into a skill they try to relate that to what they think their character's capabilities. Someone with a skill at 90% in something is consider to be a master, and should, in an otherwise even contest, expect to have the upper hand against a lesser skilled opponent, especially a significantly lesser skilled opponent. But, with the difficulty system, they don't. 

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  •  It is ok, but I would be pretty upset if I was a creator of the game, where players have to forget about rules to have fun. 

So tell me. How much fun is it to kill off the player characters each week? 

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  • I personally choose option b), i.e. I play according to the rules because I like when the game is hard and my players accept that.

It's beyond hard, it's misleading. The odds are against the players. Maybe you and your player like that, but I doubt most players would. CoC is already tough enough on players. Now even the cultists are guard dogs are better than the player characters.

Edited by Atgxtg
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Dear Atgxtg,

I am stunned, as it seems to me you have clearly misunderstood what I actually did or meant. And you added some unnecessarily sarcastic comments, which is surprising as I have already agreed with you, and most of the time I was proving you right.

1 hour ago, Atgxtg said:

Okay Tranquillitas Ordinis, I'll play...

My intention was not to have any argument (or game), just to have see if one can find a simple model of measuring a skill that could be applied to a RPG. Chess was the first thing that came to my mind because: a) you mentioned it, b) I love chess and know something about it.

1 hour ago, Atgxtg said:

Fundamentally the problem here is that the better skilled character is going to loose more often that not to a lower skilled NPC. That result doesn't just  "not look right", it isn't right. Both from a mathematical standpoint, and from a game play standpoint. Now you can jump through all sorts of hoops, try to rephase things, or deflct thing by obfuscation, but the simple fact remains that when, everything else being equally,  the higher skilled character, especially  a player characters, is at disadvantage against a lower skilled character, it's a bad game rule. 

I agreed with that in my post.

1 hour ago, Atgxtg said:

Nice bit a sarcasm there. We don't not need to find a best solution, but we certainly have a better solutions available, namely the task resolution method used in virtually any other RPG. Can you think of any other RPG where the higher skilled character has a lower chance of winning in a skill based contest than the lower skilled opponent?

What sarcasm?! I have not used any sarcasm anywhere, I meant exactly what I have written. You completely misinterpreted my intentions. I do not know much about other RPG systems, so I genuinely tried to approach the question of finding some good skill level measure. 

1 hour ago, Atgxtg said:

Is a flawed comparison percentile grading relative to other people isn't not necessary the same as success chance. If it were then half people firing a gun would miss the target half the time because they were in the lower 50% percentile, half the people taking their driver's test would fail and so on. All percentile grading does is measure a persona's ability reative to the general population.

I agree. "Success chance" and "percentile grading relative to other characters" are not the same things. In my model I assume that the "skill level" does not represent "success chance" but rather a value that tells you how good you are compared to others. I think it is a much better indicator of skill. I use "%" sign, which might be misleading, only because it is used in the CoC rulebook.

1 hour ago, Atgxtg said:

Nor is the relative distribution of skill in chess among the populace necessarily indicative of relative ability. Since the vast majority of people in the world don't play chess, the statistical mean would put the average rating much lower than what your have on your table. THat average person doesn't have anywhere near an ELO rating of 1650, but are unrated and play that way. 

You are right, the average chess skill would be lower, but I can only work with the data I have. But still, does it affect the result of my analysis that much, since Elo system cares only about relative differences, so therefore the position of the mean has no significance? It is rather the distribution variation that should trouble you. But even forgetting about math, I assume that the usual Investigator in CoC is not a person that belongs to the "vast majority of people". They usually have some intellectually-oriented skills which makes me believe that they can be modeled as "chess players".

1 hour ago, Atgxtg said:

A pity, it might be the only useful and constructive part of your apparent attempt to prove your point by trying to belittle mine. 

How was I trying to belittle you?! I just asked myself a question and tried to find an answer. That is all. Dear Atgxtg, you might be a little over-sensitive here. And what is  exactly my point, since I have agreed with you in the first sentence of my post?! It is the first time in my life, when I am having an argument with someone who does not see I have just agreed with them. This is comical.

1 hour ago, Atgxtg said:

Basically your whole argument is that you don't care if the odds favor the NPCs over the characters and that is it somehow silly if other people do. I respond with if these values and result aren't important, why bother having them in the first place? 

No it is not my argument. It is exactly the opposite. Read my message again carefully.

1 hour ago, Atgxtg said:

Actually is is an issue. But not with the skill percentages but with your method of linking skill percentage to ELO.  In COC and other BRP games, skills are rated on the same scale. That's why someone with Sword 60% can skill parry an Axe at 60%, as well as another Sword, mace, or spear. To some extent that is a necessary abstraction required to make a game.

Yes, I understand that, but at this point I was making my own model, completely unrelated to BRP or any other system. I claim my model is better, although it might have flaws that should be corrected and I tried to mention all of them I could see. I think that an assumption that all skill level is distributed in the same way for every skill is a necessary simplification. Otherwise everything becomes too complicated very quickly.

1 hour ago, Atgxtg said:

Not quite. I don't think people expect someone with a 50% skill to win half or a third the time when facing an oppoent with 100% skill. They certinaly don't expect someone with a 90% skill to lose most of the time against a person with a 50% skill. 

You say "Not quite" and then say something completely unrelated. I do not understand. It seems you are trying to say something about BRP again. Anyway, in my Elo-based model 50% skill does not win half or a third the time with a 100% skill. Also the 90% skill does not loose most of the time with 50% skill.

1 hour ago, Atgxtg said:

No, it doesn't. With an opposed roll the 90% skilled PC would beat the 50% skill NPC most of the time. With the difficult scale, he doesn't. So it doesn't predict the results "pretty well" at all. In fact it does a really bad job of it.

Again, look at my plots more carefully. And then read what I wrote again: "predict the outcome of a confrontation with a very skillful opponent pretty well". We are looking at x-axis values above 90. And this constant values are of the same order for "Realistic" model and "Difficulty level" system, unless you look at "Mr. Genius" line. For him we have a problem, what I also emphasize. I was not talking there about opponents of 50% skill value...

1 hour ago, Atgxtg said:

He also only have a 45% against a opponent with skill 50, where with an opposed roll he'd have a significant advantage and win over 75% of the time.

1 hour ago, Atgxtg said:

No. Mr. Genius vs even a 50% are not predicted relatively well by the Difficulty level. So the difficulty level method only works well for Mr. Dumb.

I agree with both statements. When I wrote "with less skilled opponents" in the piece that you quote, I meant "with much less skilled opponents". But I claim the "Difficulty level" method does not work well for "Mr. Dumb". He looses too many confrontations with unskilled opponents.

1 hour ago, Atgxtg said:

What if you rated the difficulty not by the absolute value of the NPCs skill, but in the relative skill ratings?

For instance, lets say that if the skills are within 20% of each other the player needs a hard (1/2 skill) roll to succeeds, and we shift the difficulty up on down one step per 20% difference in skill? I think you'd find the results to be an improvement over the current method. Then the odds would be closer to what they should be. They wouldn't be perfect, but they'd be better than what we get with the difficulty method.

Interesting idea, I will try that.

1 hour ago, Atgxtg said:

Which right there reveals that opposed rolls give better results than difficulty levels.Thanks for proving my point.

You are welcome. I was never against your point, again, I was just asking a question and trying to find an answer.

1 hour ago, Atgxtg said:

Yes that's another result of simplification, in that the higher skilled character wins on tied success levels. This means that a 50 vs 51 results in the lower skilled character needed to roll a higher success to win, greatly reducing their chances. Frankly I'm not thrilled with that either, but at least it still favors the higher skilled players against a lower skilled NPC. Some improvement is better than none.

Yes, this behavior comes from the way the ties are decided. But this was not any simplification on my part, this is an actual rule in the 7th ed. CoC rulebook.

1 hour ago, Atgxtg said:

Your "realistic" system was only realistic in terms of chess. Not in terms of other conflict.  Now, yes in the game all skills are treated fairly equally, but that doesn't mean the data points between contests match up.

How do you know that Elo system would not be a good rating system for other competitions? If you say that it would not, that means you have some idea of a good system in your mind. If so, what are the criteria that this better system must meet? And are you sure these criteria are not met by the Elo system? Also, the data set of chess players might not be perfect, but since the Elo system compares the relative strength of participants in a given field, it is quite agnostic with respect to several features of the skill distribution. This may justify usage of the FIDE statistics.

1 hour ago, Atgxtg said:

What do you consider to be better? You don't consider a higher skilled PC to have an advantage against a lower skilled NPC to be better?

It seems to me that you don't care what the results are, you just want to do things the simplest way possible and avoid any math. 

I meant that I expected that adding penalty dice would improve more the fate of Mr. Dumb, since up to around 40% of opponents skill level the "Opposed roll" system is unfair for him. The "Realistic" system gives him better chances and I believe it is correct.

And I apologize for not doing it at the level of PhD or 4-months math research project. I was trying to make crude approximations, but not too simple, so that everything would still seem to make sense. I was also not trying to avoid any math—this is probably the most untrue statement of all. I was just trying to avoid spending several days writing a post on a RPG forum that no one would read or consider seriously anyway. Look at these beautiful plots that I created! Why no one appreciates them!?

1 hour ago, Atgxtg said:

I did find it interesting, although I'm not sure what conclusions you think this proves. Does it prove that the difficulty level method gives results similar to the opposed method, or is just as good? If so then I'd say they don't.

My conclusion is: both "difficulty level" and "opposed rolls" are unsatisfactory. "Opposed rolls" method is better, but probably the "difficulty level" method is simpler to be improved, if someone in the future will consider making the 8th ed. of CoC. But I might be wrong, this problem probably require more serious attempts.

1 hour ago, Atgxtg said:

Simpler isn't necessary better.

Thank you master for this valuable lesson.

1 hour ago, Atgxtg said:

Again you exxagerate. It not the outcomes of "all" roll, but the general trends that you should pick up on. If you players are failing a lot of the time, desite having good skills, well, there is a good reason right there.

I meant that I need to look at all rolls to have a large enough data set to make any reliable conclusion about the game statistics. Even during a single sessions there is not enough rolls. Therefore, I do not exaggerate. Trends can be misleading, if one does not put them in a larger picture—there are plenty of beautiful paradoxes in statistics that prove that.

1 hour ago, Atgxtg said:

In which case why roll? 

I agree with that.

1 hour ago, Atgxtg said:

Look, when a player builds a character and puts points into a skill they try to relate that to what they think their character's capabilities. Someone with a skill at 90% in something is consider to be a master, and should, in an otherwise even contest, expect to have the upper hand against a lesser skilled opponent, especially a significantly lesser skilled opponent. But, with the difficulty system, they don't.

I agree, they do not, and I do not like that (as I have already mentioned before).

1 hour ago, Atgxtg said:

It's beyond hard, it's misleading. The odds are against the players. Maybe you and your player like that, but I doubt most players would. CoC is already tough enough on players. Now even the cultists are guard dogs are better than the player characters.

I agree it is misleading. I agree that the odds are against the players. I would saw it as a problem, if someone asked me an abstract question: "Do you consider this rule to be objectively good?". But to be honest I have never noticed it, in an actual game, playing with my players, posing any problems, or making the game less fun. Maybe it is because I did unconsciously (or consciously) some work to level the threats during the game? Or maybe all these numbers are misleading, and can not grasp something greater, something beyond probabilities and math, that CoC rules are able to create in the real experience of the game? I do not know. 

Edited by Tranquillitas Ordinis
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