Probability Myopia/Skill Analysis for Opposed Tests

[Decurio]

Thanks to the RQ Math Squad for proving what I knew/suspected all along.

Thanks guys!

When analyzing any given system, its all too easy to focus on one element and ignore the greater whole-and not mean to do it. Hell, I've done it.

You know, you really should have RQ Math Squad T-shirts made up or something...

 

[Rurik]

So the end result is that with all probabilities figured, it works out fine ?
Awesome.

Thanks Decurio for putting the thought into that and bringing up the issue!

Thanks Blujay and King for working up the equations.

Unless I missed something, the end result is that the odds are pretty much the same as they were before this thread started. A lot of math went back and forth, and in the end BlueJays calculator works.

Or am I missing something?

 

[bluejay]

Yes, Rurik I think that is the upshot.

 

[King Amenjar]

Yep - my spreadsheet now agrees with Bluejay's calculator page (except I don't take into account the tiny chance that both characters roll the same number when it gives them the same result) and it seems the conclusion is that at low skill levels, things are more evenly matched, but at high skill levels the difference is emphasised, e.g. 40% vs 15% is roughly 53/47 odds but 90% vs 75% - the same 15% edge - gives a more weighted 62/38.

 

[Rurik]

Yep - my spreadsheet now agrees with Bluejay's calculator page (except I don't take into account the tiny chance that both characters roll the same number when it gives them the same result) and it seems the conclusion is that at low skill levels, things are more evenly matched than at high skill levels the difference is emphasised, e.g. 40% vs 15% is roughly 53/47 odds but 90% vs 75% - the same 15% edge - gives a more weighted 62/38.

Actually 40 vs. 15 is a 25 point difference. But I think you used the right numbers (40 vs. 25) in your spreadsheet, as it gives the split you mentioned.

But the math guys agree, the opposed rolls definately have a funky curve.

 

[Rurik]

While you two are comparing numbers would it be easy to flip the "both players fail low roll wins" to "both players fail high roll wins" - does that help the curve or would that over favor the higher skill?

 

[bluejay]

Well I think that one thing KA has neatly shown here is that (in these cases where both characters succeed or both fail) if you remove the chance of a tie, whether rolling higher or lower, it is just a 50/50 chance.

The only thing that particularly matters is the difference between one skill and the other. That is effectively the 'edge' one character gets over the other (in the case that both characters succeed on their roll). Everything else is 50/50.

So, to use KA's idea again, think of it like this.

If A has 40% chance and B has 15% chance, then if both roll 15% or less it's 50/50 no matter whether it's lowest wins or highest wins. If both roll over 40% then it's 50/50 again. The real edge is for A to roll between 15 and 40 'cause then B can't beat him.

 

[Rurik]

Well I think that one thing KA has neatly shown here is that (in these cases where both characters succeed or both fail) if you remove the chance of a tie, whether rolling higher or lower, it is just a 50/50 chance.

The only thing that particularly matters is the difference between one skill and the other. That is effectively the 'edge' one character gets over the other (in the case that both characters succeed on their roll). Everything else is 50/50.

So, to use KA's idea again, think of it like this.

If A has 40% chance and B has 15% chance, then if both roll 15% or less it's 50/50 no matter whether it's lowest wins or highest wins. If both roll over 40% then it's 50/50 again. The real edge is for A to roll between 15 and 40 'cause then B can't beat him.

That can't be right - what you are saying is that 15% advantage should give the same odds whether the skill is 75 to 60 or 30 to 15, but the calculator does not show this, nor does KA's example a few posts above this.

Or am I just being thick?

 

[bluejay]

Ah, no what I said above wasn't the complete picture. If you notice in the post I added little comments in brackets to clarify.

I was only talking about the situations which you had specified (i.e. both characters succeed or both characters fail). This doesn't take into account the situation where one succeeds and the other fails.

 

[Rurik]

If A has 40% chance and B has 15% chance, then if both roll 15% or less it's 50/50 no matter whether it's lowest wins or highest wins. If both roll over 40% then it's 50/50 again. The real edge is for A to roll between 15 and 40 'cause then B can't beat him.

Could the "anomoly" be that if A rolls above 40, B has cannot lose if he rolls 40 or less, not 15 or less. He has a safe zone between 40 and 15 where he cannot lose even though he failed his roll, and would win on a 15 or less because he suceeded?

I think this makes sense, because B's ability to get a 'safe zone' of a range of 25 depnds on A failing, so that explains why A has a greater chance overall than B when the contest when it is 90 vs. 65 than 40 vs. 15.

 

[Rurik]

Never mind, you just covered that.

 

[bluejay]

Sort of... basically it is down to the higher chance of A failing so in that respect you are correct.

 

[Rurik]

Sort of... basically it is down to the higher chance of A failing so in that respect you are correct.

Yeah, it was kinda coming to me as I was typing, so it came out kinda fuggly, but I think I got it.

The thing that is a bit odd is that a character with a 45 vs. 15 has 300% of the defenders skill, but would have worse odds than a 90 vs. 60, though that is only 150% of the defenders skill.

Oh well, thanks for the hard work!

 

[atgxtg]

Sort of... basically it is down to the higher chance of A failing so in that respect you are correct.

Yeah, it was kinda coming to me as I was typing, so it came out kinda fuggly, but I think I got it.

The thing that is a bit odd is that a character with a 45 vs. 15 has 300% of the defenders skill, but would have worse odds than a 90 vs. 60, though that is only 150% of the defenders skill.

Oh well, thanks for the hard work!

That really isn't that odd. THe chance of success in a D100 game is't a matter of comparing relative skill, but of comapring the skill vs. 100. THat is why opposed rrolls really aren't.

Consider a guy with 90% against another with 10%. Then consider a character with 9% vs. a character with 1%. In both cases character A has 10 times the skill of character B, but as far as D100 are concerned it is only an 8% advantage.

Now if RQ used an odds calculation and did a chart based on 1-1 3-2 2-1 and so on it would match up.

For instance if we took the values for A and B as a total sum and used the % of A over the total (rather tha A over 100) we would get real percentages. So Doing 132% vs 66% would yield a 67/33 ratio. Good math, tough to GM without a calculator.

 

[Rurik]

That really isn't that odd. THe chance of success in a D100 game is't a matter of comparing relative skill, but of comapring the skill vs. 100. THat is why opposed rrolls really aren't.

But we were discussing opposed rolls, not straight skills. I was just commenting on the fact that in opposed rolls there is a curve, and it favors the attacker as his skill goes up (standard halving disclaimer here), even though his relative skill to the defender is decreasing. But numbers can show just about anything if you want them too.

Consider a guy with 90% against another with 10%. Then consider a character with 9% vs. a character with 1%. In both cases character A has 10 times the skill of character B, but as far as D100 are concerned it is only an 8% advantage.

Bit his skill is still 900% of the other guy, and he is still 900% more likely to win, doesn't matter 90 to 10 or 9 to 1.

Now if RQ used an odds calculation and did a chart based on 1-1 3-2 2-1 and so on it would match up.

For instance if we took the values for A and B as a total sum and used the % of A over the total (rather tha A over 100) we would get real percentages. So Doing 132% vs 66% would yield a 67/33 ratio. Good math, tough to GM without a calculator.

Any mechanic that needs a calculator is a bad mechanic.

 

[andakitty]

Amen to that.

 

[atgxtg]

Any mechanic that needs a calculator is a bad mechanic.

K-A-B-A-L

All the mods were done in true percentages of your skill. So a +1 swrod was +10% of your skill, rasing a 50% to a 55%, but a 70% to a 77%. Throw in a half dozen modifers and it was like being crunched by the numbers.

The true percentage concept is nice, and a couple of games have done it well , but not Kabal.

 

[atgxtg]

But we were discussing opposed rolls, not straight skills. I was just commenting on the fact that in opposed rolls there is a curve, and it favors the attacker as his skill goes up (standard halving disclaimer here), even though his relative skill to the defender is decreasing. But numbers can show just about anything if you want them too.

That is my point,. The dice are still rolling for D100 probablility opposed or not. That is why the results skew. THe poosed suystem is saying that it doesn't matter if the ratios are the same, but it does.

Consider a guy with 90% against another with 10%. Then consider a character with 9% vs. a character with 1%. In both cases character A has 10 times the skill of character B, but as far as D100 are concerned it is only an 8% advantage.

Bit his skill is still 900% of the other guy, and he is still 900% more likely to win, doesn't matter 90 to 10 or 9 to 1.

But Ruik, it doesn't matter as far as the dice are concered if sis skill is 900% of the other as far as the D100 rolls go. Go use the probablilty calculator and see.

Using bluejay's explaination as a basis, the 90 vs 10 character has a huge range, 80% (11-90) of "can't loose" . So the success chance is not tied to the the ratios (A/B) of the two skills but to the diffeerence (A-B), sepcially the diffeernce between said skills and 100% (100-A or 100-B).

You see once you allow people to "win" failed rolls you throw out everything that isn't a autowin and replace it with a coin toss. So the 9% vs. 1% beceomes something like 58/42 ratio instead of a 9 to 1.





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[Rurik]

But we were discussing opposed rolls, not straight skills. I was just commenting on the fact that in opposed rolls there is a curve, and it favors the attacker as his skill goes up (standard halving disclaimer here), even though his relative skill to the defender is decreasing. But numbers can show just about anything if you want them too.

That is my point,. The dice are still rolling for D100 probablility opposed or not. That is why the results skew. THe poosed suystem is saying that it doesn't matter if the ratios are the same, but it does.

Consider a guy with 90% against another with 10%. Then consider a character with 9% vs. a character with 1%. In both cases character A has 10 times the skill of character B, but as far as D100 are concerned it is only an 8% advantage.

Bit his skill is still 900% of the other guy, and he is still 900% more likely to win, doesn't matter 90 to 10 or 9 to 1.

But Ruik, it doesn't matter as far as the dice are concered if sis skill is 900% of the other as far as the D100 rolls go. Go use the probablilty calculator and see.

Using bluejay's explaination as a basis, the 90 vs 10 character has a huge range, 80% (11-90) of "can't loose" . So the success chance is not tied to the the ratios (A/B) of the two skills but to the diffeerence (A-B), sepcially the diffeernce between said skills and 100% (100-A or 100-B).

You see once you allow people to "win" failed rolls you throw out everything that isn't a autowin and replace it with a coin toss. So the 9% vs. 1% beceomes something like 58/42 ratio instead of a 9 to 1.

Now I think your arguing just for the sake of arguing. All I was saying that the opposed curve favors the attacker as the attackers skill goes up but the margin stays the same - even though the ratio is decreasing. It was just an observation while pondering the math - not even really meant to say anything about the rules.

We all know there is a curve to opposed rolls, opossed rolls are not the same odds as straight skill checks, and relative skills and the margin between skills are not the same thing. What has me confused is what we are arguing about.

If you can clear that up I will be happy to have it out with you :wink:

 

[atgxtg]

I wasn't trying to argue. I had read your questions to bluejay and was trying to explain the math in a differenrt way.

You comment that "it is still 9 to 1" led me to beleive that you though the success chance were the same. That's all.