Topic: Probability

[Forkbeard]

As part of something I was doing with another post "Weapon Breakage", I decided (finally) to calculate the probabilities for open-ended rolls and specifically for skill usage.

A thing I've known for a while that seems strange is the fact that you cannot roll a 5 or 96 with an open-ended roll. It's clearly intentional, otherwise the subsequent roll would be 0 to 99, not 1-100, but can someone tell me why or if I'm missing something (i.e. subsequent rolls are also open-ended in both directions, as opposed to high OR low)

So here's a summary of the probs for skills (ignoring the flat UM66 and UM100 1% chances), in increments of 50. I can supply others if someone finds them useful.

As you can see these probabilities are also rather odd. For instance with a 200 modifier you have more chance of Spectacular Failure than Absolute Failure?!? Any ideas why it was done this way?


Modifier 0
Spectacular Failure   < -25 =    3.60%
Absolute Failure -25 to   4 =    1.40%
Failure            5 to  75 =   70.00%
Partial Success   76 to  90 =   15.00%
Near Success      91 to 110 =    5.60%
Success          111 to 175 =    3.25%
Absolute Success      > 175 =    1.15%

Modifier 50
Spectacular Failure   < -25 =    1.10%
Absolute Failure -25 to   4 =    1.50%
Failure            5 to  75 =   22.40%
Partial Success   76 to  90 =   15.00%
Near Success      91 to 110 =   20.00%
Success          111 to 175 =   36.35%
Absolute Success      > 175 =    3.65%

Modifier 100
Spectacular Failure   < -25 =    0.18%
Absolute Failure -25 to   4 =    0.07%
Failure            5 to  75 =    3.40%
Partial Success   76 to  90 =    0.75%
Near Success      91 to 110 =    5.60%
Success          111 to 175 =   65.00%
Absolute Success      > 175 =   25.00%

Modifier 150
Spectacular Failure   < -25 =    0.05%
Absolute Failure -25 to   4 =    0.08%
Failure            5 to  75 =    1.03%
Partial Success   76 to  90 =    0.75%
Near Success      91 to 110 =    1.00%
Success          111 to 175 =   22.10%
Absolute Success      > 175 =   75.00%

Modifier 200
Spectacular Failure   < -25 =    0.01%
Absolute Failure -25 to   4 =    0.00%
Failure            5 to  75 =    0.17%
Partial Success   76 to  90 =    0.04%
Near Success      91 to 110 =    0.19%
Success          111 to 175 =    3.25%
Absolute Success      > 175 =   96.35%

[Marc R]

I suspect that at 0.01% you fail to hit the rounding threshold and turn to 0.00% with the limited set of "-25 to 4", but do hit it with the open ended set of "less than -25". . .I suspect both are statistically tiny odds regardless.

There might be something wrong with the math, since to get to 0 or -26 with a 200 bonus you'd need to first.

Roll under 6 (5%)
Roll over 95 once (0.25%)
Roll over 95 again (0.0125%)

Or perhaps in the end it's just the way that gets apportioned up. . .if the 0.0025 goes to the absolute leaving the 0.01 to the spectacular, you have your explaination.

[Forkbeard]

The actual probs are Spectacular 0.0085% and Absolute 0.0037%. Quite a difference and not a rounding issue.

The mathematical functions are as follows:


pl = prob less than
pg = prob greater than
phl = prob (high-ended) less than
phg = prob (high ended) greater than

pl(x)
  x < 6:      0.01*(phg(5 - x) + phg(4 - x) + phg(3 - x) + phg(2 - x) + phg(1 - x))
  otherwise:  phl(x)

pg(x)
  x < 6:      0.95 + 0.01*(phl(5 - x) + phl(4 - x) + phl(3 - x) + phl(2 - x) + phl(1 - x))
  otherwise:  phg(x)

phg(x)
  x < 1:      1
  x < 96:     (100 - x)/100
  otherwise:  0.01*(phg(x - 96) + phg(x - 97) + phg(x - 98) + phg(x - 99) + phg(x - 100))

phl(x)
  x < 1       0
  x < 96      (x - 1)/100
  otherwise   0.95 + 0.01*(phl(x - 96) + phl(x - 97) + phl(x - 98) + phl(x - 99) + phl(x - 100))

[Winterknight]

In lay terms, when you are into that small zone for probability on a normal distribution, width (range) plays a greater impact than heighth of the curve.  I.e., there is a narrow band of outcomes that will produce a result in the -25 to 04 range, while the range for -25 and below is potentially unlimited.  The probability of getting a specific result in either range (say, -15 vs -50) would be largely identical, and very small (I'm not going to do the math).  But, because the potential range for -25 to say -1000 is much larger than the -25 to 04, the cumulative probability of a number in that range is greater.  

And, the 0.00% must be a rounding issue, because there is never a 0% chance of hitting even a single number in a distribution, unless it's mathematically impossible (like the 5 and 96).

[Forkbeard]

Winterknight... agreed, but that doesn't explain why they chose to do it that way.

The number of decimals shown was for ease of access. Actual figures can be provided.

Math shown in my previous post.

[Winterknight]

...but that doesn't explain why they chose to do it that way.

My guess...spitballin'.  Some kind of guesstimated target values for breakpoints that had less to do with statistics, and more to do with nice numbers for play. 

Remember that the original static action table break points come from RM1, and no new math has been done seriously since.  That was also based on a 5-2-1-0.5 progression, which meant that most skills would not get much attention after rank 30, and many at less than that.  So skills were maxing at 80-100 for a strong development with 30 ranks.  Well, with some profession bonuses, I guess it could go as high as 160 or thereabouts. 

But, that's just a guess.  And most of the "they" who came up with the table math aren't around anymore, at least not as part of the current ICE, as AFAIK.

[kevinmccollum]

In RM1, there were no level bonuses outside of combat bonuses. That kept manuever rolls lower too. It is far easier to make maneuver rolls under RM2

[rdanhenry]

Honestly, if you have +200, any failure ought be spectacular, as only massively bad luck or complete mental lapse could result in failure.

[Forkbeard]

kevinmccollum, this is RMSS, so no level bonuses, just rank bonuses and stats primarily.

rdanhenry,  

Winterknight, I couldn't agree more. Ironcrown just made it up is my guess, which is why we have the 5/96 hole and why just about every table distribution I check (not to mention that weapon breakage) is almost certainly nonsense.

The fault is entirely with me, in that my assumption 30 years ago that because the modules were damn fine the rules will be... wasn't entirely sensible  

I've only just picked up a copy of Tales of the Westmarch. God I love those M.E.R.P. modules, still playing in ME after all these years. The only modules better than Ironcrown for depth are those for Harn.

All the best, and thanks for the responses.
James

[Forkbeard]

Hey Ironcrown forum is replacing M, E, R, and P together with Not-RM... WTF

[markc]

Hey Ironcrown forum is replacing M, E, R, and P together with Not-RM... WTF

 Yes it is done to aid the Tolkien Ent. people in there observation of the boards. Since they look for every instance of the word you typed.
MDC

[Forkbeard]

They need help... serious help 

[Arioch]

Yes it is done to aid the Tolkien Ents.

To help them finding their entwives, you know...

[Emaughan]

Clever Arioch,
Trying to decide if that is worthy of a laugh point or an idea point.

[markc]

Maybe both.
MDC

[Forkbeard]

While you're at it, deduct a point from Ironcrown for Math, and add several million points for stupidity to the Tolkien Enterprise people 

[vroomfogle]

Forkbeard, what would you propose as an alternative static maneuver chart that you think would be better in terms of probability for each result?

[Forkbeard]

That's a really good question. I've altered so much of RMSS over the years, no doubt I'll end up changing this too.

I tend to devise mathematical functions that fit close to the RMSS tables, but if I think the tables aren't valid I'll devise my own formulas.

With weapon breakage, where this all started, I'd need to track down a reliable source of information, if that proves difficult I'll discuss it with the players. A few head banging arguments later and we may have something that feels right.

The whole area of RMSS skills is flakey, and certainly it would be likely that each table would be different. Did you have a table in mind?

If you are interested, and I'm suspicious since you chimed it only at the moment I poked fun at Ironcrown's daft tables, then we can discuss it, but like I said I think the whole area of skills would need an overhaul.

I'm still stuck on rewriting the spell attack tables that ties in with my revised injury system (based on Phoenix Command, but not the 1/100 second rules). When that's done, maybe skills, but probably not.

I've tried to leave alone the character development side of things, because the players are used to it. I've already forced them into RM1 from MERP, then RM2, then RMSS (sad Ironcrown then went and pushed for RM2(RMC) again, but we ain't switching), so pushing them again is problematic.

RMSS is not my life, but ultimately, if I get time, I'd implement my own rules from scratch.

All the best,
James

[Forkbeard]

Sorry one thing I wanted to add, open ended should have a start point of 0, not 1, and hence remove the holes in the distribution.

James

[vroomfogle]

No need to be suspicious.   I think that much of RM, while good ideas, was often implemented in an arbitrary way.