You are not logged in. Please login or register.
Play nice. (This means you.)
Logins from the previous forum have been carried over; if you have difficulty logging in, please try resetting your password before contacting us. Attachments did not survive the migration--many apologies, but we're lucky we kept what we could!
mj12games.com/forum → Defiance → Bell Curve statistics?
Has anyone tried modifying the rules to use multiple dice rather than a single d10? I like the breadth and depth of the rules for the most part, just not the stochastic modeling that goes into it (i.e. the die mechanics). Life generally follows a bell shaped distribution, not a flat one. Problem is, changing the die mechanics is akin to basically rewriting all the modifiers from the ground up.
I'm curious if anyone has tinkered around with something like this.
Roll several dice and average them?
Gotta say, I like the dice mechanics from a purely game-oriented point of view. No messing about.
I thought about doing something similar. I was thinking of rolling 2d10, and simply multiplying every modifier and Target Number by 2 (that way you don't have to worry about round-off problems if you divide). I don't think this is particularly accurate though.
With a bell curve, the more extreme the target number (for example a 2 or a 20), the harder it is to get that number. The same applies to the modifers. The more extreme the modifier, more impacting it is to the chance of success. In other words, all modifiers would have to be "squeezed" to the center (this is the same principle that a teacher would use for "grading the curve" if they knew what they were doing). Linear, well actually I should say constant ( since all MJ12 games use a flat line )probability functions don't have this problem, because all modifers have the same modification to the probability. I could do something complicated like use a squashing function on the modifiers (for example, maybe take the tanh of the probability distribution), but I'm pretty lazy right now when it comes to my hobby projects.
But if no one else has done this, maybe I'll write a program that'll do all the number crunching for me and put the results up for people to see. If I ever have time of course.
Has anyone tried modifying the rules to use multiple dice rather than a single d10? I like the breadth and depth of the rules for the most part, just not the stochastic modeling that goes into it (i.e. the die mechanics). Life generally follows a bell shaped distribution, not a flat one. Problem is, changing the die mechanics is akin to basically rewriting all the modifiers from the ground up.
I agree that life tends to follow a bell curve, though one can see plenty of examples of bimodal distributions and certainly a goodly amount of linearity, especially when qualititative variables are involved.
Despite the fact that most aspects of the Defiance mechanics are quantitative, I decided to go with linear stats. There are several reasons for this:
1) Foremost is the ability to control game balance within a reasonable range of values. Bell curves not only make modifiers difficult, they also force a mentality of extremes on any given value, i.e. the ability for one good roll to have a hugely powerful effect.
2) Perhaps as practically important is the ability to write a point system that anyone can use, i.e. without need of any complicated formulae.
3) In a sense, if you design your system broadly enough, bell curve effects will still come about in a supra-ordinate sense. For example, there is a complicated interplay between anti-vehicle, anti-infantry, PI, SI, high FR, low FR, and high damage probability (where each modifer has a relatively smaller effect) and low damage probability (where each modifier has a relatively larger effect and can even lead to an impossible roll). Though I have not and would not attempt to define this meta-system statistically, it plays as if it were a bell curve, i.e. players who have a large variety of troops tend towards the middle of the die roll range (5+ to 7+), while those with a small variety split the difference (e.g., 3+ vs. 9+).
In the end, while a few specific effects would probably be best designed singly as a bell curve distribution - in the case of indirect fire one where you are likely to be near the target, but very unlikely to hit it dead on or miss by a far distance - the overall advantages of a mathematically simple system outweigh them in my opinion.
-Demian
Is it wrong for me to enjoy reading conversations like this?
"DANGER WILL ROBINSON!! LOTS OF MATH IN POST!!! DANGER!!!!!!!!!
:twisted:
hey, you guyz love what you do and its effective,hehe...better than games where they pull numbers out of thin air and call it "ballanced",hehe.... 8)
I agree that figuring out the modifiers for a bell curve system is less intuitive than for constant systems. But I've often wondered if it's even worth it to have a point-based system.
Now, this may be heresy for me to say for a wargame, but I've never completely understood the concept of "points armies". Jon Tuffley in his Stargrunt II game didn't provide any points system for an "effectiveness" calculus. His reasoning (which I find difficult to argue with) for this omission follows three main points:
1) Firstly, while even though it may be possible to gauge the effectiveness of a single unit, when you look at the group as a whole, the groups effectiveness is more than the sum of its parts. In other words, you have to look at the group holistically.
2) Secondly, the effectiveness of units is extremely context sensitive. For example, if you design a bunch of units that have really powerful long range weapons, that's not going to do them a load of good in heavily forrested areas.
3) Finally, and this is where I think the "heresy" part comes in, having a point total destroys the mission based atmosphere of the game. Instead of creating imaginative campaigns in which the odds are never even, a point system encourages a competitive mindset in which you simply throw armies at each other.
Unfortunately, most people are loathe to play unbalanced games. And yet many battles are unbalanced, precisely because you don't want to fight your enemy when he's as strong as you are. You maneuver and force him to split off his forces and fight when and where you choose to fight. Point totals encourage a type of gaming where these imbalances do not exist, and hence there is less creativity and imagination involved in setting up the scenarios.
But getting back to the statistical problem, I suppose you're right that considering the meta-play, there does turn out to be conditional probabilities which will in effect make the odds more bell curve like. Still though, I think the interplay of having a more diverse variance and deviation in the probability distribution would make not only for more interesting gameplay, it'll change the way you have to think about your tactics and strategy. Granted, it will be less intuitive, but I think having modifers which are also skewed to the probability distribution and density functions which follow bell curves would be interesting.
While I will be the first to admit the drawbacks of having a formal point system, I personally believe that the advantages of play balance and ease of pick-up play outweigh them. To respond to your (and Mr. Tuffley's) issues specifically:
1) Firstly, while even though it may be possible to gauge the effectiveness of a single unit, when you look at the group as a whole, the groups effectiveness is more than the sum of its parts. In other words, you have to look at the group holistically.
I would actually argue the opposite. That is, it is *impossible* to gauge the effectiveness of a single unit outside of the larger game context. This is why I explicitly point out (no pun intended) in the rules that PV comparisons between individual troopers are essentially meaningless. I designed the Defiance point system to be in fact itself "holistic". This is why I take pains to stress the need for a mixture of troop types. Without a wide variety of infantry, weapon and vehicle types, the underlying assumptions of the system - for example, the average AR or average line-of-fire distance - will break down.
Secondly, the effectiveness of units is extremely context sensitive. For example, if you design a bunch of units that have really powerful long range weapons, that's not going to do them a load of good in heavily forrested areas.
This is exactly correct, and is why Defiance is careful to define the tabletop parameters under which the point system will be balanced. I have been fiddling off and on with Defiance: Close Quarters Battle, a slight variation of the VG rules for underground and dense terrain fighting. It has required a total reworking of the point system, with the knowledge that troop "value" is context-dependent.
Finally, and this is where I think the "heresy" part comes in, having a point total destroys the mission based atmosphere of the game. Instead of creating imaginative campaigns in which the odds are never even, a point system encourages a competitive mindset in which you simply throw armies at each other.
This is perhaps the strongest argument against the "point system mindset". But there is no reason that a point system is incompatible with missions in which the odds are uneven. In a sense, one has to have a general concept of a point system to even know if and when the odds are uneven. IIRC, even Stargrunt itself has a suggestion that "2 PI equals 1 SI", which is a very basic but still formalized "point system". Players will always want some way of measuring the relative effectiveness of different troop types. Explicit point systems - well, good ones any way :wink: - simply try to engage some mathematically based reasoning on top of the general intuition we all have after playing with a system a few times. In my opinion, the ability to easily ballpark a particular mission, e.g. "you're outgunned 4 to 1 but you have access to a defensive bunker" is much easier with a statistical point system than without.
With regards to your comments on Gaussian distributions, I agree that they are more "realistic". In my opinion, there is a constant tension between "game" and "simulation" and you in essence have to trade less of one for more of another. In this context, "balance" is more of a game effect, and therefore I chose to use largely even distributions to maximize it, at the expense of some amount of realistic simulation.
Interesting discussion, Dauntless!
-Demian
My small voice:
Points systems:
I like a balanced points system because it allows casual gamers like myself to quickly guage "a fair fight" and thence to easilly create an outnumbered, outgunned scenario with little or no previous experience in the system. I also think the scenarios in the Defiance VG book provide an excellent set of variant play tied in with the strategic picture: you are outnumbered BECAUSE etc.
I tend to think that a game with no, or unbalanced points strongly favours experienced players as there is no "rule of thumb" for estimating a miniature collection's battle effectiveness other than repeated testing. Particularly with the USS Army Builder it is possible to create an army with a specific style of play instead of just finding out what the style is over several battles- especially since in my case, a half-dozen battles might constitute my entire experience with any given system.
Finally, it is easy to ignore the system of points costs and army organisations in Defiance, but somewhat harder to "make up" a consistent and effective set for a game without one.
Bell Curves etc:
However, if you like both bell curves and a clear sense of its own subjectivity, I recommend trying out the Fudge RPG; my brother in law is working on making a tactical game based on it, and others have before. Fudge is built basically around the two ideals you espouse, wherein objective measurements are pretty much ignored, and the bell curve is always there.
mj12games.com/forum → Defiance → Bell Curve statistics?
Powered by PunBB, supported by Informer Technologies, Inc.