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Okay,
I have this idea that's been bouncing around for a while. Before I go into it, I want to preface it by saying that I am not a math major, and I am probably not the first person to think of this. Please have patience as I might stumble around a bit...
I've seen Mathammer being used to summarize the probability of hits and wounds, but I want to apply it to whole games. Would it be possible to take one unit, take the characteristics for that unit, input it into an equation, and get the effectiveness of that unit? It sounds like an awfully simplified answer, but I believe it is possible. I am working on that equation right now, and any help would be appreciated.
Oh, and another thing. This equation is designed to show the effectiveness of the unit, not the player. Since we're only dealing with the unit's characteristics, we must assume that the tactics/in game movement of the unit is perfect. Therefore, we take out all the strategy and look simply at the numbers.
Before you assume I'm looking for a way to win using statistically perfect units, allow me to explain. I am doing this to assess the effect tactics have on gameplay. By taking them out for the purposes of our consideration, we can analyze the effect they have when we compare how the numbers line up to the actual end result of the game (ie, what happens when we put tactics back in). Therefore, this is intended to allow players to maximize their strategic gameplay by offering them the likelihood of success of the best unit, and then giving them a way to use tactics to change the inherent variables in our equation. As a conclusion, I feel that metagamers try to exploit the rules of the game. I am trying to exploit the rules of the mind.
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Right. Now we dive into the guts of my idea. The effectiveness of the unit would be measured in the points it costs vs. the points that it regains in battle through the destruction of other units. My first equation deals with a simple pick up game where the goal is to wipe out as many of the other player's units as possible, so complicated things like objectives aren't something to worry about.
The way I went about creating the equation is by taking what is required to win(language-wise) and breaking it down to it's base components, then translating it into mathematics, and building it back up again to form an equation.
Since the equation isn't done yet, let me give you part of it as an example:
The Effectiveness of a Unit
-measured by-
Points Cost vs Points Gained by Unit
Points Gained by Unit
-measured by-
Ability to Kill in CC vs Ability to kill in Shooting
Ability to Kill in Shooting
-measured by-
Ability to See Target, Ability to Hit Target, Ability to Wound Target, and Target's Inability to Save
Target's Inability to Save
-measured by-
Save Number times Wounds Recieved times 10, or (Sv)10W
The save number means the value in the Armor save stat line, so for a 3+ save, the save number would be 3. The reason I multiplied wounds times ten is because it strikes me that each wound on a model is worth roughly ten points-or at least that is how most unit construction rules make it out to be. I then combine that value with all the others I detailed. Note that the single facet of a unit's usefulness I just detailed was part of a branching tree of values, one you will begin to see as I finish my equation.
Right. I don't want to carry on for pages and pages and have you lose interest, so I'm going to wrap up the preview of my idea there. If you like it, I look forward to working with you to improve upon it.
So-what do you think? Am I on to something? Am I totally apes**t? Or do you want more of an explanation before you can decide how it looks?
Last edited by N4styN1d64; February 29th, 2008 at 06:30.
Hive Fleet Toxicus W/L/T: 3/1/2
i think you may be on to something. of course.
because we are dealing with an RNG as the main variable non of the predictions or estimations will have any practical meaning, but that doesn't mean it'd be any less cool.
Music must give birth to orgasm and revolution
Latest LO Blog Post<+Tarnag> Who could help but love a name like Ultramoose, I think of a Moose with a rocket strapped to it breathing fire and wailing on a guitar
actually, I was hoping that if we did it right, it would produce a positive or negative number in terms of the point surplus or point deficit the unit made over the course of the game.
Like I said, I'm not fluent in Mathese, so.............what's an RNG?
Hive Fleet Toxicus W/L/T: 3/1/2
random number generator
too much in warhammer relies on a random number 1-6 or 2-12 to make any sort of conclusive statement.
best you can get is averages and probabilities.
Music must give birth to orgasm and revolution
Latest LO Blog Post<+Tarnag> Who could help but love a name like Ultramoose, I think of a Moose with a rocket strapped to it breathing fire and wailing on a guitar
Oh, yeah. Well... the way the numbers get imput, the point value assigned to, say an armor value is arbitrary. It is the best guess as to the amount of points an armor value will save on average. That way, the final solution will be an average.
Hive Fleet Toxicus W/L/T: 3/1/2
that could be interesting. im not good at that kind of math. but good luck ill be interested to see what algorithms you come up with
Music must give birth to orgasm and revolution
Latest LO Blog Post<+Tarnag> Who could help but love a name like Ultramoose, I think of a Moose with a rocket strapped to it breathing fire and wailing on a guitar
Thanks for your input. I'll get the first draft of the equation posted and then I'd like to get it playtested and see if it holds up. Thats where the LO community will come in handy.
Hive Fleet Toxicus W/L/T: 3/1/2
ok. Got the first(very) rough draft of the equation. Hope its not to hard to read.
E={[(S x 3)\(sv)][(S x I x 3)/(24)] + [(AW)(AW)-(OW)(OW)](10P)} - {[1.5s(0.75)][(BS)(n)][(S)(S)-(T)(T)][10P]}
Where E is a positive or negative number representing how many points the unit made/lost,
s is the speed of the unit,
Sv is the save value,
I is the initiative,
AW is the units weapon skill,
OW is the opponents average weapon skill,
S is the units strength,
T is the units toughness,
P is the probability of an unsaved wound
BS is the units ballistic skill,
and n is the number of shots the unit fires (on average).
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I had to use my iPod touch to write this(its the middle of the night here) so I apologize for the weird things like writing (A)(A) instead of A squared- there's no superscript button on this thing.
Please let me know what you think.
Hive Fleet Toxicus W/L/T: 3/1/2
very interseting.
its way tooo late for me to test this but ill give'r another look in the morning.
Music must give birth to orgasm and revolution
Latest LO Blog Post<+Tarnag> Who could help but love a name like Ultramoose, I think of a Moose with a rocket strapped to it breathing fire and wailing on a guitar
I don't believe this will be successful.
I'm doing 3rd year actuarial studies and the math, statistics, and probability I'm dealing with is far beyond what any normal person would like to know.
I think what you need to do is run some regressions to find the numbers you are looking for. I don't think we'll be able to crunch them out with some formulas. We'll have to run hundreds of games with many units and check each variable each game and plug the numbers in a regression, and do an analysis.
Let me explain. Say there are two guns, one is range 18" and the other is range 36". We know how well each gun kills marines, but we don't know how often it gets to shoot at marines, or any unit in particular.
What we can do is run hundreds of games, and basically count how many times each gun was in range and fired.
That way, we can put a weighting on each weapon depending on the chance it is in range.
I'd rather just use my subconscious memory from the over one hundred games I've played to answer whether a weapon's range is a problem. This is a better way to analyze units, math should only be used in answering questions that are specific and might be applicable often enough on the battlefield, making sure that the people that use the math know the limitations of the question.