[AVERA] Movement Abstraction

[J. Scott Timmerman]

So far, in my logarithmic multi-genre system, I've created the tactical movement rules for grid-based tactics.  These rules work with either squares or hexes.  The rules are such that, when working with small amounts of time, acceleration becomes important, but with large amounts of time, you can pretty much ignore the acceleration rules.

The unfortunate consequence of this is that when rounds do turn out to be a second long, the movement rules become more complex.  It's not terrible, and the numbers map directly to reality, with speed being measured in meters per second.  The big issue is trying to give a logical reason for this, and why acceleration works differently just based on what another character is doing (which affects round length, and in turn, affects the importance of calculating effects of inertia).

There is an abstraction I've been considering, which puts the movement rules on a level of complexity down below that of D&D (which is where I'd hoped to be).  I've been thinking of setting Speed rating to be an integer value, measuring 0 to 3 for humans.  Distances would be integer numbers as well, convertible directly from a number of meters by a chart. 

* If a character is currently traveling a certain speed, that character subtracts that Speed Rating from the Distance Rating to determine the Duration exponent of their action. 

* During acceleration or deceleration, the character treats their Speed rating as the highest speed during movement, minus one.  In effect, this is using the highest Speed, but adding one to the final Duration of the movement action.

* In movement with sharp or excessive turns or obstacles, the character's maximum speed would be reduced, enabling, say, a human to have a speed range of only 0 to 2, or even 0 to 1. 

In my mind, these rules allow for a level of movement abstraction which:
a) avoids the ambiguity in action interruption mentioned above
b) allows for movement to work smoothly without a tactics grid (using only distance exponents)
c) cuts down on "square counting" and generalizes movement ranges

I also have rules, which I'm now calling "Unit tactics" which are an interesting way of thinking of movement tactics without a grid.  I'm trying to refine it right now, and will probably post these later.  They basically take the Distance exponent to its logical conclusions and use groupings of characters and tactical formations to abstract movement.  The rules remain simple (pretty much the same) for small-scale, but work well for large-scale when you don't have a tactics map.

My main question is, do you think the basic idea [Distance] - [Speed] = [Duration] is appealing from a player perspective?  Do you think it would achieve the goals above?

-Jason T.

[J. Scott Timmerman]

Hmm.. Looks like I forgot to note this in my post.

The abstraction rules don't completely ignore the lessening importance of acceleration over greater distances.  I should say that, after a certain threshold, you no longer take a -1 penalty to speed to account for that acceleration.

I should also say, to clarify (for those who haven't read previous posts on this game) that the numbers we're working with are really exponents of 2.  That's why simple subtraction can be used in the duration formula rather than division.

-Jason T.

[contracycle]

I think it would help a lot if you gave an example of this in use so we we could see how it works.  It is not immediately apparent to me how it is intended to be used.

[J. Scott Timmerman]

Rather than illustrate it visually, I'm going to go ahead and write verbally.

Okay, let's take two characters, X and Y.  After explaining how a move would work in this abstraction, I'll explain it on a tactical grid to clarify.

The scene is combat.  For simplicity, let's use a gladitorial arena with no obstacles (dirt ground).  The characters start roughly 15m from each other.  In Abstraction, this would be Distance Exponent (DE) 4.

Let's say X wants to charge Y at full speed, and Y is bracing for the charge.  In Abstraction, X starts at speed 0 going to speed 3.  Her effective speed is 2 (effective speed during acceleration is the higher of the starting and ending speeds, minus 1).  This makes the Time Exponent (TE) for her action 2 (= DE - Speed = 4 - 2).

Translated to our tactical grid, X starts at position (5,5) and Y starts at position (20,5).  When X charges Y, she looks at a chart that says an acceleration action to 8m/s travels 16m and lasts TE 2.  This is enough to cover the 15m of distance, so she takes the acceleration action, combined of course with her aimed attack.  Same result, but we have the chart instead of the subtraction formula.

As a note, TE 2 translates to 4 seconds.  X combines that action with a strike (to disable his arm), and 4 seconds is plenty of time for Y to brace his pointy weapon (to kill her).  Since both players are considered to have taken the "aim" action for this amount of time, they gain a bonus to their roll equal to half the Time Exponent of the aim action (round down), in this case, +1 (TE = 2, 2/2 = 1).

(There are other tactical factors involved in the limitations of this aim bonus and implications of the attack goals, but rather than resolve the attacks, I won't go into them right now because we're not discussing the attack mechanics.)

Now, from the beginning, say instead that they wanted to charge each other, to clash.  They each want to go full speed in doing so.  Always the compassionate one, X is going to disable Y's movement, whereas Y is going to attempt to kill her again.

Half of DE 4 is DE 3, so each one will have to cover (roughly) a DE 3 movement.  Here's where things in the abstraction differ.  DE 3 isn't enough space to get up to Speed 3, only Speed 2.  So the characters end up taking a TE 2 action [3-(2-1)=3-1=2] all the same to do so, and the aim action is +1 again.

However, back on the grid, and seeing that each character has to cover 7 or 8 meters, we see that we can split this up into 2 acceleration actions: One from 0m/s to 4m/s which travels 4m and lasts TE 1, and another acceleration from 4m/s to 6m/s which travels 5m and lasts TE 0.  So we are aiming during two actions, a TE 1 and a TE 0, which do not add up to a TE 2, and therefore gives no aim bonus (1/2 round down = 0).  In effect, it's only taking them 3s in this version; not long enough to steady their weapons.

As you can see, the grid tactics I was using before, with the acceleration chart was indeed complicated.  My question is whether you feel that my new idea works well.  I hope this example is easily understood.  Any questions, just ask.

-Jason T.

[Hans]

I'm replying here, based on our conversation on die rolling mechanics here.

My main question is, do you think the basic idea [Distance] - [Speed] = [Duration] is appealing from a player perspective?

My answers has to be no.  Everything you describe here seems much more complicated than any simple grid system I have ever seen for a simulationist combat system, and I don't see it boiling down to just that formula.  Mathematically, your formula IS fairly simple.  It is really ln(Distance) - ln(Speed) = ln(Duration), which is a statement of fact, ignoring the constants; the ln of both sides of Distance/Speed = Duration.  I'm just not getting what the point of expressing it this way is, and why it is worth any extra complexity over a non-logarithmic scale, even in the design process.  Which brings me to...

Do you think it would achieve the goals above?

I'm not sure.  I don't really see any clear goals in this thread, although I might be missing them.  However, looking back at your very first post on AVERA (at least I think it is AVERA) you said:

The rules are written so that a player (even a GM) doesn't have to understand why the rules work.  Relatively simple math is performed to determine the characters' success or failure.  I don't intend for the game to model reality perfectly, but well enough that the logic required to produce good in-game strategy does not seem backward to anyone familiar with our reality, or fantasy realities.  The numbers are abstracted.  The mechanics make an attempt at being goal-based, to cut down on differences between different methods of achieving a goal.

and you also said:

Perhaps people have a hard time understanding the game.  Some of the suggestions that have been given interfere with the basic statistical theories behind the game, and so I haven't adopted them.

I suggest to you that an apriori theory of how the game SHOULD work (as expressed in the green quote) may not be compatible with the very pragmatic design goals you have expressed in the purple quote.  Your design goals are fine, and if forced to chose between the theory and the goals, I would say scrap the theory every time.  None of what you describe above regarding movement makes me think the system you are describing meets the goals you express in the purple quote. 

[J. Scott Timmerman]

Okay.  Would it be enough to scrap sprinting/walking entirely, and assume that Speed is always 2?  Going yet another step, Since speed is a constant, I could just calculate it into Distance, doing away with it altogether (for humans, at least).

Putting the above into words more comprehensible to the usual player, you get to move 4 spaces per round, times 2 for every TE the round has.

Would you happen to have any better ideas on this?

-Jason T.

[J. Scott Timmerman]

Or - I feel pretty dumb for not thinking of this sooner - I could simply institute my rule of thumb as an actual game rule.  I.E., the TE for a movement with any given Distance is equal to half of the DE (round up), or the DE minus top speed (3 for humans), whichever is higher.  So, say I want to move DE 10, that would take TE 7.  If I want to move DE 5, that would take TE 3.

That way, speed remains a factor in the tactical movement decision.  Or do you think this formula is still too numbersome and full of thinkyness?

-Jason T.

[contracycle]

What I don't know is, what problem are you trying to solve with this approach?

[J. Scott Timmerman]

You know, if one person can't tell my goals from the initial post, that would be one thing.  If two people can't, maybe I just haven't included enough background information in that initial post.  I've always been bad at explaining myself.  I'm going to have to get one of my playtester friends to write explanations of the rules for me.

First of all, let me say that I may have mis-said a couple times when I said I'm trying to create pure simplicity here.  The game itself needs just enough complexity that there's hardly ever a no-brainer decision.  The movement rules I have already highlight economy in movement.  The attempt here, with this thread, is to make the handling rules as simple as possible outside the real decisions of the game itself. 

Until now, my placeholder tactical movement system used a grid, with rules that said flat out what was going on.  This was useful for playtesting, but as you'll see in my example post above, in the "Before" sections when I mention the grid, the placeholder system was fairly cumbersome.  My efforts with this thread are to simplify the view of that system without wrecking the underlying math.  In short, I want to keep economy in movement a decisionmaking factor while removing explicit references to distance and acceleration, which complicate the system.

Besides this, I want a system that is a unified whole.  Everything else (Time, progress, resources, etc.) works on a sliding scale of exponents.  My next step, as I had planned, was to convert tactical movement rules (and movement rules in general) to work like everything else.  Later on, I'll post a more detailed version of how these might work in a large-scale situation.

So, that said, here are the goals as I initially posted them in this thread:

In my mind, these rules allow for a level of movement abstraction which:
a) avoids the ambiguity in action interruption mentioned above
b) allows for movement to work smoothly without a tactics grid (using only distance exponents)
c) cuts down on "square counting" and generalizes movement ranges

Hope I've communicated myself well enough here.

-Jason T.

[Hans]

The movement rules I have already highlight economy in movement.  The attempt here, with this thread, is to make the handling rules as simple as possible outside the real decisions of the game itself. 

I'm not exactly certain what you mean by "the real decisions of the game itself" here, but we are getting closer.  I think what you are saying is you want the rules to be simple enough that a person can concentrate on "what is the best tactical decision for my character at this moment" and not "what the heck can my character even DO at this moment"?  Does that sound right?

Until now, my placeholder tactical movement system used a grid, with rules that said flat out what was going on.  This was useful for playtesting, but as you'll see in my example post above, in the "Before" sections when I mention the grid, the placeholder system was fairly cumbersome. 

I not exactly finding this.  What you said was:

The unfortunate consequence of this is that when rounds do turn out to be a second long, the movement rules become more complex.  It's not terrible, and the numbers map directly to reality, with speed being measured in meters per second.  The big issue is trying to give a logical reason for this, and why acceleration works differently just based on what another character is doing (which affects round length, and in turn, affects the importance of calculating effects of inertia).

I can't see, from this, why it is that the movement rules are more complex with versus without a grid.  Also, I have to ask, why do you need to give a logical reason?  Do you mean "I need a logical reason to explain this to myself?" or do you mean "I need a logical reason to explain this to the reader/player?"  Frankly, your comment in the first post about "with large amounts of time, you can ignore acceleration" seems perfectly reasonable to me; its one of the few bits that I understood completely.

My efforts with this thread are to simplify the view of that system without wrecking the underlying math.  In short, I want to keep economy in movement a decisionmaking factor while removing explicit references to distance and acceleration, which complicate the system.

Aha!  Now I am starting to get this.  If I may rephrase, you want to make movement, especially changes in velocity, an issue in the tactics of the game, but you do want to abstract this down to a level where the mechanics are pretty simple.  Does that sound right?

Besides this, I want a system that is a unified whole.  Everything else (Time, progress, resources, etc.) works on a sliding scale of exponents.  My next step, as I had planned, was to convert tactical movement rules (and movement rules in general) to work like everything else.  Later on, I'll post a more detailed version of how these might work in a large-scale situation.

I am very sceptical about this.  I will tell you why.  It sounds to me like what you are trying to do is have one system that can go all the way from two gladiators duking it out to relativistic velocity space craft lobbing missles at each other.  The way you intend to allow this is through the exponents.  I am sceptical that this is even an achievable goal, let along a worthwhile one.  It has always been my experience that the best tactical games are those that are designed explicitly for the scale and content they are dealing with, and not those that are trying to be general across a large range of possiblities.  But, hey, it's not my game, and that bit is not what you are asking about.   I will simply assume from here on out sliding scales of exponents in a unified whole are a good thing.

So, that said, here are the goals as I initially posted them in this thread:

In my mind, these rules allow for a level of movement abstraction which:
a) avoids the ambiguity in action interruption mentioned above
b) allows for movement to work smoothly without a tactics grid (using only distance exponents)
c) cuts down on "square counting" and generalizes movement ranges

Point a)  - I don't see anything that refers to either ambiguity or action interruption.  Therefore, I can't answer this.
Point b) - From your post, I can picture the following thing happening in a game:

GM: What do you do?
Player: I want to attack that orc over there, by the doorway.
GM: Ok, that's Distance 3, and your starting from a standing start.  Your max Speed is 2.  Since you are accelerating, that means the Duration of the move to get to the orc is 2 (Distance - Speed (+1 for accel) = Duration).
Player: Cool, what does that mean?
GM:...

And there I have to stop.  The numbers are there, but I can't put them into any context.  Specifically, I have no idea what Duration 2 means.  How much nastiness can the orc get up to during a Duration 2 action?  How many arrows can he shoot at me?  How many hostages can he kill? 

BUT...assuming that YOU (or the GM in general) have some idea of how much stuff can happen in a Duration 2 action, or how far roughly in real life a Distance 3 is, or how much velocity Speed 2 equates to, the rule you give above is trivial to implement.  I heartily endorse it over anything more complicated.

Point C - If you aren't "square counting" then how do you, the GM, know the distances?  I can think of three possible answers to that:
* There is a real map, on paper, on the table, it just doesn't have a grid on it:   If that is the case, all it seems to me you have done is turn "square counting" into "ruler measuring", or, more likely "eyeballing it".  Not a problem, a perfectly reasonable thing (happens all the time in miniatures games like Warhammer), but I don't think you have gotten rid of a bad thing and replaced it with a good thing.  You have just replaced one thing with another thing.
* There is a real map, but it is in the GM's head.  If that is the case, what you are suggesting may be a slight improvement; it may be somewhat easier for a GM to remember small integers (Distance 3) over larger numbers (30 feet).  This works great for one on one type combat (the gladitorial bout you mention).  But the moment you go to multiple participants, the problem for the GM is greatly complicated, and chances are the GM is going to have to put the map down on paper anyway.  See above.
* There is no real map, the GM is just making stuff up. If this is the case, I don't really see the point of a complicated tactical system. 

[J. Scott Timmerman]

I'm not exactly certain what you mean by "the real decisions of the game itself" here, but we are getting closer.  I think what you are saying is you want the rules to be simple enough that a person can concentrate on "what is the best tactical decision for my character at this moment" and not "what the heck can my character even DO at this moment"?  Does that sound right?

That is a better way to put it, yes.  I am notoriously bad at putting things into words without being incredibly wordy.  The inaccurate description of the problem with the grid system that you point out is one other example.

I can't see, from this, why it is that the movement rules are more complex with versus without a grid.

It's a matter of numbers reduction.  With speed in m/s and distance in meters, there is an issue of division (to determine time in seconds) and then conversion by table (to find the Time Exponent).  With distance in an Exponent, and speed and acceleration reduced to either exponents, or implicit results of the (hopefully simpler) conversion formula, we get simpicity while retaining the strategical choice.  I revised this formula to DE/2 for short-range movement (DE 6 or less, <100m), and DE-3 for long-range movement (DE 7+, or 100+ meters).

If I may rephrase, you want to make movement, especially changes in velocity, an issue in the tactics of the game, but you do want to abstract this down to a level where the mechanics are pretty simple.  Does that sound right?

Yes.

It sounds to me like what you are trying to do is have one system that can go all the way from two gladiators duking it out to relativistic velocity space craft lobbing missles at each other. 

My formulae don't account for Light-Relative speeds.  I want to be able to use the system for horses, giant monster snails, and maybe even cars.  The system intends to be a multi-genre game, and players will deal with things of various velocities.  It looks as if there may be many similarities in how these things work in the end.  I'd be happy if the movement rules for inhuman situations turned out to be like those for the human case.

I am sceptical that this is even an achievable goal, let along a worthwhile one.  It has always been my experience that the best tactical games are those that are designed explicitly for the scale and content they are dealing with, and not those that are trying to be general across a large range of possiblities. 

Thanks for the input.  I'll try to focus on just the human case before getting the other ones down.

Point a)  - I don't see anything that refers to either ambiguity or action interruption.  Therefore, I can't answer this.

That's really another issue of granularity versus precision.  Say, a character starts a DE 5 move, which rounds to TE 3.  In the same round as that movement started, another character finishes an action at TE 1.  The next round, that other character finishes another action at TE 2.  Theoretically, by this point, the moving character should have been able to take a TE 2 action to accelerate to Speed 3, moving DE 4, and another TE 1 action moving Speed 3 over DE 4, making a total of DE 5, in less time (it has not yet been eight seconds, only six).

The grid system I was using before would have said that character should split movement actions like that in the first place, and take one acceleration action and one move action.  With the abstraction, in the interest of simplicity, players won't try to optimize their actions like that unless there's a tactical advantage.  If I wanted to, I could dampen this reward for metagaming and just assume that all moves stop at their destination, and so human movement uses the same formula no matter what.  Other tactical pressures will be important in a player's decision, though, so if anything I'd be making this decision just to make things simpler rather than to remove the ambiguity or metagaming reward.

BUT...assuming that YOU (or the GM in general) have some idea of how much stuff can happen in a Duration 2 action, or how far roughly in real life a Distance 3 is, or how much velocity Speed 2 equates to, the rule you give above is trivial to implement.  I heartily endorse it over anything more complicated.

What it means is, the Orc can fail his action to attack by 2 and still hit the character within TE 2.  I.E., If the orc has X chance to hit the character within 1 second (Duration 0), the orc then has a higher probability to hit within 4 seconds (Duration 2), in a single roll.  You've seen the math on this in the other thread.

Furthermore, if the orc manages to get a hit/shot in within 1 or 2 seconds (a heroic orc?), the orc can still attempt another action before the Duration 2 action is even completed, meaning, before the player gets to the orc.

Sorry that my information is so spread out.  I just haven't wanted to overload anyone with information on a thread.  Here are the definitions of some terms I use.  Instead of ln, I use log base 2. 
DE = (log2 Distance in meters)
TE = (log2 Time in seconds)
Magnitude = (log2 number of people)
Speed = (log2 {m/s})

In the abstraction, "typical" human acceleration and top speed are assumed to be 2m/s^2 and 8m/s respectively, perhaps more for mathematical ease than for accurate simulationism.

I suppose the big issue you're pointing out is how a player of this game might see space in terms of DE.  My best answer is to explain in plain English, that 0 = 1m (1s, 1 person, etc.), and every +1 doubles that.  Does this aid visualization?  My guess would be no.  This is definitely something I'll have to work on.  Of course, conversion tables will exist for all kinds of things, but the hope is that after a couple of sessions, they won't be a crutch.

It's a matter of wrestling with the fact that people don't want to have to stretch their minds around different rules just to play a game.  I've accepted the possibility that my game might never catch on because of its flavor here.  But there is still hope, and those that have expressed interest and even a liking for the way my game works at least exist.

Point C - If you aren't "square counting" then how do you, the GM, know the distances?  I can think of three possible answers to that:
* There is a real map, on paper, on the table, it just doesn't have a grid on it:
* There is a real map, but it is in the GM's head.
* There is no real map, the GM is just making stuff up.

Up to this point, as I've said, I have used a grid, and I don't forsee the system as ever being incompatible with a grid.  I just don't like reliance on a grid.  Some things can certainly be handled more quickly without one.  Part of my effort is to increase the size of this category, and to make certain aspects of this category simpler.

With my (still theoretical) Unit Tactics system, I was planning on using a system of markers.  I still don't have all the bugs worked out (bugs meaning mostly complexities).  In simple situations, this could be done in one's head.  As is the goal with everything in this system, a player won't have to see the math behind Unit Tactics to be able to use it.

As is the major problem you've pointed out with the Exponents, a similar problem exists with Unit Tactics in being legible and de-abstractable into the shared imagined space.  I'm hoping the selection of terminology in the creation of this system can aid that de-abstraction process.  But I know this issue really can't get as easy as a grid map or LARPing.  If I can't get it simple enough to the point where it's ever easier than using a grid, perhaps a grid will have to be used for all complex situations.  But there are some promising ideas I've come up with, at least when I restrict myself to 2 dimensions.

-Jason T.