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On attack/defence Probability distributions

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On attack/defence Probability distributions

from Elemental Forums

Having just acquired the Elemental Beta yesterday, I have been reading the beta forums.

I noticed that it seems that Stardock is planning to use a system where attack and defense rolls are a single randomly generated number between 0 and the attack rating, with every number having an equal chance.

I don't really like that system, since it is too random: You would need absolutely ludicrous amounts of defense for a powerful creature to be able to withstand to a horde of lesser ones. Brad proposed the idea of having a minimum roll of Defense/10 for defense, but that seems rather arbitrary to me, since that means a single point of extra defense could be the difference between tough and absolutely invulnerable.

I propose a more bell-shaped distribution for attack/defense rolls, instead of such arbitrary minimum rolls, similar to how master of magic did it. If you have, for example, a single defense roll for every point of defense you have, with each roll having a chance to block a single point of damage/attack, you naturally get that powerful creatures are almost impossible to harm with weak attacks, without making them too strong against normal ones. Since probabilities lower, but never get to zero, large armies of weak troops can still be a threat to a strong unique creature, without them killing it instantly.

If you have an army of a thousand archers, and an even distribution of defense/attack rolls is used, the average damage of a single archer would be very difficult to get below, say .05 per volley. That would be the equivalent of 1 attack versus 9 defense. With a thousand archers, you would still get 50 damage per volley. That means the target is killed very quickly, unless he has thousands of hitpoints/strength.

But if you use the minimum system, a single extra defense point would make it invulnerable, which is too big a change for such a small stat difference. Without a minimum defense roll, to get the damage down to a survivable, say, 5 per volley for this tough monster against the weakest archers imaginable, you would need 99 defense, which is ridiculous.

If you however, use a system of 1 roll per point of attack/defense, with each roll having a 50% chance of adding one to the total, the same monster needs a mere 7 defense in order to reduce the average damage of a single volley to 4. 8 defense, would halve that to 2, 9 halve that to 1. 2 attack versus that same 7 defense would result in 20 damage per volley however, a great improvement. That may be too steep a distribution, since it can quickly make a unit with a lot of defense very tough to harm, but this type of distribution is still, I think, a good idea. A better one than an arbitrary minimum roll I think.

 

 

elemental
29,566 views 38 replies
Reply #26 from Elemental Forums Top

There's definitely a good argument here. I'm surprised a dev hasn't responded to this yet, but, then again they are just now starting to look at the battle engine so a lot of these decisions could be up in the air still. If that's the case then we'll have to wait and try it out before we can really say what they have planned won't work. I don't like things  being too random either though so I think a bell curve would be a pretty good idea. Then again I don't see why they don't just take something like D&D 2.5 and simplify it. Give everything Hit Points, Attack, and a Armor Class, then make those moddable and have base stats give bonuses to them. Then later you plan in that spells or items in game could change these stats and other values. From a non-programing standpoint it all sounds pretty easy, even though it's not. It could still be "boiled down" without the need for a lot of randomness.

Quoting SaberCherry, reply 23
I really hope the attack/defense formulas are moddable, because I fear that they will be the simple flat distributions that I don't like.
End of SaberCherry's quote

I'm pretty sure the values themselves will be modifiable, I'm not sure about the formula for how they'll be used though. I hope that's moddable as well.

Reply #27 from Elemental Forums Top

Quoting MagicwillNZ, reply 25
I have always preferred the linear probability models for combat, because combat is where crazy and unlikely stuff should happen. Having played with both GURPS (3d6) and DnD (d20) quite a bit, I can say that the d20 model makes for much more satisfying combat and the 3d6 model is just far too consistant.
End of MagicwillNZ's quote

For a RPG I agree but for large-scale tactical combat I'm not in favor of too much randomness.

 

Star Control: Origins
Reply #28 from Elemental Forums Top

In my own little browser game I am going for a base value pluse a random value. I think this makes for nice variation. An attack can have a base damage at 5 and then 1-5 random on top of that (random example here).

There is one VERY important thing to remember. If you calculate damage for each unit in a battle then such calculations are problematic.

Imagine 1000 swordsmen doing an attack at 3D6. 1D6 will give you on average 3.5. If you simulate 3D6 dice 1000 times then you will always get a number close to 3500x3 = 10500. The randomness is gone :)

If you calculate as a whole then the randomness can get out of hand. 1000 x 3D6 (where you first calculate the dices and then multiply by a 1000) will give you very varied results.  1, 1 and 4 roll will give 6000 damage and 3, 5, 5 will give 13 000.

I have no idea about how the Frog is thinking here, but this is not an easy thing to get right.

 

I am rambling and not sure if this add to the discussion. But statistics and numbers in games sure are fun things to consider.

Reply #29 from Elemental Forums Top

Quoting Raven, reply 26
Then again I don't see why they don't just take something like D&D 2.5 and simplify it. Give everything Hit Points, Attack, and a Armor Class, then make those moddable and have base stats give bonuses to them.
End of Raven's quote

I don't like D&D rules because armor doesn't absorb damage.  I've never understood the reasoning there...

Reply #30 from Elemental Forums Top

Quoting SaberCherry, reply 29

I don't like D&D rules because armor doesn't absorb damage.  I've never understood the reasoning there...
End of SaberCherry's quote

It's been more then a few years, but if I remember correctly, the old system was more about "deflection". Your armor kept you from getting hit entirely. The higher (or was it lower?) your AC, the harder it was to hit the character.

Note: After all the years I played old school D&D I'm ashamed of my-self for not remembering the rules exactly, sorry.

Reply #31 from Elemental Forums Top

Personally I think there should be some randomness. Roll a d6/d20/d100 etc then add the attack or defense score to it. So if you have a 5 att and roll a 0 you will have scored a 5.  I want every unit no matter how weak to have some chance be it remote to get that lucky hit on a strong unit or hero. Call it a critical/lucky hit if you will.

Reply #32 from Elemental Forums Top

Quoting SaberCherry, reply 29



Quoting Raven X,
reply 26
Then again I don't see why they don't just take something like D&D 2.5 and simplify it. Give everything Hit Points, Attack, and a Armor Class, then make those moddable and have base stats give bonuses to them.


I don't like D&D rules because armor doesn't absorb damage.  I've never understood the reasoning there...
End of SaberCherry's quote

Actully it does absobe some of the energy of the hit hence the protection.  If you were in Chain Armor  and I walked up to you and hit you with a baseball bat that Armor would absorb most of the energy (damage in game terms) of the hit. If you were not wearing armor then your body would absorbe this energy and you would be hurting. That is basically the concept. D&D uses this concept in a easy to use mechanic that does not need a lot of record keeping. There are better systems out there but this works just fine. Personally I would per if the AR of armor was the amount of damage the Armor can absorbe before damage gets through.

Reply #33 from Elemental Forums Top

Quoting Bellack, reply 32

Actully it does absobe some of the energy of the hit hence the protection.
End of Bellack's quote

Those must be way newer rules then what I played with. We always ran 2.5 Edition. My buddy Tavis, our GM, had litterally EVERY book that was ever printed, even the old "Myth Dranor" boxed campaign .

Reply #34 from Elemental Forums Top

Quoting Raven, reply 33



Quoting Bellack,
reply 32

Actully it does absobe some of the energy of the hit hence the protection.


Those must be way newer rules then what I played with. We always ran 2.5 Edition. My buddy Tavis, our GM, had litterally EVERY book that was ever printed, even the old "Myth Dranor" boxed campaign .
End of Raven's quote

I think he refers that a failure (in 2e) could mean a deflection or just that the armor absorved the damage, the shield parried the hit, whatever you wanted really to describe the result.

In newer editions HP not only represent "health", but also morale and so on, so this gets more abstract in general.

Reply #35 from Elemental Forums Top

No one has mentioned the Dominions open d6 system have they?

 

Saber outlined a version similar to it which I think is superior than just a straight d100 kind of system.

 

Essentially the open d6 (or dX) system has each 'side' roll a single d6 and apply whatever the difference modifier is.  However, the open part of it means that when a '6' is rolled you reroll the die and add to the previous roll.  Which means you can gain a large number of rerolls if you roll multiple 6s.

 

It has the advantage of making large differences in attack vs. defense (or damage vs. protection/resistance) still valuable, but not unbeatable.  If you also apply an open system to damage rolls you can model critical hits as well.

Reply #36 from Elemental Forums Top

Quoting Raven, reply 33



Quoting Bellack,
reply 32

Actully it does absobe some of the energy of the hit hence the protection.


Those must be way newer rules then what I played with. We always ran 2.5 Edition. My buddy Tavis, our GM, had litterally EVERY book that was ever printed, even the old "Myth Dranor" boxed campaign .
End of Raven's quote

2 editions rules were pretty bad and not balanced at all.

Reply #37 from Elemental Forums Top

I personally prefer the system of a bellcurve (say 3d6) system for each individual warrior. Given your example of 1000 swordsmen vs 1000 swordsmen. Sure one would "think" that the randomness is completely gone, and that the same amount of damage is delivered. However what actually happens is that some individuals get quickly slaughtered, other individuals are barely scathed yet killed many opponents, and others are injured and injured a few opponents. one example of how it would be distributed ... but this is the most amazing sort of randomness because you have some idea of what is going to happen, but you have no idea which soldiers will survive, which will level up, and which will simply die and disentegrate into nothing. you can increase odds for survival by giving a favored soldier better armor, but its always possible that a less-well equipped soldier could become the hero of the day and get his own level ups. The more isolated the damage is into one individual, and the least likely the occurance, the greater the experience and level gain of the individual soldier. So you could have a soldier gain as many as 5 or 10 levels in one battle, but such a thing would be very rare.

Perhaps a battle where a soldier gains 5 levels from one battle happens a couple times a game, where 10 levels only happens once every couple of games.

Reply #38 from Elemental Forums Top

Quoting joasoze, reply 28
In my own little browser game I am going for a base value pluse a random value. I think this makes for nice variation. An attack can have a base damage at 5 and then 1-5 random on top of that (random example here).

There is one VERY important thing to remember. If you calculate damage for each unit in a battle then such calculations are problematic.

Imagine 1000 swordsmen doing an attack at 3D6. 1D6 will give you on average 3.5. If you simulate 3D6 dice 1000 times then you will always get a number close to 3500x3 = 10500. The randomness is gone

If you calculate as a whole then the randomness can get out of hand. 1000 x 3D6 (where you first calculate the dices and then multiply by a 1000) will give you very varied results.  1, 1 and 4 roll will give 6000 damage and 3, 5, 5 will give 13 000.

I have no idea about how the Frog is thinking here, but this is not an easy thing to get right.

 

I am rambling and not sure if this add to the discussion. But statistics and numbers in games sure are fun things to consider.
End of joasoze's quote

You could simply make one roll and have that result bring in data from some table somewhere that gets the values for the rest of those rolls.