Rifts/Palladium Mass Combat Tool

[Meneliki]

Hey all,

In my struggle to find a decent solution to mass combat in Rifts, I ended up just coming up with my own. It's based on percentile rather than D20 rolls to determine army hits. Here's a quick demo for those interested: https://www.youtube.com/watch?v=MXVmJmQmM6k&t

Let me know what you think.

Thanks!

M

[Hotrod]

That's a neat tool. I have a few thoughts for you:

First, I think you might be interested in a little Monte Carlo simulation I did of the basic chances to hit when we compare strike vs parry/dodge bonuses. This pits attacker vs defender starting from -19 (strike of attacker << parry/dodge of defender) and increasing to +19 bonus advantage (strike of attacker >> parry/dodge of defender). I tallied up the results of 15,000 strike/parry rolls for each of the following combinations:

-19: 4.75%
-18: 4.80% +0.05% (There may be no difference here at all, for that matter)
-17: 5.1% +0.3%
-16: 5.6% +0.5%
-15: 6.3% +0.7%
-14: 7.2% +0.9%
-13: 8.5% +1.3%
-12: 9.9% +1.4%
-11: 11.6% +1.7%
-10: 13.6% +2.0%
-9: 15.9% +2.3%
-8: 18.7% +2.8%
-7: 20.9% +2.2%
-6: 24.3% +3.4%
-5: 27.5% +3.2%
-4: 31.2% +3.7%
-3: 34.7% +3.5%
-2: 39.0% +4.3%
-1: 43.0% +4.0%
+0: 47.5% +4.5%
+1: 52.4% +4.9%
+2: 56.5% +4.1%
+3: 61.0% +4.5%
+4: 64.7% +3.7%
+5: 68.8% +4.1%
+6: 72.3% +3.5%
+7: 75.4% +3.1%
+8: 78.0% +2.6%
+9: 81.2% +2.2%
+10: 83.6% +2.4%
+11: 86.2% +2.6%
+12: 87.9% +2.7%
+13: 89.6% +1.7%
+14: 91.2% +1.6%
+15: 92.5% +1.3%
+16: 93.6% +1.1%
+17: 94.4% +0.8%
+18: 94.8% +0.4%
+19: 95.0% +0.2%

Any strike/parry difference of 20 or greater is no difference than the difference of 19, since natural 20's always win (except against another natural 20). Since these are randomized attack and defense rolls, there's a little statistical wiggle at play.

The % difference per bonus shows a couple of interesting trends.

Strike and parry bonuses make the biggest difference in absolute terms when your opponent has similar bonuses. You will gain the most hits per strike bonus in absolute terms when your strike bonus is roughly equal to your opponent's parry bonus. If you already have a +10 advantage over your opponent, you'll be gaining about half as many hits per attack for each additional bonus as you will if you have no strike bonus advantage over your opponent's parry bonus.

Proportionately, you increase your hits per additional +1 to strike the most when you have disadvantage of -1 to -16 against your opponent's parry bonus. The peak area is -13 to about -6, where you are proportionately gaining around 15% more hits for each +1 increase in strike bonus. Once your strike bonus is +6 higher than your opponent's parry bonus, you're proportionately gaining only 5% more hits for each +1 increase, and this drops as go go up. If you're enjoying a +14 strike bonus over your opponent, any further bonuses won't make enough difference in your hit frequency for you to notice.


tl;dr: The importance of strike and parry bonuses depends on what you're fighting. Huge strike bonuses help the most against foes with huge parry bonuses, and vice-versa. Going from a big advantage to a huge one doesn't help nearly as much as going from no advantage to a big advantage, or from a big disadvantage to no advantage.

[Hotrod]

You should also check out Lanchester's Laws. Thunderf00t made a nice video about them. They are mathematical models of how battles happen, and they're similar to your approach in many respects.

[Meneliki]

That's a neat tool. I have a few thoughts for you:

First, I think you might be interested in a little Monte Carlo simulation I did of the basic chances to hit when we compare strike vs parry/dodge bonuses. This pits attacker vs defender starting from -19 (strike of attacker << parry/dodge of defender) and increasing to +19 bonus advantage (strike of attacker >> parry/dodge of defender). I tallied up the results of 15,000 strike/parry rolls for each of the following combinations:

-19: 4.75%
-18: 4.80% +0.05% (There may be no difference here at all, for that matter)
-17: 5.1% +0.3%
-16: 5.6% +0.5%
-15: 6.3% +0.7%
-14: 7.2% +0.9%
-13: 8.5% +1.3%
-12: 9.9% +1.4%
-11: 11.6% +1.7%
-10: 13.6% +2.0%
-9: 15.9% +2.3%
-8: 18.7% +2.8%
-7: 20.9% +2.2%
-6: 24.3% +3.4%
-5: 27.5% +3.2%
-4: 31.2% +3.7%
-3: 34.7% +3.5%
-2: 39.0% +4.3%
-1: 43.0% +4.0%
+0: 47.5% +4.5%
+1: 52.4% +4.9%
+2: 56.5% +4.1%
+3: 61.0% +4.5%
+4: 64.7% +3.7%
+5: 68.8% +4.1%
+6: 72.3% +3.5%
+7: 75.4% +3.1%
+8: 78.0% +2.6%
+9: 81.2% +2.2%
+10: 83.6% +2.4%
+11: 86.2% +2.6%
+12: 87.9% +2.7%
+13: 89.6% +1.7%
+14: 91.2% +1.6%
+15: 92.5% +1.3%
+16: 93.6% +1.1%
+17: 94.4% +0.8%
+18: 94.8% +0.4%
+19: 95.0% +0.2%

Any strike/parry difference of 20 or greater is no difference than the difference of 19, since natural 20's always win (except against another natural 20). Since these are randomized attack and defense rolls, there's a little statistical wiggle at play.

The % difference per bonus shows a couple of interesting trends.

Strike and parry bonuses make the biggest difference in absolute terms when your opponent has similar bonuses. You will gain the most hits per strike bonus in absolute terms when your strike bonus is roughly equal to your opponent's parry bonus. If you already have a +10 advantage over your opponent, you'll be gaining about half as many hits per attack for each additional bonus as you will if you have no strike bonus advantage over your opponent's parry bonus.

Proportionately, you increase your hits per additional +1 to strike the most when you have disadvantage of -1 to -16 against your opponent's parry bonus. The peak area is -13 to about -6, where you are proportionately gaining around 15% more hits for each +1 increase in strike bonus. Once your strike bonus is +6 higher than your opponent's parry bonus, you're proportionately gaining only 5% more hits for each +1 increase, and this drops as go go up. If you're enjoying a +14 strike bonus over your opponent, any further bonuses won't make enough difference in your hit frequency for you to notice.


tl;dr: The importance of strike and parry bonuses depends on what you're fighting. Huge strike bonuses help the most against foes with huge parry bonuses, and vice-versa. Going from a big advantage to a huge one doesn't help nearly as much as going from no advantage to a big advantage, or from a big disadvantage to no advantage.

That's an interesting analysis of relative probability. Seems to be some diminishing returns as the bonus disparity increases. Would be interesting to model something like this in another utility.

Thanks for the feedback!

[Natasha]

Hey all,

In my struggle to find a decent solution to mass combat in Rifts, I ended up just coming up with my own. It's based on percentile rather than D20 rolls to determine army hits. Here's a quick demo for those interested: https://www.youtube.com/watch?v=MXVmJmQmM6k&t

Let me know what you think.

Thanks!

M

I like it. I'd go with the geometric mean instead of arithmetic mean in your utility, though.

[Meneliki]

Hey all,

In my struggle to find a decent solution to mass combat in Rifts, I ended up just coming up with my own. It's based on percentile rather than D20 rolls to determine army hits. Here's a quick demo for those interested: https://www.youtube.com/watch?v=MXVmJmQmM6k&t

Let me know what you think.

Thanks!

M

I like it. I'd go with the geometric mean instead of arithmetic mean in your utility, though.

Well, I was going for simplicity to be honest. Not sure what advantage the geometric mean would provide. But then.. I'm a bit of a rookie at these things lol

[slade the sniper]

You should also check out Lanchester's Laws. Thunderf00t made a nice video about them. They are mathematical models of how battles happen, and they're similar to your approach in many respects.

"Generally, Lanchester's square law does not do a good job of explaining National Training Center engagement data, just as it has had limited success with actual combat data. Quantifying all of those factors that affect combat is too complex."
Lanchester's Square Law in Theory and Practice, A Monograph by Major Ronald L. Johnson, Corps of Engineers, United States Army Command and General Staff College, Fort Leavenworth, Kansas, 1989, pg. 41 https://apps.dtic.mil/dtic/tr/fulltext/u2/a225484.pdf

The biggest issue is that theory rarely works in practice. As a start point, it works, but then you have to start adding in modifiers for skill, weapons, terrain, weather, etc. I used the Square Laws for my project initially, but then found that when modeling actual conflicts with them, the data is just not there to support the theory.

-STS

[Natasha]

Hey all,

In my struggle to find a decent solution to mass combat in Rifts, I ended up just coming up with my own. It's based on percentile rather than D20 rolls to determine army hits. Here's a quick demo for those interested: https://www.youtube.com/watch?v=MXVmJmQmM6k&t

Let me know what you think.

Thanks!

M

I like it. I'd go with the geometric mean instead of arithmetic mean in your utility, though.

Well, I was going for simplicity to be honest. Not sure what advantage the geometric mean would provide. But then.. I'm a bit of a rookie at these things lol

Rates indicate using the geometric mean. Other indicators include significant variances and small sample sizes.

I get going for simplicity. So, feel free to ignore the rest of this.

We still have to account for the scaling factors "per group" and "per army". What we're calculating is "damage per troop per group per army". Even though the factors are always one, they exist, which indicates a multiplicative relationship, not an additive one. The geometric mean summarises multiplicative relationships.

Also, the geometric mean is less sensitive than the arithmetic mean to abrupt changes. Consider adding a cyborg to a couple of plastic man suits of armour, for example. The geometric mean's shift is large, but the arithmetic mean's shift is larger.

Finally, implementing the geometric mean might not introduce too much complexity. If your programming language provides a function that raises a number to a power, you can write
gm = pow(x[sub]1[/sub] * x[sub]2[/sub] * ... * x[sub]n[/sub], 1/n)
to get the geometric mean in instead of
am = (x[sub]1[/sub] + x[sub]2[/sub] + ... + x[sub]n[/sub]) / n
to get the arithmetic mean. Where x[sub]1[/sub] is the median damage of group 1 and so on.