Combat

[RedFred]

...although it does seem to me that it would have been just as easy for the programmers to give battle outcome odds as hit point resolution odds. I wonder why they chose the latter.

[Googlie]

Much, of course, depends on the morale of the attacker and the defender. The default is Disciplined, with attackers losing 12.5% for a drop to Green and another 12.5% to Very Green. (Defenders can't lose more than 12.5%) Bonuses are 12.5% for each enhanced level up to a 50% bonus for Elite.

Thus, in big_canuk's above example, a Disciplined 6-1-2 rover against a forested sensored Disciplined 1-3-1 would have odds of 6 against 5.62. At every level above, a same morale attacker would hasve the advantage over the defender (both Hardened would be 6.75 against 6.32; Veteran would see 7.5 vs 7.03; Commando? 8.25 vs 7.73. Elite would see 9 vs 8.43.

But give the plasma defender ECM, and suddenly another 50% kicks in, making the Elite 9 vs 12.65 - a totally different story.

Now give him pulse 3 armor instead of plasma, and yet another 25% kicks in, making him 15.82 in strength at the Elite level vs the Elite Missile Rover's paltry 9.

Only at the both Very Green level does that defender have an outright advantage (4.5 for the attacker with his 25% penalty vs 4.92 for the defender with just a 12.5% penalty) or in circumstances where the defender's morale is at least 1 greater than the attacker's.

Googlie


[This message has been edited by Googlie (edited December 19, 2000).]

[Fitz]

quote: Originally posted by big_canuk on 12-18-2000 08:59 PM WE: The modifiers are multiplicative, not additive. If a 3+ defender in forest, with a sensor is attacked by a 6 attack rover, then the odds would be 6:3x1.5(for the +)x1.5(for the forest)x1.25(for the sensor)= about 6:3x2.83 = 6:8.5

I disagree. I am pretty sure the odds are additive.
Your total bonus should only be 3x2.25 (or 6.75), not 3x2.83 I could be wrong though. I'll break out a calculator if I game tonight, and double check.

And native life odds are simple. Merely divide the units odds with the reactor by the reactor level. Level two reactor infantry vs mindworm is displayed as 6 to 2, in actuality it is 3 to 2. Additionally, the correct odds are displayed in the lower MFD center panel, so if you are using the calculate before battle function, just look down there instead of at the popup. Easy.

The other factor to take into account is that you are treated as if you only hat 10 hits in psi combat, regardless of reactor level. An alternate way of thinking about this is that you will take (damage x reactor level) for each 'cycle' of combat. If you have fusion, for every '1' point of damage you take, the unit will take '2' points of damage. Simple really.

[Googlie]

Fitz:

They're multiplicative.

I scenario tested all levels of morale and defenses for the rover vs the scout and jotted down the odds, then tested them with a calculator. There is some rounding done in the odds display, but not in the underlying math that the game program uses.

G.

[MariOne]

WE, stop flattering me , but...."CHARACHTER"?????


First disclaimer:
I do NOT test "everything"!!!!
I still did not investigate the details of many game aspects, because so far common sense, or first impressions drawn from direct experience, sufficed me.

I also LEARNED A LOT, from interaction with other players in ACOL (thx cousLee, JAMiAM & Bingmann, mainly), and from this forum.
Many time my assumptions were proven wrong, or I took for granted some mechanisms which instead worked in an unexpected way.

---

Back to topic, I did not "statistically" test the combat mechanism.
I know tho how it's "supposed" to be, and from my experience all the rules and statements I could find in the manual and datalinks, are consistent with the way you can see the strength/odds calculated in the combat display. Only exception, the reactors should not be counted when calculating the odds for PSI combat.

To be more precise, the "odds" are not always exact.
The "strength" is. The odds are then calculated to round them to the TWO INTEGERS best approximating the actual fraction. Sometimes I see that 1.09 vs. 0.89 are incredibly expressed as 3 to 2 (and not 27 to 22, assuming equal hitpoints of course).


Few facts that I can feel pretty confident to confirm:
- Attacker's weapon vs. Defender's armor are taken into account in conventional combat
- exceptions: psi combat, probe combat, artillery vs. artillery, SAM vs. SAM
- Modifiers ARE multiplicative
- Modifiers are applied to the relevant basic figure (Attacker's Weapon / Defender's Armor, exceptions apart) to produce a single, all-comprehensive "strength" value for the unit throughout a specific fight
- to obtain the "odds", the "strength" is multiplied by the HitPoints! thus damage and/or reactor are taken into account
- the fractional "odds" are corrected to give integer numbers (minimum common denominator)
- a sequence of independent rounds are resolved, each one applying the original strenght ratio (NOT ODDS!), till one unit dies (exception: artillery)

*****
- Only with equal damage and equal reactors, the odds correspond to the strength ratio applied to each blow. Otherwise they just represent a gross indicator of your overall chances in this combat taking into account all the factors
- to say it simpler, if you have greater strength but 3 hitpoints against 20, you'll have greater chances to win each single blow, but overall you'll likely die. One single blow going against you would do you in, while you'd need a sequence of 7 lucky strikes
*****

- as far as I understood it, and my observation didn't deny it but neither allowed me to confirm it with statistical significance, the strength ratio works indeed as others have already reported it here.
You sum the two strengths (NOT ODDS!) and pro-rate them to the certainty (1, or 100% if you prefer)
- examples:
3 vs. 1 = 3/4 vs 1/4, or 75% vs 25%
3 vs. 2 = 3/5 vs 2/5, or 60% vs 40%

COMPLICATION
This would suggest that each blow is assigned to one or the other fighter accorting to the statistical chances above.
Even that way, the fact that multiple events will determine the outcome of the battle, would make it actually a "set" of outcomes, with the surviving unit being able to win with a 0%-90% range of sustained damage.
A probabilistic tree, where each pair of branches stemming out of a node are weighed with the % of a single blow, should be used. Binomial coefficients would typically be involved, and the outcomes expressed by a bell-like curve.
Even disregarding the detail of the final damage, the win/loss chances will be obtained summing all the many paths leading into one or the other major outcomes, and that total "not necessarily" corresponds to the odds of a single round of fight.

MORE, ALSO A SINGLE SHOOTING ROUND DOES NOT HAVE JUST A SIMPLE "HIT / GET HIT" OUTCOME!!!

I have seen damage being inflicted in "1 hitpoint" OR "3 hitpoints" tokens
I am PRETTY confident of having seen these combinations for a single round:

3 - 0
3 - 1
1 - 0
0 - 1
1 - 3
0 - 3

I am NOT sure whether "ties" actually occur, but they might well do (both units get equally hurt)
3 - 3
1 - 1

(Reactors get "ignored" that way in psi combat: the damage you suffer is multiplied by the reactor you have, e.g. you may well have 20 hitpoints thanks to Fusion, but if a 3-pointer counts as 6, it's just as you had only 10 hitpoints)

Well, I DON'T KNOW how the strength ratio influences the density of probability of the above classes!
A rather excruciating field testing and data collection & analysis would be needed.
A SLOW computer would also help, as you can't freeze a single combat during its rounds! You should rivet your eyes to the combat screen, and record your voice reading the decreasing hitpoints values for the two units!!!!
Be my guest!

Googlie, will you be our champion here?

-----

So, I guess we will have to make do with the odds we read, biased by our experince and intuition.
I agree for instance that good odds tend generally to favor you more than their nominal ratio.
But I also lost many combats where I had 5 to 4 "odds" in my favor, or even 9 to 7.

Maybe, as once JAM told me, only wimps activate odds before battle in pbems

[MariOne]

well, well, well!

I put down few formulas in excel, adopting the simplified model:
- each round giving only a you/me outcome, basesd on the strength
- assuming 4 rounds required to win (you can then win with a 0-3 damage taken)

I calculated the statistical ODDS for winning such a BATTLE, given the probability to win a single ROUND.

A small advantage in the round, get significantly increased in the final odds, thus confirming RedFred's impressions!

Here I paste a raw table where I report the chances of scoring a single blow along with the corresponding final battle victory chances.
NOTE: the X to Y here is the "strength" ratio, NOT the game's proposed odds!

Strength ratio Battle ODDS
5 to 4 (55.6) - 62.0%
4 to 3 (57.1) - 65.3%
3 to 2 (60._) - 71.0%
2 to 1 (66.7) - 82.7%
7 to 3 (70._) - 87.4%
3 to 1 (75._) - 92.9%
4 to 1 (80._) - 96.7%

I hope UBB doesn't screw the table.
I can always upload the .xls and link to it.

You see that a plain laser against a plain scout patrol (2:1 strength) actually allows you to win the battle 7 out of 8 times! (although 3 of those 7 you'd have been hit by 2 or 3 blows too)

Incidentally, the 1.09 against 0.89 strength I quoted above, produces a 61% to win the battle - very close to "3 to 2" overall odd reported by the game! I stand auto-corrected!

I wonder how a more precise model, counting the lesser and/or mixed hits, would influence these simplified conclusions...
[This message has been edited by MariOne (edited December 25, 2000).]

[Aredhran]

Bored on Christmas Day ?

[big_canuk]

Thanks Mario!

I knew that the maths were more complicated than my feeble (and prolly inaccurate) depiction.

If you are not going to post that excel table, could you email it to me. My email is in my profile.

I agree with you on the simultaneous 3 - 1, 1 - 3, etc damage outcomes. I think I diagree on the ties though. I don't believe I have seen them, and if they occured, then destruction of both units would be possible, which I believe is not the case.

A special case also may occur, when you attack with greatly positive odds, but are severely damaged with only 1 hitpoint left. I seems, that usually (always?), the first battle resolution is one of those 1 - 3 types, and the attacker is destroyed.

I will try to make some observations in my current games. While I will not do a "comprehensive study", if I (we) understand the math, and do some properly conducted samples, we should be able to help out with the simple odds, as you have done above, but also help with the dissimilar reactor odds which often indicate positive odds, when in fact they are negative.

Thanks again!

[Sikander]

MariOne,

Thanks for your excellent analysis. I feel somewhat vindicated that my strength to strength model seems to be holding up. The confusing point seems to be the variable number of hit points removed on each exchange shown in the animated exchange. I have an idea why this is, which I shall throw out:

The game actually does resolve combat in the way I said in my original post. Single rounds are conducted where the modified strengths of each unit (weapon strength for the attacker and armor or weapon value (air to air) for the defender) are compared and assigned a representative proportion of the random number range. A random number is generated, and a hit is generated for either the attacker or defender, and one hit point is removed from the loser of that round.

So why do combats only seem to last a few rounds, and why are multiple hit points seemingly removed with little rhyme or reason?

My best guess is that it would be dull to watch two 40 hit point units of even strength fight it out to the death. It might well take 79 rounds of combat to declare a winner. Thus the game resolves a certain number of rounds (my guess is 3 or 4), while only giving the player updates at the intervals. The whole time consuming process is actually taking place at high speed, but the animations and combat data are only updated occaisionally to speed the process up. This would explain why 3 to 1 results occur, as this is only the report of 4 actual exchanges between the combatants. This may also explain why a very low hit point unit seems to be regularly destroyed in the first round. It is actually being destroyed in one of the first 4 (or whatever) rounds, and is shown exploding in the first combat report / animation.

Am I crazy, incoherent, or does this make sense to anyone else?

[MariOne]

Combat odds table

b_c, good point about ties
Nevertheless, I am pretty sure and you confirm that, that I saw 3-1 outcomes. That could lead to killing each other too...
Or the game filters out these "border" conditions, either Sikander's idea holds.

The odds with dissimilar reactors should indeed reflect the actual chances taken the hitpoints into account.
If your strength is 3.5:2 but your hitpoints are 10:20, your odds should rouglhy reflect that with a 35 to 40 (7 to 8).

Sikander, this is a very original idea!
I was trying to figure a solution dividing the 0 to 1 range in more than two classes, to accommodate the 3-0, 3-1, 1-0 outcomes (and the opposites). I just had no clue about the width to be assigned to each interval.
I also thought that two separate independent tosses could have been made, one for the attacker and one for the defender. That also required tho 3 intervals, big/small/no hit, and rules to decide the ties.

We should now try to imagine which solution could have been looked "simpler" to the Firaxian programmers, and that means headache to me. Couldn't they just disclose the source code for combat sorting?

Your approach sounds very intriguing.
But then I ask to myself, why the "single hitpoint" rounds have been grouped into 3-0, 3-1 and 1-0 only?
Why 2-0, 2-1 & 3-2 have been left out?
And why, contrasting with your model, sometimes the combat is updated after a single round (1-0)?

Besides, the only "proof" that combat rounds are resolved by strength ratio, is written in the often wrong and/or outdated manual (SMAC), which at page 97, Ch4, "Combat" section reports:
Combat is decided by totaling the attacker's strength and the defender's strength. The probability of either side doing damage is equal to that side's portion of their combined strengths. This process of assessing damage repeats until either the attacker or defender is destroyed.
Nothing is said in the Datalinks.

I found no inconsistency with the above and my superficial observations, I am far tho from being able to *confirm* that it "actually" (knowing FurXs ) works that way.


About my xls, that is not actually a lookup table.
I used a table to get to the results breaking down the calcualtion into logic steps, and I left the formulas there for you to see.
I let the possibility to input the A & D strengths.
The simplified model ignores many of your last posts issues.

The table could be easily extended to the one-hit approach, for two 10-hitpointed units.
Taking in consideration damage (patial hitpoints at the start) would need adding some formulas to filter out the rows considering more hits than a unit can suffer.
Extending it to higher reactors would make the table cumbersome.
You can produce by yourself an actual lookup table, by hand as I partially did, or using the dedicated Excel function.

Damn, the Woody Allen movie with Mira Sorvino has begun! (I'm a VCRless luddite for those who don't know me...)

[This message has been edited by MariOne (edited December 27, 2000).]

[big_canuk]

Mario:

quote: Originally posted by MariOne on 12-27-2000 03:06 PM The odds with dissimilar reactors should indeed reflect the actual chances taken the hitpoints into account. If your strength is 3.5:2 but your hitpoints are 10:20, your odds should rouglhy reflect that with a 35 to 40 (7 to 8). [This message has been edited by MariOne (edited December 27, 2000).]

ahhh.. , but this is the point I was trying to make. The odds are NOT 7 to 8.

Let us take you example of a laser infantry attacking a scout. At 2:1 odds the actual chance of winning is 82% not 66%. If we extend this to a laser infantry attacking a fusion scout, then the odds would be 1:1. The real chance of winning would be (help with math please), but something like 82% for the 1st 1/2 of the battle, and 82% plus a touch for the outcome where we died it the 1st half anyway, and so a total chance of winning of 64% plus a bit, maybe 65%. We took some dammage in the first round, so this would lessen the advantage to maybe 60% or 3:2 odds.

These are the situations where we need extra info, so that we can attack at negative "odds", if we have to, against a higher reactor, and so that when we have the higher reactor, that we do not get lulled into thinking that the odds in our favour means that we will actually win more than loose, when attacking a stronger unit.

I will play with your table and see if I can post some real odds for reactor 2 attacking reactor 1 and visa versa.

Thanks again!

[VoodooChild]

I know i'm chiming in late, I have skimmed past a couple of the replies, so I don't know if this has been covered....

There are two aspects of combat that I don't think have been covered so far. Diminishing chances and Collateral damage.

Diminishing Chances: I believe that if an attacker has a 10 gun after modifiers, that if that unit is hit, the attackers gun will inflict less damage if the attacker scores the next hit. The same could be said about a defender's armor. Run a test against even odds combatants and you will see that the first hit is the most important since it will produce the likely winner.

Collateral damage: I have seen that even when the odds are absurd that the victor will take a minor hit after a set number of "rounds" I believe that this is not done as a part of a combat round, but more as Round 1, Round 2, Round 3, Round 4, Collateral Damage, Round 5, etc.. It appears that both combatants take this minor hit, and it might be what your thinking the ties are.

More food for thought

[big_canuk]

Mario:

Helppppp!!!!

After going over you table for too many minutes, I thought I understood all you did and why you did it. All seemed logical. So...

to expand the table to a fission 2 attacking a fusion scout, I changed the inputs to:

7 0
7 1
7 2
7 3
----
6 4
5 4
4 4
3 4
2 4
1 4
0 4

Alas, the total percentage adds up to 106%. What did I do wrong?

BTW, I've been away to long! Wow, are you a whiz with excel, or does everyone do as clear and well-annotated job as you.

[MariOne]

Combat odds table

Ok, I uploaded an updated version of the sheet.
I added 2 tabs allowing to enter any hitpoint up to 20 for the 2 units.
This will allow to take into account the effect of a Fusion reactor and of damaged units.
One tab keeps the simplified model giving 3 fixed hitpoints for each marked hit.
The second adopts Sikander's model of "1 hit - 1 hitpoint" underlying mechanism.

NOTE:
these tables correctly implement the Probability Theory, GIVEN that a sequence of rounds resolved using the Strength Ratio as chance of the single event holds.
So, we should not question the results they give.
We should in case question the underlying assupmtions.
That is, we should verify whether the results provided by our theory correspond to the empirical observations we might collect, or not, in which case we'd have to adjust the theory.


VooCh, your concepts are interesting.
I have to say tho that so far my impressions do not support them. On the contrary, I can recall many cases observed which negate them.
Of course this is far from statistical significativity.
I have seen tho many battles between equal forces where the lead changed 3 times during the same battle. And it's not unusual to see favored units win a battle unscathed.


b_c, a few figures to comment the indications of my tables.

- I entered the (A)3.5*10hp vs (D)2*20hp example.
The game's plain multiplicative odds (7 to 8, that is 7/15 to 8/15) tell a chance of 46.67% for the attacker.
The simplified-3hp-tokens model gives a value of 47.70%.
Sikander's single-hits model yelds a prediction of 34.92% (!).

- A battle between two 10hp units with 2:1 strenghts gives 82.7% for the laser with the basic table, face to a 66.67% for the single blow.
The same using Sikander's, jumps to 93.52%!
And to 98.45% also assuming both units Fusion (20 hp)!!!
(it would mean, you lose 1 time out of 64! too much, methinks)

- your example of 2*10hp vs. 1*20hp
You can't treat a whole event splitting it like that, you lose all the partial outcomes which actually would continue as further ramifications, too complicated to keep track.
Just extend the tables, we apply the same approach to the new dimensions.
The token3 model favors the laser attacker, which retains an overall 55.93%.
Sikander's instead favors the defender, leaving the attacker with 48.27%.
If tho you take one hitpoint out of the laser (10%damage), the token3 model will allow him to die with 3 blows instead of 4, and his chances of survival drop to 37.72. Perchance, in this case that's EXACTLY the result of Sikander's model! (down to the 2nd decimal only).
Interesting also to see how one notch advantage in morale for the laser (strength 2.25 vs 1) whill boost his chances to slighlty above 60% in both models.

---

I guess that testing time awaits us.
A first one using two scout patrols, as suggested, gave me the "impression" that even 2-2 rounds are possible! This would fill a missing link in favor of Sikander's model.
I'll have to test it on a SLOWER PC (I have a P133 at the office!).

[MariOne]

b_c, I'm no XL wiz....

I just used to earn a living teaching it, for 10 years...
And it all began with Lotus 1-2-3 back in '85! (and it was the DOS-based version of course. and which was DOS version itself? 3.3? geez!)
Aside: old DOS 1-2-3 had macros written as label columns, in the same sheet (no multiple sheets at the time...). That is, the code of an internal executable algorythm was stored in no different way than any other data, in the same data space... This gave us an environment where the "user code" could auto-edit itself while running! Wonderful to implement the Core Wars "viruses"... /Aside


About the wrong total %, I can only suppose that you let some reference slip when inserting the new rows...
You see that we structured the table in the same way.
I added a test function on the combinations colum, to filter ou rows exceeding the available hitpoints, and allow for some parametric flexibility...

I better shut up now, before Aredhran posts his BLAH!
---
PS: the previous post was actually a X-post with your help cry! If only I'd remember to hit refresh from time to time...
And... my skills are now out-of-date, and since long, I'll need to catch up, maybe learn to make my webspace a decent page...

[This message has been edited by MariOne (edited December 28, 2000).]