civ5 Combat and Odds (Video analysis)

AriochIV pointed me to this video:
http://www.gamespot.com/pc/strategy...-2010-interview-jon-shafer?tag=videos;title;5
which shows several combats.

The following is an analysis of the combats that were shown, and a few guesses made about what the odds mean.



Combat is fought in "rounds". In ranged combat there is only ever one round and only the attacker can deal any damage. Units all have 10 hitpoints (hp). Even though graphically some units are represented by more than 10 little men or fewer than 10, the underlying mechanics work off 10 hitpoints.

Each round, the attacker and defender trade blows simultaneously. This is unlike civ4 combat where each round only one combatant got to deal damage i.e. a combatant would "win" each round. The amount of damage that is dealt per round by each combatant will likely depend on a few different things but in particular the unit's strength. One could probably assume at this stage that an injured unit has less strength and so less ability to deal damage in each round. Note that Japan's unique ability allow them to deal damage each round as if they were full health.

I'm not entirely clear yet what the exact meanings of "minor victory", "major defeat" and "stalemate" etc. are.

At 0:30, the battle predicts major defeat.
The odds bars have little divisions in them with the upper section flashing and the lower section solid, and it looks so far like all of the smaller bars make up a fraction of 10 of the whole bar (more evidence of units having 10 hitpoints). In the 0:30 battle, the higher of the sub-divided bars flash suggesting they are the predicted damage on each side. My guess is that the 2nd (lower) bars are the predicted remaining hitpoints after combat. Notice that in this particular battle, it's predicted that the attacker will take 9hp of damage with 1 hp remaining. The defender is already damaged at the time the battle starts which is why the top part of its bar is black (4 hitpoints are black, so the unit is 6 hitpoints). The defender is predicted to take 3 hitpoints of damage, being left with 3.
In the battle, the attacker dies outright (confirming the predicted battle outcomes are not the actual outcomes as has been suggested on other parts of the forum) rather than living with 1hp, and the defender takes the predicted 3hp of damage (note the -3 in red that appears after battle).

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In the ranged combat at 0:40, the defender is expected to take 3hp of damage from full health. This time, the bars indicating the predicted ramaining health are green, probably an indication that the battle odds are "good" for the combat being queried. The defender loses 3hp as predicted.


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In the battle at 0:49, the attacker and defender are both predicted to lose 5hp. The defender starts with 7hp (losing 3hp previously) and is predicted to walk away with 2hp. The defender actually loses 4hp and the attacker loses 7hp.
Notice that after the battle, the attacker loses 7hp and the defender loses 4. Again, the outcome was slightly different than what was predicted.

*************
At 0:57, attacker is expected to take 1hp damage, and defender to die. Outcome is exactly as predicted.


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At 1:10, ranged combat. Defender predicted to lose 5hp, but actually loses 7. In the second ranged combat, defender obviously predicted to lose all remaining 3hp.


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The next naval battle shows the first 2 ships expecting to and actually dealing 3hp damage each, and the final expecting and actaully dealing 4hp. Note that the 3rd unit to attack was a battleship rather than a destroyer. The fact that both the first two units expected to do 3hp of damage, gives a little bit of weight to the assumption that the defender's health is not relevant to how much damage they will receive from a hit.
(no picture for this one)

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Battle at 1:38. Defender is expected to die and the predicted outcome this time is "Total Victory". Notice that the attacker is more than double its strength. This might be the threshold needed to get the "Total Victory" prediction (at least for full health units anyway), and my guess here is that "Total Victory" means guaranteed victory. I have a feeling that the game designers have done a similar thing to civrev and made combat so that beyond a certain point, battles like this cannot turn out as upsets.


*************

The things I'm left wondering are the meanings of the "major", "minor", "stalemate" etc. outcomes; how damage per round is worked out (probably very hard to work out from vids this early); what the predicted damages actually are (e.g. are they average combat outcomes or the most likely (i.e. mean vs. mode) or perhaps even less exact predictions?).

Another thing to notice is the absence of actual probabilities (i.e percentages or numbers between 0 and 1) for any outcomes. In civ4 you were told the probability of killing the defender - this is absent so far in civ5.

The largest deviation of actual remaining defender hitpoints outcome and predicted defender hitpoints so far is 2 from what I've seen. I wonder if there are examples of where the predicted outcome was off by 3 or more? (please post if so)

Excellent analysis, PieceOfMind. It fits what I had been thinking, but I hadn't taken the time to collect the data in one place. Nice reference.

Could the descriptive spectrum
(Victory<-Total, Major, Minor, Stalemate, Minor, Major, Total->Defeat) be determined by the comparing the ratio of expected damage (using a 1 for 0) for regular combat and flat damage for Ranged?

:30 | (9hp vs 3hp) 3:1 = Major Defeat
:49 | (5 vs 5) 1:1 = Stalemate
:57 | (1:10) 1:10 = Total Victory
1:10 | (5hp Ranged) = Major Victory
1:38 | (0 vs 10) = Total Victory

2:1 could be Minor (1-4 hp for Ranged)

Thyrwyn said:

Could the descriptive spectrum
(Victory<-Total, Major, Minor, Stalemate, Minor, Major, Total->Defeat) be determined by the comparing the ratio of expected damage (using a 1 for 0) for regular combat and flat damage for Ranged?

:30 | (9hp vs 3hp) 3:1 = Major Defeat
:49 | (5 vs 5) 1:1 = Stalemate
:57 | (1:10) 1:10 = Total Victory
1:10 | (5hp Ranged) = Major Victory
1:38 | (0 vs 10) = Total Victory

2:1 could be Minor (1-4 hp for Ranged)

Click to expand...

That's a good guess IMO.

Do you know of any other vids or screenshots of battles that were not the same as in this video? This one seemed to be heavy on combats (making it useful for this topic) but even at the end they started repeating footage. I haven't been keeping atop of all the footage from preview articles.


EDIT
Just noticed in the closed demo footage that there was also the category "Decisive Victory". Not sure if this exists anymore though.

I will classify things like that:

Safe attack > 0 hp lost
Total victory > 0,.... to 1 hp lost
Major victory > 1,... to 2 hp lost
Decisive victory > 2,... to 3 hp lost
Minor victory > 3,... to 4 hp lost
Stalemate > 4,... to 5,... hp lost

something like that.

I have a feeling that the game designers have done a similar thing to civrev and made combat so that beyond a certain point, battles like this cannot turn out as upsets.

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I hope this isn't the case in Civ 5, and the battle system may make it unnecessary. The problem in Civ 4 is that, unless you could withdraw, either the attacker or defender had to be eliminated at the end of the battle. So if you had a 97% chance of willing, 3 times out of 100 (and you'd probably have more than 100 battles in a game) your more powerful unit would not just be "defeated", it would die.
From what we've seen from Civ 5, if you're "promised" a "total victory", the worse that could happen is you'd destroy the enemy, but lose 2 hp instead of none or 1, or maybe loose 4 hp and leave the opponent alive with 1. That's an upset, but it's not as frustrating as losing a highly-promoted unit with a great general attached even though you've only used it with "safe" odds (as could happen in Civ 4).

PieceOfMind said:

Another thing to notice is the absence of actual probabilities (i.e percentages or numbers between 0 and 1) for any outcomes. In civ4 you were told the probability of killing the defender - this is absent so far in civ5.

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Very nice analysis PieceOfMind.

On this point, I don't mind if there are no probabilities listed, so long as they give me a general outline of what is most likely to occur. A small deviation from that is fine by me.

In all honestly, I would prefer it if there was literally no such thing as probability whatsoever, and the system would literally tell you exactly what the outcome would look like before it was to happen. I suppose there's a segment of people who like the "randomness" of combat, or what have you, but I would love it if every move was certain.

Gre_Magus said:

I hope this isn't the case in Civ 5, and the battle system may make it unnecessary. The problem in Civ 4 is that, unless you could withdraw, either the attacker or defender had to be eliminated at the end of the battle. So if you had a 97% chance of willing, 3 times out of 100 (and you'd probably have more than 100 battles in a game) your more powerful unit would not just be "defeated", it would die.
From what we've seen from Civ 5, if you're "promised" a "total victory", the worse that could happen is you'd destroy the enemy, but lose 2 hp instead of none or 1, or maybe loose 4 hp and leave the opponent alive with 1. That's an upset, but it's not as frustrating as losing a highly-promoted unit with a great general attached even though you've only used it with "safe" odds (as could happen in Civ 4).

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Some good points.

So if sometimes battles result in neither unit dying, then what mechanism is it that stops the battle? Is it simply a limimted number of combat rounds? Perhaps 1 round. Perhaps 3? I'm fairly certain that in the case of ranged it attacks it's only 1 round.
In the case of the 0:30 battle, from the battle animation the battle looks like it takes place in 3 rounds, but maybe that it's just a complicated animation for 1 round?

In the 0:49 battle though, the rifles look like they fire 3 times while the muskets look like they fire twice. It's hard to tell because the animations don't seem to match up very well in that battle. The third shot from the riflemen looks like it does nothing.

Another thing to notice is the absence of actual probabilities (i.e percentages or numbers between 0 and 1) for any outcomes.

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I hate this kind of thing. I hope there is some kind of advanced option (or at least some willing modders) that will provide this info.
I want to know what the probability distribution is of the various possible outcomes, much like Battle for Wesnoth.
I can't plan an optimal strategy unless I know what's actually going on in a statistical sense. There's just no good reason to hide this data from the player.

JonoLith said:

Very nice analysis PieceOfMind.

On this point, I don't mind if there are no probabilities listed, so long as they give me a general outline of what is most likely to occur. A small deviation from that is fine by me.

In all honestly, I would prefer it if there was literally no such thing as probability whatsoever, and the system would literally tell you exactly what the outcome would look like before it was to happen. I suppose there's a segment of people who like the "randomness" of combat, or what have you, but I would love it if every move was certain.

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It's interesting that what you want is sort of opposite to what some others told me about what I planned or did for ACO...
(see the bolded in this quote)

http://forums.civfanatics.com/showpost.php?p=7776009&postcount=28

Roland Johansen said:

Anymore? I didn't put forth a different position earlier, did I?

Anyhow, I just don't think that I'll be using the average hitpoints left very often in gameplay. I do think that I will use the chance to lose no hitpoints as that means that my unit doesn't need to heal. That last information is very useful when I am moving my SOD from enemy city to enemy city. It means faster conquest with less units needing to stop to heal if I pick the ones that have a high chance to lose no hitpoints (likely the drill promoted units).
The average hitpoints left isn't that interesting as it doesn't tell you a lot about the time you need to heal (as many might expect it does). That has to do with the distribution of damage that leads to this average hitpoints left. This distribution is typically so variable (high variation for the mathematicians) that the average isn't very interesting for gameplay. It's hard to estimate by looking at this average if you'll likely be healing for 1, 2, 3 or more turns because of this variability.

But maybe other players will use the average hitpoints left in their combat tactics, so it's still a useful piece of information. Just not for me.

Edit: By the way, I would be interested in something like this:
Victory: 75% (3XP)
0 turns to heal 20%
1 turn to heal 27%
2 turns to heal 37%
3 turns to heal 16%
Defeat 25%
etc.

But it would of course depend on the healers present on the tile and other factors, so that information should be extracted from the game when such a calculation is made. (I don't know how hard that would be). I guess that with the information of the healing speed, PieceOfMind could easily calculate the turns to heal with the values from his present calculations. His own 'Unit Healing' strategy article would be useful for this part.

Click to expand...

(emphasis added by me)


And the following message to me was before I even made ACO, but while I was planning on making it:
http://forums.civfanatics.com/showpost.php?p=7719281&postcount=31

oyzar said:

It is not terribly hard to see if you are close to a break point from the damage dealt and the total hp of the attacker / defender though... expected values means pretty little, but the probability of winning a given round is nice to have...

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Note that when oyzar refers to a "given round", he's talking about individual combat rounds. The main thing to note is that he didn't think expected values meant much.

I suppose you could argue that in civ4's combat model, expected hitpoints was less interesting because you always knew one of the units was going to die (or one would retreat) and the probability of attacker surviving was more important.

Still, in civ5, I suspect most people would find it useful to know the actual probability of the attacker surviving. Assuming units can heal for free like they did in civ4, it's going to be optimal a lot of the time to send in units that are less likely to die.

Ahriman said:

I hate this kind of thing. I hope there is some kind of advanced option (or at least some willing modders) that will provide this info.
I want to know what the probability distribution is of the various possible outcomes, much like Battle for Wesnoth.
I can't plan an optimal strategy unless I know what's actually going on in a statistical sense. There's just no good reason to hide this data from the player.

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Well you might have guessed by now that I'm already interested in ideas on such a mod. If you've used ACO you'll already know how much information I like to have about probabilities of combat outcomes. For me at least, it's like having the individual breakdown of income and expenses in the economy screen or the breakdown of the sources of hammers and the hammer multipliers in the mouse-over in the civ4 city screen. I'm big on interface details like that.

For the benefit of the unitiated who are reading, this is the sort of thing I did with ACO (with a lot of help from EmperorFool!!)

ACO is excellent, much kudos for developing it. It would be fantastic if you developed something similar for Civ5, if that info isn't available.

I think knowing about hitpoint outcomes would be more useful than Roland's number of turns to heal, since number of turns to heal will no doubt depend for example on whether the unit moves, whether its in friendly territory or not, and so forth.

* * *
Another thing on this point that I've been thinking about; I had previously assumed that the amount of damage done in a round (or the probabilities of this) were determined solely by the relative strengths of the units, and not by how much health/hit points they have left, like in Civ4 or Dungeons & Dragons.

But: Japan's faction ability (Bushido) is that units always attack at full strength.

Which seems to imply that damaged units are less effective on offense (but maybe not on defense). Any thoughts on how this might be implemented?

I'm not convinced battles happen in rounds. It seems like units just do damage to one another simultaneously in one shot based on relative strength, hp, and combat modifiers, plus some random factor. It may well be that the expected damage is just this without the random modifier.

Ahriman said:

ACO is excellent, much kudos for developing it. It would be fantastic if you developed something similar for Civ5, if that info isn't available.

I think knowing about hitpoint outcomes would be more useful than Roland's number of turns to heal, since number of turns to heal will no doubt depend for example on whether the unit moves, whether its in friendly territory or not, and so forth.

* * *
Another thing on this point that I've been thinking about; I had previously assumed that the amount of damage done in a round (or the probabilities of this) were determined solely by the relative strengths of the units, and not by how much health/hit points they have left, like in Civ4 or Dungeons & Dragons.

But: Japan's faction ability (Bushido) is that units always attack at full strength.

Which seems to imply that damaged units are less effective on offense (but maybe not on defense). Any thoughts on how this might be implemented?

Click to expand...

From what I've seen, I'm fairly certain that the defender's health has no impact on how much damage they receive, but the attacker's health does have an effect (obviously, if Japan's unique ability changes that!, as you noted).

It's true this is a bit different from civ4, but it probably makes more sense in a system where there is ranged combat. It might be weird (or just plain unfair) if the first ranged attack did, say, 3hp damage, and the next did 4 or 5 (on average in each case).

I suppose the same would work the other way. So an initially injured defender would be less capable of dealing damage to the attacker, but the attacker's health wouldn't affect how much damage the defender dealt.

So all in all, combat is still fairly symmetric apart from the fact that combat bonuses will usually favour the defender and defenders do not get a chance to retaliate in ranged combat.

funkeymonkeyman said:

I'm not convinced battles happen in rounds. It seems like units just do damage to one another simultaneously in one shot based on relative strength, hp, and combat modifiers, plus some random factor. It may well be that the expected damage is just this without the random modifier.

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Perhaps. I know I keep saying this but that would make it pretty similar to Advance Wars, only with slightly more variance in the random factor.

It's true this is a bit different from civ4, but it probably makes more sense in a system where there is ranged combat. It might be weird (or just plain unfair) if the first ranged attack did, say, 3hp damage, and the next did 4 or 5 (on average in each case).

I suppose the same would work the other way. So an initially injured defender would be less capable of dealing damage to the attacker, but the attacker's health wouldn't affect how much damage the defender dealt.

So all in all, combat is still fairly symmetric apart from the fact that combat bonuses will usually favour the defender and defenders do not get a chance to retaliate in ranged combat.

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I don't understand what you're saying here, and I don't see how this is symmetric.

Imagine that being damaged reduces your effectiveness while attacking, but not while defending.
[Recall from an early preview that they said damaged units would still defend at full strength]
Imagine two identical units on flat ground with no modifiers.

Suppose they start at full health; they perform the same, and the odds are basically even. The attacker expects to take as much damage as they inflict.

Suppose now that they start at half health. The attacker is weakened, but the defender is not, so the identical units no longer have even combat odds.

If both attacking and defending units degrade as they take damage (like in Civ4) then there is no bias, but this is not the case if only attackers degrade.

* * *
I hope combat still happens in rounds, because this has a tendency of centralizing the probability weighting of the outcomes.

For example, compare:
a) Picking a single number between 0-15, with uniform probability. Call this X.
b) Pick a number from 0-5 with uniform probability three times, and add them together. Call this Y.
These have the same max, min and mean, but the variance of X is much higher than the variance of Y.

Of course, its entirely possible to replicate the same distribution with a single probability draw, but combat calculators have a strong tendency to use uniform probability distributions, because people think about these models in terms of die rolls.

Check out the IGN preview here. This appears to be the latest build, judging by the unit icons at the bottom-left of the screen.

There is a "Decisive Victory" (and so presumably "Decisive Defeat") option (see 0:20, 0:44, 0:50, 1:02, 1:12, 1:18 and 2:08 on the video). There is no "Total Victory" shown in this video, so it could have been renamed (EDIT: Total and Decisive victory both appear in the closed E3 demo so they probably are separate). "Major Victory" is at 0:20, 2:06 and 2:09.

My guess is something like:
Total victory - the enemy will die, you take slight (0-1) damage
Decisive victory - the enemy will die, you take minor (1-2) damage
Major victory - the enemy takes 4-6 damage more than you
Minor victory - the enemy takes 1-3 damage more than you
Stalemate - you take equal damage

"Ranged Combat" is its own category (see 0:56, 0:57, 1:20).

Also, in the closed E3 demo, there was a "Safe Attack" category when Rome captured Gloucester from England.

How would a ACO work. In order to truly convey all information on possible outcomes a somewhat 3d probability graph would have to be developed with defender health after battle, offender health after battle and probability being the X Y & Z axis respectively. This would take much effort to understand and be very difficult to mod in. I am personally satisfied with the simple text.

The variance may be "artificially" lowered. Instead of picking a number between 0-15 or 3 between 0-5 and adding them, maybe it's picking one between 5 and 10.

In terms of die rolls it's 1d6+4 instead of 1d16-1 or 3d6-3.

How would a ACO work. In order to truly convey all information on possible outcomes a somewhat 3d probability graph would have to be developed with defender health after battle, offender health after battle and probability being the X Y & Z axis respectively.

Click to expand...

You'd do it like Battle for Wesnoth.
One column with probability of attacker health (
eg: 25% 9 health, 25% 8 health, 25% 7 health, 25% 6 health) and one column with the probability distribution of defender health (eg 25% 4 health, 25% 2 health, 50% 0 health).

You don't need to know the cross-probabilities (conditional probability that the enemy has 2 health given that you have 7 health).

Ahriman said:

I don't understand what you're saying here, and I don't see how this is symmetric.

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Symmetry's a tricky thing to discuss, but I think we're on the same page with what I'm meaning by it.

Imagine that being damaged reduces your effectiveness while attacking, but not while defending.
[Recall from an early preview that they said damaged units would still defend at full strength]
Imagine two identical units on flat ground with no modifiers.

Suppose they start at full health; they perform the same, and the odds are basically even. The attacker expects to take as much damage as they inflict.

Suppose now that they start at half health. The attacker is weakened, but the defender is not, so the identical units no longer have even combat odds.

If both attacking and defending units degrade as they take damage (like in Civ4) then there is no bias, but this is not the case if only attackers degrade.

Click to expand...

It helps I think to compare it to how it works in civ4.

Consider just a single round of combat in civ4. There is an amount of damage (in hp) that the attacker would deal to the defender if he wins the round, and there is an amount of damage the defender would deal to the attacker if he were instead to win the round. There's also a probability that the attacker will win that round (p). Probability that defender wins the round is obviously 1-p.

The amount of damage the attacker would deal to the defender depends on the attacker's effective strength, the defender's effective strength and also the attacker's health. Note it does not include the defender's health explicitly, though the defender's health will still affect its effective strength. It might be confusing that I mention both the attacker's effective strength and his health. It looks like I'm counting his health twice, and in effect this is sort of how it happens.

To find the amount of damage the defender would deal to the attacker in the round of combat, everything is calculated the same way but with attacker and defender interchanged.

Examples:

Ex1
Equal strength units vs'ing each other.
Each unit would deal 20 hitpoints of damage if they won the round.

Ex2
A half-health (50hitpoints) attacker of at 5.0/10 strength (e.g. a knight) vs. a 5 defender.
The attacker would deal less than 20hp of damage, and the defender would deal more than 20hp of damage.

Ex3
A 10 attacker vs. a 5.0/10 defender.
The attacker would deal more than 20hp of damage, and the defender would deal less than 20hp of damage.

I'm assuming at this stage that in civ5, the situation is similar to: (quoting myself from earlier this post )

The amount of damage the attacker would deal to the defender depends on the attacker's effective strength, the defender's effective strength and also the attacker's health.

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except that the "effective" strength of both combatants no longer takes health into account. In other words, the three things that will matter for determining how much damage the attacker does to the defender will be the attacker's full strength, the defender's full strength, and the attacker's health. Note that in each case by "full strength" I mean after situational modifiers are taken into account. With such a system, the attacker would expect to do the same amount of damage whether the defender started at 10hp, 5hp or 1hp - it doesn't matter (ignoring the case of expected damage being more than defender initial hp).

Flipping this around to get the amount of damage the defender expects to deal to the attacker, and everything is still symmetric between attacker and defender.

To put it slightly awkwardly, but perhaps in a way that makes more sense, the defender defends as if he were full health, but does not attack as if he were at full health. By "attack" in that sentence, I mean the defender dealing damage to the attacker. So interpreting the statements from Firaxis that the defender defends as if at full health still makes sense, because their effective strength when receiving damage from the attacker does not depend on their health. But their effective strength when retaliating against the attacker during combat does depend on their health.

Hope that makes sense.


EDIT
Just to continue a point before I forget... Remember I said earlier that in effect the attacker's health gets counted "twice" but the defender's only once when determining how much damage the attacker dealt to the defender each round. On the flip side, the defender's health would count twice and the attacker's health only once when determining the amount of damage the defender would deal to the attacker in each successful round. This is pretty much the reason it was so important to do your attacks at full health. Because the attacker is by definition the person playing his turn, he gets to choose the battles to start. It would be rare to initiate a battle against a full health defender using a damaged attacker. But it was certainly not rare to attack a damaged defender using a full health attacker. Basically it was easy to avoid the double penalty of injured attackers by simply never commencing battles with injured attackers, or at least only doing so when the odds were good. In civ5, there is no longer as much advantage in initiating combats with full health attackers against injured defenders. When the defender is injured, the expected damage to the defender remains the same (unlike in civ4 where the defender would receive more damage per hit if he were injured) but the defender still has the disadvantage of being less damaging to the attacker and obviously starting with fewer hp and hence being closer to death.

Piece of Mind, I think I can understand you're explanation, but it is hard to follow -

Flipping this around to get the amount of damage the defender expects to deal to the attacker, and everything is still symmetric between attacker and defender.

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I think some of the confusion comes from the use of the term "attacker" and "defender". It seems like your using it to mean two things:

1. The Attacker is the unit that moved into the Defenders tile (i.e., the unit's whose turn it is)
2. In a given combat round, the Attacker is the unit that is doing damage to the other unit, which is by extension the Defender.

So let's call them (1)Attacker/(1)Defender and (2)Attacker/(2)Defender.

Unit (A) attacks Unit (B) .

So Unit A is (1)Attacker and Unit B is (1)Defender.

During the first round of Combat Unit A swings at or shoots at Unit B. It is now (2)Attacker and Unit B is (2)Defender.

During the second half of that same round, Unit B gets a chance to swing or shoot back at Unit A. Unit B is the (2) Attacker and Unit A is the (2)Defender.

Is that what you mean?

To put it slightly awkwardly, but perhaps in a way that makes more sense, the defender defends as if he were full health, but does not attack as if he were at full health. By "attack" in that sentence, I mean the defender dealing damage to the attacker.

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Hmm. Possible. But this is a pretty weird parsing.

If you're right, the way I would say it is "damaged units inflict less damage, but do not suffer more damage".
Get rid of "attacker" and "defender" altogether.