Combat Explained....
- Thread starter Arathorn
- Start date
Roland Johansen
Deity
From the patch 1.52 change log:
-firepower in combat now based on max strength
You're going to have to change that in your article too...
Also from the change log:
-combat info now shows odds of success
I wonder if this includes first strikes as I remember something about the game not considering first strikes when picking the best defender. If the ingame probabilities are calculated exactly correct, then this may also help with testing.
-firepower in combat now based on max strength
You're going to have to change that in your article too...
Also from the change log:
-combat info now shows odds of success
I wonder if this includes first strikes as I remember something about the game not considering first strikes when picking the best defender. If the ingame probabilities are calculated exactly correct, then this may also help with testing.
KrikkitTwo
Immortal
- Joined
- Apr 3, 2004
- Messages
- 12,418
So basically that means that hitpoints now hurt 2 ways
1. chance of doing damage
2. amount of damage you have
Where as they used to hurt 4 ways
3. damage you do
4. damage they do
So a 5/10 unit is 1/4 a 10/10 unit
making it better than a 5/5 unit (which is about 1/8 of a 10/10 unit)
This should eliminate a lot of spearman v. tank complaints (because a 4/28 tank will have the edge v. a spearman now)
1. chance of doing damage
2. amount of damage you have
Where as they used to hurt 4 ways
3. damage you do
4. damage they do
So a 5/10 unit is 1/4 a 10/10 unit
making it better than a 5/5 unit (which is about 1/8 of a 10/10 unit)
This should eliminate a lot of spearman v. tank complaints (because a 4/28 tank will have the edge v. a spearman now)
Zombie69 said:
I don't think it's so bad. A wounded tank will still have a tough time taking out infantry, or even rifles in a city. Frankly, if you're taking a city that's guarded by anything less than that, it's a forgone conclusion anyway - this just makes it a little faster. It also works both ways. Even though your suicide artillery has dropped that infantry to 10 str, they'll still put up a pretty good fight when you try and take them out.
yeah, it's a double-edged sword. I have found that once you have done some collateral damage on a city even strong units falls pretty quick because of the multiplier effect of damage on a unit's overall strength. so it will take a bit more effort to take a city. another way of looking at it is when you take a city your units will be more damaged, because the defenders DID more damage.
so you'll have units that end up weaker from the attack, but won't be as ineffective as they would have been with that amount of strength before
so it's a bit of take some, lose some - but I am in favour of the change because it is easier to understand and estimate a units effectiveness
so you'll have units that end up weaker from the attack, but won't be as ineffective as they would have been with that amount of strength before
so it's a bit of take some, lose some - but I am in favour of the change because it is easier to understand and estimate a units effectiveness
Celebithil
Warlord
- Joined
- Sep 2, 2004
- Messages
- 219
Krikkitone said:
I think a 5/10 unit still is worse than a 10/10 unit, but not as much as before. If they fight each other the chance of hitting are 50% for both and the damage done is 28 (for the 5/10 unit) respectively 14 (for the 5/5 unit), so the 5/10 unit needs 4 hits to kill the 5/5 unit, but the 5/5 unit also only needs 4 hits (because the 5/10 unit only has 50hp remaining). Hence the odds of winning with both units is 1/2.
A 4/28 unit will also still be a little worse than a 4/4 unit. However the differences aren't as big as they used to be (odds of winning with the 4/28 unit are now 5/16 versus previously 1/32).
These calculations are done assuming the new system's only change is that damage done is calculated using full strenght power.
Thalassicus
Bytes and Nibblers
Do you know if it's possible to have a single formula give the odds of success, for use in spreadsheets?
It seems to be a statistics question, but I haven’t taken a course in that in some time
Without first strikes taken into account, it could be described like this:
Players A and B have a P(A) and P(B) chance to win a round in a game
When they win a round, they receive points equal to Ta and Tb
X points are required to win the game
Find the formula for W(A), the probability A will win the game
(EEp, the memories!
)
Even first strike could likely be worked into a formula, it's probability-based and dependent on the same variables (although harder to deduce).
It's going to be incorporated into a table to compare the cost-benefit of different naval vessels (where terrain doesn't play as much of a factor) based on strength, cost, and other factors (like chance to withdraw or board). The strength is used to calculate combat odds, cost is used to find the number of units required to have an even battle, and the final average hammers lost or gained are then calculated. The break even point can then be found where one unit type will (on average) lose the same number of hammers when engaging another in combat, and combat stats adjusted accordingly depending on which unit is ment to counter the other.
It seems to be a statistics question, but I haven’t taken a course in that in some time
Without first strikes taken into account, it could be described like this:
Players A and B have a P(A) and P(B) chance to win a round in a game
When they win a round, they receive points equal to Ta and Tb
X points are required to win the game
Find the formula for W(A), the probability A will win the game
(EEp, the memories!
)Even first strike could likely be worked into a formula, it's probability-based and dependent on the same variables (although harder to deduce).
It's going to be incorporated into a table to compare the cost-benefit of different naval vessels (where terrain doesn't play as much of a factor) based on strength, cost, and other factors (like chance to withdraw or board). The strength is used to calculate combat odds, cost is used to find the number of units required to have an even battle, and the final average hammers lost or gained are then calculated. The break even point can then be found where one unit type will (on average) lose the same number of hammers when engaging another in combat, and combat stats adjusted accordingly depending on which unit is ment to counter the other.
Roland Johansen
Deity
Somebody already did this and made a program to calculate the probabilities: program to calculate chances of victory in combat
I think the basic idea is the following. Based on the comparitive strengths of the units, you can calculate how much damage each unit does if it wins a round of combat and the chance that it wins a round of combat (see the first post of Arathorn in this thread). Using these amounts of damage, you can calculate how many times a unit has to score a hit to do a total damage that is equal to or exceeds 100 hitpoints. Say that unit A has a chance to win a round of combat of A_chance and needs to score a hit for A_times to kill unit B and that unit B has a chance to win a round of combat of B_chance and needs to score a hit for B_times to kill unit A (note that A_times, B_times, A_chance and B_chance are directly dependent on the relative strengths of the units (and their starting hitpoints) as described in Arathorns article.
Then the chance for A to win the battle is:
{sum x= 0 to B_times - 1} (A_times -1 + x)! / ( (A_times -1)! * x! ) * A_chance^A_times * B_chance^x
Note that A_chance + B_chance =1 and x^y is a notation to denote x to the power y. It's a bit difficult to describce the formula without the correct mathematical symbols. It looks a bit ugly in this format, I can't help that.
I think the basic idea is the following. Based on the comparitive strengths of the units, you can calculate how much damage each unit does if it wins a round of combat and the chance that it wins a round of combat (see the first post of Arathorn in this thread). Using these amounts of damage, you can calculate how many times a unit has to score a hit to do a total damage that is equal to or exceeds 100 hitpoints. Say that unit A has a chance to win a round of combat of A_chance and needs to score a hit for A_times to kill unit B and that unit B has a chance to win a round of combat of B_chance and needs to score a hit for B_times to kill unit A (note that A_times, B_times, A_chance and B_chance are directly dependent on the relative strengths of the units (and their starting hitpoints) as described in Arathorns article.
Then the chance for A to win the battle is:
{sum x= 0 to B_times - 1} (A_times -1 + x)! / ( (A_times -1)! * x! ) * A_chance^A_times * B_chance^x
Note that A_chance + B_chance =1 and x^y is a notation to denote x to the power y. It's a bit difficult to describce the formula without the correct mathematical symbols. It looks a bit ugly in this format, I can't help that.
Thalassicus
Bytes and Nibblers
I think that's what I was looking for. Have I got this right?
a, b = # rounds to win combat
P(A), P(B) = Probability of A and B to win a round
Do you know how to enter sigma notation with upper and lower limits in Excel? The Sum function name is reserved for adding together cells. I've tried Sigma() and Summation() and looked around the menus...havn't found anything.
a, b = # rounds to win combat
P(A), P(B) = Probability of A and B to win a round
Do you know how to enter sigma notation with upper and lower limits in Excel? The Sum function name is reserved for adding together cells. I've tried Sigma() and Summation() and looked around the menus...havn't found anything.
Thalassicus
Bytes and Nibblers
Thank you! I plugged that formula into my calculator and it worked great! The only change was the upper limit of the summation to b, rather than b-1 (additional iteration).
Thank you very much!
Now I just need to figure out how to get it into Excel...
This'll make it much faster to balance new units than going back and forth to calculate combat results constantly
Thank you very much!
Now I just need to figure out how to get it into Excel...
This'll make it much faster to balance new units than going back and forth to calculate combat results constantly
Thalassicus said:I think that's what I was looking for. Have I got this right?
a, b = # rounds to win combat
P(A), P(B) = Probability of A and B to win a round
Do you know how to enter the summation formula (Sigma) in Excel? The Sum() function name is reserved for the summation of cell contents. I've tried Sigma() and looked around the menus...havn't found anything.
Hmmmm, couldn't you just use the sum based on their summing up of cells. And just have a series from 0 to b-1 of those cells?
Req
Thalassicus
Bytes and Nibblers
Yeah, that would work. I'd think there would be a formula somewhere for it, though. Graphing calculators have it after all: Sigma(expr, var, low, up)...
I'll go with cell iterations. Do you know the syntax for a formula-defined cell reference? I think it's something like L1:"L"&(I7-1) (for the range of L1 to L (B-1), but I've used dynamic cell references maybe three times in ten years...don't have the syntax right
It's remarkably hard to find anything in the "help" files on some topics.
I'll go with cell iterations. Do you know the syntax for a formula-defined cell reference? I think it's something like L1:"L"&(I7-1) (for the range of L1 to L (B-1), but I've used dynamic cell references maybe three times in ten years...don't have the syntax right
It's remarkably hard to find anything in the "help" files on some topics.
DaviddesJ
Deity
Ignore this post.
Thalassicus said:Yeah, that would work. I'd think there would be a formula somewhere for it, though. Graphing calculators have it after all: Sigma(expr, var, low, up)...
I'll go with cell iterations. Do you know the syntax for a formula-defined cell reference? I think it's something like L1:"L"&(I7-1) (for the range of L1 to L (B-1), but I've used dynamic cell references maybe three times in ten years...don't have the syntax right
It's remarkably hard to find anything in the "help" files on some topics.
Errrm, what are you trying to do? What's a formula-defined cell reference?
Req