Retreat Odds?

[Nkot]

I have a quick question about retreat odds in BTS, well, actually, two. My first one is when you have a unit and the odds are 42.4% Winning and 28.8% Retreating does that mean that it has about a ~30% chance of losing? Also, how is it determined how much your retreat odds will go down due to how much you chance of victory will go up? The reason for me asking the second question is because I'm not sure if it is always better to promote a HA Flanking I -> Flanking II instead of Strength I -> Strength II. I'm currently leaning yes, but if you guys could enlighten me that would be great.

 

[seizer]

The way retreating works is that it cuts into the odds for losing. So if you have 50% chance to lose and 50% withdraw chance you end up with 25% chance to retreat. This means that flanking promotions are better if you expect to lose the battle, while combat is better when you expect to win. To your second question the answer is, as always, that it depends on the circumstances.

For instance, if you are facing fortified unpromoted archers in grasslands cities Strength is probably the better option, while if the city is on a hill and with CG I archers, flanking is the better choice. There's one caveat: if you want to use the HA's to soften defenders and don't mind them dying Strength is always better; with flanking there's a greater chance of not dealing any damage at all.

 

[oyzar]

Strength promotions are generaly better when you are close to even or better than even in ods(30%+) otherwise flanking give higher survivability rate most of the time. There is of course the fact that flanking stop beeing usefull after the second promotion while combat 4-6 rocks so most of the time i just go with combat on mounted units. And yes 42% chance of winning and 28% chance of retreating means you have a 30% chance of dieing(.576*x=.28.8) So i assume this was a unit with 50% withdrawl chance. Which means that it was proably way better to get two strength promotions as that would leave you well over 70% chance of winning + like 10% chance of a withdraw.

 

[Nkot]

Strength promotions are generaly better when you are close to even or better than even in ods(30%+) otherwise flanking give higher survivability rate most of the time. There is of course the fact that flanking stop beeing usefull after the second promotion while combat 4-6 rocks so most of the time i just go with combat on mounted units. And yes 42% chance of winning and 28% chance of retreating means you have a 30% chance of dieing(.576*x=.28.8) So i assume this was a unit with 50% withdrawl chance. Which means that it was proably way better to get two strength promotions as that would leave you well over 70% chance of winning + like 10% chance of a withdraw.

Interesting. I went back to the game and checked and the actual odds for a HA with Strength I,II were 66.7% for victory and 6.7% for retreat (~27% chance of losing). So really they are about the same chances of losing then with the Strength's being a little lower.

This leads me to believe that a HA with Flanking I,II is more versatile because your not going to lose too much more often if you rely on solely them instead of Strength HA's. I mean you at max have a 50% chance of losing with Flanking I,II HA's, but you couldn't say the same with Combat I,II HA's.

 

[xanadux]

But if both options give the same chance of surviving, combat is better because it gives a much higher chance of winning (killing the other unit).

You could leave most of your HAs unpromoted, and check the odds with a combat 2 HA and with a flanking 2 HA and then use the appropriate one. Flanking 2 is definitely best when odds are quite low (and almost useless when they are very high).

 

[oyzar]

There is of course also the factor that more strength means you deal more damamge to the unit... Also killing the unit is obviously also better than withdrawing.

 

[Giaur]

I believe there are several numbers that could tell you more:
50 percent - when strength is equal
66 percent - 10 percent advantage
73 percent - 20 percent advantage
78 percent - 30 percent advantage
88 percent - 40 percent advantage
I your unit is weaker, just reverse situation f.e. AI unit is stronger by 20 percent - AI unit has 73 percent chance to win.

So the full table is as follows (it will be helpful for my purpose) ...
12 percent - -40 percent
22 percent - -30 percent
27 percent - -20 percent
33 percent - -10 percent
50 percent - when strength is equal
66 percent - +10 percent
73 percent - +20 percent
78 percent - +30 percent
88 percent - +40 percent

If you have unpromoted Harcher and it has 22 percent chance to win, promoting him to Combat should give you 33 percent chance to win and 66*0.2= 13.2 percent retreat odds. 46.2 odds altogether
Promoting the same unit to flanking2 should give you 22 percent chance to win (plus immunity to FS, which is not considered in my model) and 78*0.5=39 retreat odds. 61 odds altogether.

66*0.2 means 100%-chance to win, in this case 33 percent is chance to win, while 0.2 means 20% - base retreat chance for every horse archer
78*0.5 means 100%-chance to win -22 percent, while 0.5 means 50% - expanded retreat chance - 20% +30% (from flanking promotion).

Generally, I wanted point something. And it is that 33 percent, despite it's not very friendly result, it means that you are getting close to outnumber enemy. So promote to Combat2 then or use catapults.

Another thing I wanted to point is that Combat is most fair promotion. Because promoting to Cover, Shock, Pinch, Formation, Charge will never give you desired 25 percent advantage. It will give you 25 percent advatage (according to my table) only in one particular case - a) defender has no bonuses. b) only when you attack. Usually it's much lower bonus. It's better sometimes to promote unit to Combat rather than City Raider, because Combat will give you greater odds.

Pikeman attacking Knight has different odds than the same pikeman defending against the same knight (in open ground of course). It's wierd I know.

 

[oyzar]

pikeman against knight is actually not that different 5/6 = 10/12 so both ratios are same hence the same win %. For strength to be better you need an insane amount of bonuses. Just to compare an archer to an attacking maceman(city raider 3 vs combat 3) 3*x/(8*1.3)=y 3*(x-.75)/8=y gives 3.250017 = x and y = 0.937506 . What this means is that under 225% total defensive bonus it is better to get city raider and above it is better to get combat. Probably something like 60% success for the maceman. with a longbow the x is the same(about 225% defensive bonus) but the longbow will have 87.5% more strength than the maceman and hence wastly outpower it... of course a mix of the different promotions might be better at some other places along the defensive bonus curve.

 

[Giaur]

Oyzar: I hate using ratios, because i never know if 6:4 is equal to 11:7

I made some test, but it proved nothing. I am not sure if it's better to give Combat promo to Maceman (str 8) if they are to fight against archers (str 3). I always thought that it's worth to do that, but odds did not differ too much. It may be very important to do so when cumulated (with all bonuses) strength of attacker and defender are almost equal f.e. 5.9 vs 6.0 will give completely different result than 5.9 vs 5.8.
I made also Knightvs Pikeman test. When both units are unpromoted ratios are equal no matter who attacks. But giving both units Combat promo makes that it matters who attacks. Extreme verion assumes that Pikeman have 2C1Formation while Knights have 2C. In this case using Pikeman to attack (not to defend) gives temporarily 1 additional combat promotion. I do not remeber the exact numbers, but it was sth like that:
attacking) 89 percent
defending) 78 or 73 percent

 

[oyzar]

I said in the above post that strength promos are only better when there is a total of 225% defensive bonus allready which is almost never... as for 2CF pike vs 2C knight is 12(10*1.2) vs 16.2(6*1.2*2.25) when pike is defending and 5.33(10*1.2/2.25) vs 7.2(6*1.2) so should be the same for both cases no? Where is my math wrong?

 

[Giaur]

btw. Combat do not actually behaves like combat. Base strength ratio matters then. Only when both units have the same base strength Combat increases strength.
btw.2 Even saying this, I am not quite certain that it's true in every case. What about example:
If combat3 maceman vs combat2 maceman is equal to
combat4 maceman vs combat3 maceman

Battle system is very unnatural ...

 

[Giaur]

Wait. Crossposting

 

[oyzar]

ok i did a test in worldbuilder and you are indeed right. Seems i have some misconceptions about how combat works. So how exactly do combat math work?
11.3 != 26.2

 

[Giaur]

I believe it is like that ...
a) C2 Knight attacks C2F Pikeman:
10 + 2 (20% strength) vs 6 + 6 (100%) + 2.7 (20% +25% promotions)
It's 12 vs 14.7

b) C2F Pikeman attacks C2 Knight
6 + 1.2 (20% strength) vs 10 - x (20% knight strength - 25% formation - 100% base pikeman bonus = -105%)

But how to decrease strength below 0. It's of course BS. I opened the game and checked Knight's strength. It's 4.87.
So I believe it's sth like 200%-105%=95% of 10 strength.

Why is that? Do not ask me. I always had problems with understanding that and I claim that battle system is unnatural.

 

[Giaur]

105/205=4.87

It could be understood for a while, but I doubt that I will remember that tommorow morning

 

[oyzar]

thank you. Even if you didn't understand it, i understood how it worked. Quite different from what i though but you are right.. everything except attackers combat promos are applied to defender. as for the b) how you get 4.87 is simply 10/2.05(1+1.05)=4.87 . I though the combat was multiplied which would make it the same for offense and defense... It is not however.. Which might make combat better sometimes... I'll have to do some more math to find out when combat beat against specific promos though. If you compare shock to the second combat from the knight that gives:

a) C1S Knight attacks C2F Pikeman:
10+2(20% strength) vs 6 + 7.2(+100% base +20% strength +25% f -25% s = +120%) or a total of 12 vs 13.2 which is better than the strength case

b) C2F Pikeman attacks C1S Knight:
6 + 1.2(20% strength) vs 10/1.8(-100% pike +20% strength +25% s -25% f)
7.2 vs 5.56 which obviously is still better for the knight.

Edit: crosspost

 

[Giaur]

That is correct. 100/(100+105) My mistake.

 

[Giaur]

btw. Combat should be multiplied, but Firaxis thought different.

 

[oyzar]

This also means that the maceman attacking the archer should proably have strength promos. Basically when you are attacking the strength is applied to your own strength but the specific promos(shock cover pinch formation etc) are pplied to their strength. compare a combat 3 and a cr 3 maceman against an archer with a total of 200% defensive bonus.
a) c3 mace vs 200% def archer
8*1.3 vs 3*3
10.4 vs 9
b) cr3 mace vs 200% def archer
8 vs 3*(1+2-.75)
8 vs 6.75

gaah too late to think straight.. seems like the CR is still better even though the mace have 26% more basestrength than the archer :/

 

[oyzar]

maybe it is the def bonus that messes up? but why would it matter if the def bonus wasn't there?
10.4 vs 3 and 8 vs 1.71 this is indeed better in the case for the mace with combat... This just makes it harder to determine when the different promos are better :/

Yeah of course 6.75 is only 75% of 9 so 1/.75=1.33 which is greater than the 30% you get from combat. It is realy dependant on how much bonus the defender have allready what is best..