Drill IV or Combat IV? You decide! Includes graphs

[PieceOfMind]

Hi PeaceofMind,

a lot of work here... nice tool that you have here! I am still digesting the conclusions... I just wanted to point out that the two last ratios should be exchanged

Cheers

Ah of course... fixed. Thanks for noticing.

 

[PieceOfMind]

When you look at the graphs of your third situation, you need to realise that the great thing about using drill IV units to defend cities is not purely their chance to win the first battle, but mainly the fact that they don't take a lot direct or indirect damage (from collateral damage attacks). So the drill IV units are great when facing an enemy who is going to attack with siege units. You have a slightly smaller chance to win the first fight when compared to the city garrison III units, but the next fights, your defenders will have suffered far less collateral damage. Another effect is that usually siege units will have a lower base strength than the defenders especially when compared with the alternative city attack units and this would have a positive effect for the drill IV units when compared with the alternative city garrison III, guerilla units.

When attacking a city with a large defence bonus, you'd rather face 8 city garrison III, guerilla I units than 8 drill IV units.

Indeed. Sometimes the way I like to think about the Drill IV promotion is putting myself in the enemy's shoes. I imagine that I'm maybe playing multiplayer and my human opponent has somehow upgraded a large number of longbows to Drill IV.

With all this in mind, I would hope this really helps put in perspective the value of the promotions given by the protective trait. Because Drill I by itself is near useless and since the average player doesn't face many real threats to their cities (I'm not talking about you elite Deity guys ) most would quickly dismiss the value of these two promotions. In the hands of an experienced human player, and preferably against another human player, Drill IV is an amazing promotion in some situations. Churchill, being Prot/Cha, only needs 8xp from his military city before he can build CG1/D4 longbows. If he built most of his cities on hills and managed to get this 8xp military city he would be practically unkillable soon after he reached Feudalism.

I can already imagine an invasion tactic being to send various packs of Drill IV longbows into enemy territory along hills and forests, forcing the opponent to waste a lot of resources taking care of them or otherwise allowing you to see much of their territory. If you think it's bad when someone in MP puts their warrior/archer on the forest hill next to your capital, wait til you've got D4 longbows on your hills lol. Note that D4 longbows on hills enjoy a modified strength of 9 or 10.5 if fully fortified, with 4-7 first strikes to boot.

EDIT... small correction

 

[UWHabs]

Then Churchill upgrades those D4 longbows to D4 redcoats...

 

[DanF5771]

The term "fire power" is used in the code. Your d_A and d_D are called "DamageToAttacker" and "DamageToDefender" there and I'd prefer sticking to these terms in further discussions. I had also already presented them in my modified verbose combat help hover text ( 14HP / 28HP ) in the above picture together with the Attacker's odds to win a combat round (42.8%). I was a bit worried when I saw your calculation of the Maceman's DamageToAttacker (your d_D = 27HP -> rounding error?), but your last results seem to be correct.

Now I wonder whether putting the two dimensions together into a 3-D graph would work, with:
x-axis: odds for winning a combat round (reflects R=A/D)
y-axis: ratio of rounds needed to kill/retreat for defender/attacker (reflects fire power and HPs)
z-axis: odds for attacker to win combat (or your other interesting measures)

Promoting the attacker along the Combat line would mean a shift along the x-axis (also y-axis, when crossing jump-points) whereas promoting along the Drill line would mean a shift along the y-axis (since the defender would need to win more combat rounds to avoid getting killed).

But my math skills are too limited, especially when it comes to using the combat rounds info with its discrete nature (first strikes/chances, binomial distribution, bayes rule ) to work out the continuous ratio for the y-axis. Would that even be possible/make sense?

 

[PieceOfMind]

The term "fire power" is used in the code. Your d_A and d_D are called "DamageToAttacker" and "DamageToDefender" there and I'd prefer sticking to these terms in further discussions. I had also already presented them in my modified verbose combat help hover text ( 14HP / 28HP ) in the above picture together with the Attacker's odds to win a combat round (42.8%). I was a bit worried when I saw your calculation of the Maceman's DamageToAttacker (your d_D = 27HP -> rounding error?), but your last results seem to be correct.

Now I wonder whether putting the two dimensions together into a 3-D graph would work, with:
x-axis: odds for winning a combat round (reflects R=A/D)
y-axis: ratio of rounds needed to kill/retreat for defender/attacker (reflects fire power and HPs)
z-axis: odds for attacker to win combat (or your other interesting measures)

Promoting the attacker along the Combat line would mean a shift along the x-axis (also y-axis, when crossing jump-points) whereas promoting along the Drill line would mean a shift along the y-axis (since the defender would need to win more combat rounds to avoid getting killed).

But my math skills are too limited, especially when it comes to using the combat rounds info with its discrete nature (first strikes/chances, binomial distribution, bayes rule ) to work out the continuous ratio for the y-axis. Would that even be possible/make sense?

If you wouldn't mind, can you please tell me how you did those combat odds help text? That would help me immensely with this work. If it's someone else's work can you please direct me where to find it?

Also, do you know a simple way to set the HP of a unit? I would have liked to try out the 50HP mace example in game but fiddling around trying to get a mace to lose 50HP is too difficult.

I also noticed the 27hp/28hp difference. I'm looking into that at the moment. I think there is a small error coming in when the units are damaged like that. At the moment I'm trying to read the code from the game's battle odds calculator, and make sure everything agrees.

About the d_A and d_D not being called firepower, I just noticed this when I read over Deep0's code a bit further (he wrote the in game calculator as far as I can tell). So basically firepower is not dependent on unit health.

I was thinking about trying to construct a 3D graph. I wondered though if I had produced such a graph whether it'd be very easy to read. Naturally 3D graphs are a lot harder to interpret when you are looking at fine details. So far I have sort of looked at two independent variables simultaneously anyway, where unit health or R is one variable, and promotion choice is the other. Contour plots are often an easier way to read 3D data like this too. I should be able to get this code to produce a 3 dimensional array, with a bit more work.

 

[PieceOfMind]

your d_D = 27HP -> rounding error?),

I was rounding down I think rather than rounding to nearest. As a float value it comes out as about 27.54 so that would explain it.

 

[DanF5771]

I've just presented my code changes for the "verbose" combat help here (requires recompiling the dll).

Changing a unit's HPs can be done with Python. Enable debug mode (chipotle in .ini) and query the x-, y-coordinates of a unit's plot via the plot hover text while pressing <Shift>. Then open the Python Console and enter:[pre]gc.getMap().plot(x,y).getUnit(0).setDamage(iDamage, -1)[/pre] to set the HPs of the first (Index=0) unit to 100-iDamage.

The unit's fire power DOES depend on its health. Remember that MaxCombatStrength = BaseCombatStrength * Modifier so that it and the derived CurrentCombatStrength, CurrentFirePower and StrengthFactor are actually of the order of hundreds and thousands.
So in the example the Maceman has a MaxCombatStrength = 8*100 = 800 and a CurrentCombatStrength = 800*50HP/100 = 400 leading to a CurrentFirePower = (800+400+1)/2 = 600 (all integers!) --> The StrengthFactor = (300+600+1)/2 = 450
DamageToAttacker = 20*(600+450)/(300+450) = 20*7/5 = 28HP.

This is how the game calculates, I guess you are using the ratios for strengths and fire powers and floats which might lead to rounding errors and numbers different from in-game values. IMHO it's better to exactly copy the calculations handling the integers.

 

[CrusaderKevin]

wrong It's simply that d1-d3 is definitely crappier then c1-c3.

And since I expect to attack with somewhere around 70-80% odds when fighting in the field... probably 90% of the units won't even live to see d4. If I want to add a specific counter promotion too, even for a protective, non cha leader, I need 17xp. For a non protective - 26xp. If I get 2xp/fight and attack at ~80%, what are the chances that my unit will win 7 times in a row(for a protective with racks)? Or let's say 5 times, assuming I spit it with 7xp and I'm protective. It's perfectly useless that d4 is good, if d1-d3 are subpar and mathematically the unit won't live to d4 too often...

Perhaps one of the smartest arguements fr the combat line I've heard all day. I'm pretty much convinced about te combat line being better now, although I was unsure before....

 

[Phatkarp]

Ditto that.

I did vote for D4 over C4, though, because in a straight-up comparison I think it is superior. (That is just my "smell test" impression, though I think the excellent analysis in this thread confirms it.)

My take-away from all this is to use the combat line for most of the time, but perhaps groom and nurse a few drill units to get to the devastating D4 promotion.

I'm currently playing a game where I've settled all my great generals into a military super city. With my civics I'm able to produce Machine Guns with D4. I don't know how effective they are because no one has attacked them yet.

 

[PieceOfMind]

It's true that needing to live through D1-D3 is a small problem. All I do is nurse units up to D4. It seems that in the process you can milk enough xp to be able to earn great generals to boost the xp of your main unit factory enough to pump out 4 promotion units. Granted, in my current game I'm playing as Washington (Charismatic which makes it easier), I already have 4 military instructors in my military city and theocracy and vassalage, so I'm getting D4 units every time, before 1500AD.

Part of the strategy is using your highest xp factory to produce the troops that will get the drill promotions, and use your other military cities for the knights and trebs etc.

@Dresden,

It's true I've been using some floats in the calculations. Doing the calculations the same way to obtain the battle parameters is a good idea (eg. calculating d_A and d_D) but for the actual probabilities calculation I'm considering leaving the floating point arithmetic, as realistically it should come as more accurate. Obviously for my own code I don't need to include it in the game so time complexity is not a big issue, so I'll prefer accuracy over speed.

 

[Tephros]

I have to say Drill soley because of a Japan game where drill 5 samurais saved the game for the time. Combat 6 just would not have worked there. But I voted equal because that it is situational.

Yeah Drill 5 (Drill 5?) FTW when you're being zerged by archers... :no:

Actually when I first land troops on the new world in a terra map it could be useful. That usually is being zerged by a continent full of barbarian archers/axes/spears.

 

[huerfanista]

I rarely use drill unless I'm playing as Churchill (cha/pro). That said, I never have any problem getting tons of drill4 redcoats. After all, with theo, barracks, and 1 GMI they come out 1 promo away from drill 3, and they rack up XP like nobody's business. I always use seige to knock down the defenders a bit before attacking, so I rarely lose any units beyond seige.

 

[Skallagrimson]

I don't see it as either/or. My city defenders lean more heavily on the drill line due to the importance of any kind of an edge against collateral damage and surviving with more hit points. But then I also stack combat units in cities on defense too because there are often opportunities to reach out and touch that Monty stack when it marches on open ground toward the city he wants to besiege. In my city raid stack I keep a few defender units to stack defense (one for each terrain type, and C1 + drill line for open field defense).

A good defense includes offense, and a good offense includes defense.

There is no spoon.

 

[muxec]

Another interesting experiment. Imagine a city with knocked down defenses and 2 rifles defending. A stack of 3 cannons and 3 rifles comes in. Cannons have CR2, rifles have C1+pinch. Attacker first attacks with all 3 cannons, than moves rifles in. Which promo-set on defenders gives higher chance to hold the city CG3D1 on both or D4 on both or one D4 and one CG3D1?

 

[huerfanista]

Another interesting experiment. Imagine a city with knocked down defenses and 2 rifles defending. A stack of 3 cannons and 3 rifles comes in. Cannons have CR2, rifles have C1+pinch. Attacker first attacks with all 3 cannons, than moves rifles in. Which promo-set on defenders gives higher chance to hold the city CG3D1 on both or D4 on both or one D4 and one CG3D1?

I think that what you're really asking here is "which promo will leave the attackers with the most damage after they take the city," since I don't think you have any chance of keeping it after this particular battle.

 

[PieceOfMind]

huerfanista, I think he means which promotions on the rifles the attacker moves into the city. He did say the rifles move in so he know the attackers are going to win. How does one defend the newly captured city with the 2 rifles moved in?

 

[nanomage]

Another interesting experiment. Imagine a city with knocked down defenses and 2 rifles defending. A stack of 3 cannons and 3 rifles comes in. Cannons have CR2, rifles have C1+pinch. Attacker first attacks with all 3 cannons, than moves rifles in. Which promo-set on defenders gives higher chance to hold the city CG3D1 on both or D4 on both or one D4 and one CG3D1?

i doubt he means one should give CG to attacking rifles.

However, it's quite a problem in combinatorics to find which promo-set offers a greater chance of keeping the city. I'd advise to solve it experimentally, writing a small program or (long and hard) experimenting with WB.

 

[PieceOfMind]

i doubt he means one should give CG to attacking rifles.

No but after 3 cannon attacks, the second rifle to attack probably won't even need a promotion, hence upgrading to CG once he reaches the city. That way he also isntantly heals. Of course, using D4 on the second attacking rifle could be the obvious solution, with the extra rifle moving into the city taking CG3.

But yeah, the question was ambiguous, I can see it being interpreted both ways.

 

[vale]

I have a big issue with the way expected experience gain is calculated here. If a Drill IV or Combat IV unit loses in combat it isn't gaining 0 experience. At minimum it is losing the experience needed to gain those promotions. You might think it is skewed to say that is a 17 xp loss (since Charismatic/Protective/Aggressive/Oromo/Samurai/Quechua will make that not such a huge loss) but this strict xp loss calculation allows you to ignore the loss of hammers and movement time as part of the calculation. It also ignores the fact that xp becomes less valuable the more a unit has (first 17 xp is much more useful than the second 17 xp for example).

I am sure if you redo the calculations with -17 in place of 0 on unit loss, Combat IV will start to look more competitive with Drill IV on the low ratio side of the xp chart.

 

[PieceOfMind]

I appreciate that Vale. I did this experiment a fair while ago and I don't wish to revisit it now. What you've described is a clear limitation though.

Originally I used the expected xp data for attacks at very high odds, personally. At this point, the effect of lost xp is small. Obviously if you want to look at 50% odds battles etc. it will be a much larger problem.

Also, another reason the expected xp directly may be useful is if you're trying to milk great general points. That's one of the reasons I like using drill units as city attackers because I can earn gg points at almost twice the rate when doing the mop up duties after siege attacks.