Drill IV or Combat IV? You decide! Includes graphs

[PieceOfMind]

The analysis has been continued in this post later in the thread (#58), which has a lot more relevant information...

Before voting, please feel free to consider the following information.

I have compared both Drill IV and Combat IV in a few different areas. For the moment I have ignored the side benefits on these promotions, like the healing for Combat IV, and the lower collateral damage on drill promotions. If you believe these are too significant to ignore mention them in your post. Of course, not all units can choose between the two promotion lines, but for the units that can, it can be a tricky decision for many players.

In this experiment, we treat the strength ratio of the attacker to the defender (A/D) as the independent variable, and examine a few other variables. Namely...

1) Probability of attacker winning combat
2) Probability of attacker winning combat unscratched
3) Average hitpoints attacker has after combat
4) Average xp earned by attacker.

For each graph, there is a control where the attacker has no promotions. There are no first strikes (other than on the Drill IV attacker) and no retreat odds involved. The Drill IV attacker has Drill I, II, III and IV. The Combat IV attacker has Combat I, II, III, and IV.

By considering different values for the ratio A/D, we effectively include many different combinations of tile defenses, unit damage and unit strength. [EDIT... It has been brought to my attention by DanF5771 in this post that unit health does in fact have a unique role, since it affects firepower in an unusual way. So here we are technically only comparing undamaged units. I will later on post some more findings with unit health as a variable as well.]

Note: Though I have called this an experiment, it is in fact deterministic. No simulations are involved - these are exact computations (up to machine accuracy anyway).

1) Probability of attacker winning combat

Spoiler :

2) Probability of attacker winning combat unscratched (i.e. taking no damage)

Spoiler :

3) Average hitpoints attacker has after combat

Spoiler :

4) Average xp earned by attacker.

Spoiler :

If you are confused about the meaning of the "average" quantities, consider this example.

Suppose there is an oversimplified battle where the attacker will come out of the battle with either 100HP, 50HP or 0HP. Suppose 90% of the time he will win the battle, and 10% of the time the defender will win the battle. Further, suppose he has 50% chance of having 50HP and 40% of having 100HP (50+40 is 90). Then his average hitpoints after battle would be 10% * 0 + 50% * 50 + 40% * 100 = 65HP.
If he would win 3xp if he won the battle, then the average xp earned by him would be 10% * 0 (when he loses the battle) + 90% * 3xp (when he wins the battle) = 2.7xp.

Please don't hesitate to ask anything about any of the data presented here.

In fact, if you think there is another important variable or experiment I should try then please ask. I'll be more than happy to run more tests.

 

[oyzar]

Your graph is showing what people have always known, combat is better than drill unless you are above 1.5 of defenders strength(mop up), for pure combat. The benefit of drill 4 to give -60% from colleteral is not taken into account here though. Since most combat in civ4 is stack combat, drill 4 is quite a lot better than it seems from these graphs due to the ability to take way less damage from colleteral. There are also several units that have potential for 1(protective units, samurai, event) or 2(oromo warriors) free drill promos. With those promos things get changed quite a bit(since drill 1 is the main reason the combat line is better).

Against inferior AI(meaning you are playing on a level where you can win most of the time, combat 4 is probably best most of the time, since most players play on such levels(after all it is no fun not winning), i expect combat 4 to get a clear majority).

 

[Tephros]

Don't forget to mention that Drill IV reduces collateral taken, and Combat IV allows faster healing in neutral territory.

I was wondering how the data was generated? How many trials?

The last graph looks weird... I'd rather see what the exp earned is only if they win. Clearly if the strength ratio is 0.5, the odds of winning are slim, but if they do they'll get more than 3 exp.

Drill units are okay in specific situations, especially when your opponent has inferior technology but superior numbers, especially siege units.

 

[PieceOfMind]

Your graph is showing what people have always known, combat is better than drill unless you are above 1.5 of defenders strength(mop up), for pure combat.

That's your opinion.

The benefit of drill 4 to give -60% from colleteral is not taken into account here though. Since most combat in civ4 is stack combat, drill 4 is quite a lot better than it seems from these graphs due to the ability to take way less damage from colleteral.

True. I can't include that in the graphs unfortunately but I agree it's an important point.

There are also several units that have potential for 1(protective units, samurai, event) or 2(oromo warriors) free drill promos. With those promos things get changed quite a bit(since drill 1 is the main reason the combat line is better).

I could do a similar thing for Combat I and Drill I. In my opinion the fourth Drill promotion matches the fourth Combat promtion much better than the earlier ones, and in some cases that can be enough to avoid the Drill line... if you are not expecting units to survive to get 4 promotions.

While the increase in effectiveness from Combat I to Combat IV is fairly gradual, with Drill promotions there is a big jump from III to IV, and the Drill II and III promotions are pretty much the same promotion.

 

[Indiansmoke]

There is also the fact that most mounted units are immune to first strikes...this is a MAJOR dissadvantage of drill.

 

[oyzar]

The 1st drill promo is very weak, the second and third ones are as you say equal and double as strong as the 1st drill promo. They are slightly worse than a combat promo(for pure combat). The 4th drill promo is better than a combat promo for pure combat, but obviously you need to get drill 1, 2 and 3 first.

What i ment for units starting with drill one is that you should compare drill 4 to drill 1 c3. In that case things might look different.

Obviously this changes a lot once you bring other promos and defensive bonuses into the picture and is only valid when attacking(combat promo's get significantly worse when defending with other defensive bonuses or unit specific promos). But it is the best comparison you can do.

 

[PieceOfMind]

Don't forget to mention that Drill IV reduces collateral taken, and Combat IV allows faster healing in neutral territory.

I did mention it.

I was wondering how the data was generated? How many trials?

Using a program I've been working on for a long while. Just so I can create experiments like this. Technically it is a completely deterministic program so there is no trials involved or inherent error. The only errors could be due to bugs in my code. I can't gurantee 100% accuracy obviously but I have tested the code reasonably thoroughly.

The last graph looks weird... I'd rather see what the exp earned is only if they win. Clearly if the strength ratio is 0.5, the odds of winning are slim, but if they do they'll get more than 3 exp.

Ok. xp earned by attacker:

Round these values down to get the actual value.

R   Control  Drill IV   Combat IV
0.50	8.0	8.0	5.7
0.55	7.3	7.3	5.2
0.60	6.7	6.7	4.8
0.65	6.2	6.2	4.4
0.70	5.7	5.7	4.1
0.75	5.3	5.3	3.8
0.80	5.0	5.0	3.6
0.85	4.7	4.7	3.4
0.90	4.4	4.4	3.2
0.95	4.2	4.2	3.0
1.00	4.0	4.0	2.9
1.05	3.8	3.8	2.7
1.10	3.6	3.6	2.6
1.15	3.5	3.5	2.5
1.20	3.3	3.3	2.4
1.25	3.2	3.2	2.3
1.30	3.1	3.1	2.2
1.35	3.0	3.0	2.1
1.40	2.9	2.9	2.0
1.45	2.8	2.8	2.0
1.50	2.7	2.7	1.9
1.55	2.6	2.6	1.8
1.60	2.5	2.5	1.8
1.65	2.4	2.4	1.7
1.70	2.4	2.4	1.7
1.75	2.3	2.3	1.6
1.80	2.2	2.2	1.6
1.85	2.2	2.2	1.5
1.90	2.1	2.1	1.5
1.95	2.1	2.1	1.5
2.00	2.0	2.0	1.4

 

[oyzar]

Generating these values aren't very hard. I already have a spreadsheet that does the same... Since drill doesn't affect strength of units of course it is going to earn more experience.

 

[PieceOfMind]

The 1st drill promo is very weak, the second and third ones are as you say equal and double as strong as the 1st drill promo. They are slightly worse than a combat promo(for pure combat). The 4th drill promo is better than a combat promo for pure combat, but obviously you need to get drill 1, 2 and 3 first.

What i ment for units starting with drill one is that you should compare drill 4 to drill 1 c3. In that case things might look different.

Obviously this changes a lot once you bring other promos and defensive bonuses into the picture and is only valid when attacking(combat promo's get significantly worse when defending with other defensive bonuses or unit specific promos). But it is the best comparison you can do.

I may look into Drill3C1 vs. Drill4 as well in that case.

Other promtions which change the defense modifiers are sort of covered by this in that they affect the Ratio R anyway.

 

[PieceOfMind]

Generating these values aren't very hard. I already have a spreadsheet that does the same... Since drill doesn't affect strength of units of course it is going to earn more experience.

For that reason I would hope it's a consideration for deciding which promotion is better. I would like voters to decide rather than me put too much bias in.

Are you able to use your spreadsheet to quickly confirm some of these results?

What method do you use in the the spreadsheet for calculating probabilities etc.? Do you use simulations?

 

[RRRaskolnikov]

The 1st drill promo is very weak, the second and third ones are as you say equal and double as strong as the 1st drill promo. They are slightly worse than a combat promo(for pure combat). The 4th drill promo is better than a combat promo for pure combat, but obviously you need to get drill 1, 2 and 3 first.

Hi, nice discussion...

This is exactly why I prefer the combat line... if I am protective I might consider Drill 2 but Drill 1 is just bad as first promotion.
Plus drill only help when you have already won... Attacking rifles against LBs are better with drill... fine... but combat rifles will also do the job. On the contrary, if you are on par with your opponent, drill troops will be doomed...

Cheers

edit: + as Indiansmoke said, AIs love their mounted units, and they love to give them flanking 2

 

[troytheface]

the graphs are good. you can also use sets and subsets which can be an accurate binary analysis of computer configuration.
(Drill IV + Less Collateral Damage)</=(Combat IV + V +Heals Extra )

 

[SnowlyWhite]

Against inferior AI(meaning you are playing on a level where you can win most of the time, combat 4 is probably best most of the time, since most players play on such levels(after all it is no fun not winning), i expect combat 4 to get a clear majority).

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...

 

[PieceOfMind]

Hi, nice discussion...

This is exactly why I prefer the combat line... if I am protective I might consider Drill 2 but Drill 1 is just bad as first promotion.
Plus drill only help when you have already won... Attacking rifles against LBs are better with drill... fine... but combat rifles will also do the job. On the contrary, if you are on par with your opponent, drill troops will be doomed...

Cheers

edit: + as Indiansmoke said, AIs love their mounted units, and they love to give them flanking 2

I would say there is quite high value on Drill promotions even with this fact in mind, so long as you bother to have a few spears or pikes with your Drill IV troops.

I wouldn't agree that drill only works when you have won or are fighting an inferior opponent. If you are attacking a city, and if you use a few catapults or whatever first, you can bring their HP down enough that drill troops become good city attackers, and can be used to milk for quite a bit xp in many cases. One way of thinking about it is that you progress along the drill line faster than you do the combat line.

When the ratio is nearly 1, the drill promotions actually come out a fair bit stronger than combat I think. However it's not common for people to regularly play the close-to-even odds.

Drill promotions definitely shine when the unit is on reasonably defensible terrain. I posted this example not long ago:

http://forums.civfanatics.com/attachment.php?attachmentid=195991&d=1228197822

A drill IV C1 CG1 Longbow defeated 5 catapults, 2 swordsmen and a horse archer before becoming damaged enough that the next longbowman took over and died on the next attack.

EDIT With the responses this thread is getting I reckon this is going to be a very interesting outcome.

 

[PieceOfMind]

For those interested, here is the same analysis for Drill I compared with Combat I.

Spoiler :

 

[SnowlyWhite]

another issue being the (I don't know how it's named in English ) point for str ratio when drill units start getting a good chance, namely the ~.9 str ratio. Which is an issue given that units which get access to drill line are usually the ones with the low str. from their age(tanks aside, but tanks don't get drill anymore). Which means a ton of siege sacrificed.

Worst of all, as mentioned before, the units with high str. from their age are for a long time immune to 1st strikes. The only point where drill can become interesting is at rifles due to their native 25% vs cav. and already pretty high str.(it's the only point where a unit from this line gets almost same str. as it's mounted counterpart).

 

[J-man]

What about Drill 4 + combat 1 and Combat 5, or even Drill 4 + combat 2 and combat 6?

 

[RRRaskolnikov]

@PieceOfMind: A CG3 Drill 1 LB would do about the same no?

About mop up troops, really I don't see the point using drill troops here. If you have done the jobs with cats, trebs, etc first, any troop will do. And with a medic3 they will likely be healed in one turn after the battle.

"When the ratio is nearly 1, the drill promotions actually come out a fair bit stronger than combat I think. However it's not common for people to regularly play the close-to-even odds."

well, if you fight 15 combat one rifles with 15 drill one rifles, you are not likely to be the winner...

Cheers

edit: Tx for all the datas!

Spoiler :

IMO drill is made for Charlemagne so the lone HRE units which survive get some XP

 

[PieceOfMind]

Because it was requested earlier, the comparison between Drill IV and (Combat I + Drill III).

Spoiler :

Later on I might put a few of these together, like D4, C4, D3+C1.

What do people think about D4C1 compared with C5?

 

[JTMacc99]

There is also the fact that most mounted units are immune to first strikes...this is a MAJOR dissadvantage of drill.

Agreed. Plus, Drill IV doesn't lead to Combat 5.

On the other hand, the whole unscathed thing is great.

In other words, I'm voting for it depends.