A Mathematical Analysis of the Value of Various Skills

[fatetriarrii]

Hahaha! I have the full game now, so nothing can stop me from checking the value of skills, based on the real numbers!

First, I have seen a claim that the anti ~ skills are worthless, so I am going to compare them to the other availible skills at various levels. This will be hard because of the sheer number of pathways that the unit can take, so I will start small. I will use the following equation (the underlines are just to highlight the variables):

((Damage_if_a_Hit Were_Scored / Possibility_to_Hit) * 10 - Enemy_Health) - ((Enemy_Damage_if_a_Hit Were_Scored / Enemy_Possibility_to_Hit) * 10 - Health)

The "x100" is just to make the numbers bigger (meaning, not negative). Ok, Peasant against various infantry, level 2.

The possible upgrades are:

Dodge
Endurance
Swordsman
Officers

and at level 2 the following is added:

Drill
Anti Infantry Specialist

I will ignore drill and Officers, as they do not effect combat directly and the impacts of it are very (incredibly) hard to place numbers on. So, peasant vs peasant, the normal stats are:

Damage_if_a_Hit_Were_Scored = (7 Damage - 1 Armor + 1 Concuss) = 7

Chance_to_Hit = 3/50 Attack Chance * 99/100 Inverse of Opponent's Dodge Chance = 297 / 5,000

7 * 297 =

2,079 / 5,000 =

0.4158 * 100 =

41.58 - 25 = 16.58 damage

The peasants, of course, are an even 16.58 - 16.58 right now, but lets try adding upgrades:

Dodge:

3/50 enemy attack chance * 47/50 inverse of allied dodge chance = 141 / 2,500 (or 282 / 5,000)

7 * 282 / 5,000 * 100 =

39.48 - 26 (increased health) = 13.48

Ok, 16.58 - 13.48 = 3.1 greater damage. Not too bad. Now for Endurance:

41.58 - 31 (greatly increased health) = 10.58!

So, 16.58 - 10.58 = 6, making Endurance almost twice as good a first choice in Peasant v Peasant as Dodge! Now for Swordsman:

9 / 100 Improved Attack * 99 / 100 = 891 / 10,000 (445.5 / 5,000)

7 * 445.5 / 5,000 * 100 = 62.37

62.37 - 25 = 47.37

So swordsman first upgrade comes out, 47.37 - 16.58 = 30.79, making it an incredible increase over everything else. So, first upgrade, go swords.

I will spare the reader the equations this time, but will produce some if you want proof. Here are the combinations and their difference. The Anti - Skill's instant kill will be represented as a percentage of enemy health (because, if there are 20 legionaries, and one insant-dies, that is 1/20th the total health).

Dodge + Endurance = 9.1

Dodge + Swordsman = 33.89

Dodge + Anti-Infatry = 5.35

Endurance + Swordsman = 36.79

Endurance + Anti Infantry = 8.25

Swordsman + Anti Infatry = 33.04

So, at least in Peasant v peasant at level 2, anti infantry is NOT worth it, the worst combo is Dodge + Anti Infantry (guesses at what the corresponding worst first 2 upgrades are?) and the best combo is endurance + swordsman. I will get around to more units later.


*NOTE* All above numbers have been rounded up by my calculator, and so might not be the EXACT one.

[honvedseg]

Endurance may not be all it's cracked up to be for some units. For a unit with a low armor value, the difference between having a high and a normal level of endurance may be moot. If a unit is hit for 16 damage and only has 25 points of health, it will take 2 successful shots to kill. If you bump the 25 points up to 30 with "Endurance', it will STILL take only 2 shots to kill, offering you NO benefit. Of course, adding still another couple of health points then brings it to where 3 hits are required, so you've suddenly increased its survivability by 50%.

As another example, if you have a unit with 25 health and an armor value of 12, against a unit that does 17 points of damage, it will take 5 points of normal damage (17 - 12) and a point of concussion per hit. Four good shots will take it out. Adding a level of "Endurance" for 5 more health will allow the unit to take one extra hit before dying (25% increase in lifespan), but adding 4 points of armor instead ("Block") will reduce the damage per hit to a mere 1 normal point plus 1 concussion, enabling it to last until the 13th hit, rather than the 4th or 5th. That's a HUGE increase in survivability (around 250-300%).

"Swordsman" seems to be close to a universal promotion for melee troops, since a dead opponent inflicts NO damage, and sometimes the best defense is a good offense. A few of your units though, like your Legate, have other more pressing priorities, and a high enough attack level already, to make it worth expending your first upgrade on this. The majority of your standard melee troops will probably still want this as either their first or second promotion.

There doesn't seem to be one easy upgrade path that works best for every unit. Tailor your promotions to the units that can make the most of them.

[fatetriarrii]

Hovensdog, what you say is true. I intend (sometime ) to continue with the other units vs a peasant, and then go to other infantry and cavalry...

I believe the reason why the numbers came out like they did was because this is peasant v peasant. The swordsman skill is a 50% increase on attack, while endurance is only around a 20% increase on health. Dodge, though a 500% percent increase, does not increase a stat that was very useful in the first place.

Finally, I think that anti-infantry might be worth a whole bunch more in, say, peasant v praetorian fighting (I would like to see the little level 3 peasant w/ swordsman, anti-infantry, and protection from infantry woop a level 5 praetorian, might do it too).

The only conclusive evidence here is that, if you have only one peasant against one enemy peasant who is level 1, and you can only attain level 3, your best bet is to get swordsman + endurance. I'd like to see that scenario crop up, too.

[lcjr]

Finally, I think that anti-infantry might be worth a whole bunch more in, say, peasant v praetorian fighting (I would like to see the little level 3 peasant w/ swordsman, anti-infantry, and protection from infantry woop a level 5 praetorian, might do it too).

I don't see that happening anytime soon.

Swordsman only increases your chance to hit and peasants simply don't do enough damage to pierce heavy armor.

The Anti skills only add +5% chance of inflicting a critical per level of skill. Best I can tell melee units start with 0% chance of inflicting criticals. At least the files show nothing, perhaps there is a hardcoded value? Now on missile units who start with a basic "Killing Shot" of 25 adding the combination of Weakspot Targeting and Anti skills seems to really pay off. Although there is no way to be sure that the Anti skills apply to missiles. They may be purely melee skills.

Furthermore is there even an infantry instant kill? Trample and critical by missiles have their own icon but has anyone seem an infantry instakill? Maybe infantry criticals just do more damage or bypass armor? Without some insight from the devs a lot of this is pure speculation.

Protection From skills say "an extra chance to avoid an enemies attack". Theres no way of knowing if this is a separate chance from your agility/dodge or adds onto it. From the description it sounds like it's a completely separate check if so 10% isn't much.

Now Block and Missile Protection add directly to armor and seem far more useful. Or at least give results you can see in your units stats

When you did your calculations for Dodge did you factor in the damage penalty that comes with it?

Also Health increases with each level a unit gains so that will probably cut down the % gain on Endurance. +8/lvl for Elephants, +1/lvl all others.

[fatetriarrii]

yes, I included basic health increases, and no, I ddi not include or know of ddamage reduction

Now, I will perform the following calculation of level 3 Peasant v Praetorian based on the above method. As mentioned above, the path will be swordsman, anti-infantry, and protection from infantry. As stated in the guide, protection from will be regarded as a seperate calculation from dodge.

Peasant

1 damage ( ) * 3/50 * 9/10 * 100 + 25 * 1/20 - 25 = - 19.65

Praetorian

26 ( ) * 3/20 * 99/100 * 9/10 * 100 - 28 = 319.49

...Peasants lose...

and now for the peasants who get all the suggested upgrades (by me )

Swordsman, Protection from Infantry, and Armour Penitration.

Peasant

3 damage * 3/50 * 9/10 * 100 - 25 = - 9.2

Praetorian

26 * 3/20 * 99/100 * 9/10 * 100 - 28 = 319.49

I now believe (I, ermm.., checked more than those two) that the second would be the best in this situation, with Protection from turmping dodge (though I must admit that block might have been more worthwhile, and having NCO's or Drill would probably be best, but those aren't calculatable).

[lcjr]

Arrow I will spare the reader the equations this time, but will produce some if you want proof. Here are the combinations and their difference. The Anti - Skill's instant kill will be represented as a percentage of enemy health (because, if there are 20 legionaries, and one insant-dies, that is 1/20th the total health).

I'm thinking your formula is off here. IF there is an insta-kill it would only apply to 5% of actual hits. It would be more like 1 in 20 HIT die. So if you've got miracle peasants hitting 50% of time wouldn't it be more like 1 in 40 get instakilled?

[fatetriarrii]

Well, lcjr, you might be right, but the manual seems to immply that it is a seperate calculation. The precise words are:

"The 'Anti' skill gives a % chance of an instant kill in melee against the appropriate opponent, over and above all other damage."

This also sates, right were everyone can see, that it does not work at range. So critical hit is worth more to a skirmisher vs an elephant than anti-elephant specialist.

[lcjr]

"The 'Anti' skill gives a % chance of an instant kill in melee against the appropriate opponent, over and above all other damage."

I would agree that does imply you need to hit first which is logical. Would be a little unbalanced if you just get to kill x% of the enemy just by engaging them.

This also sates, right were everyone can see, that it does not work at range. So critical hit is worth more to a skirmisher vs an elephant than anti-elephant specialist.

Everyone who read the manual that is After spending many hours on Chariots of War and playing the demo to death figured I knew everything I needed too. Still think keeping the Envelop and Outflank from the earlier games is a bit redundant though.

Anyway back to the subject at hand I have taken the Anti skills on several melee units, after I ran out of my preferred skills, and have yet to see any icon that would indicate it's working.

edit> Started a campaign with Auxilia gave they had Swordsman and Anti-Infantry by the first ambush. In the process of racking up 65 kills I got two "horseshoes". Considering infantry doesn't trample I would assume that the icon used for Anti??? Odd choice if it is. That and 2 out of 65 is only 3%.

Scout the Etruscans 86 kills/0 shoes
Aequi Raiders 68 kills/0

Not that impressed with the skill so far.

[fatetriarrii]

Actually, all units trample. It has been mentioned before (skirmishers trampling). It is just that only cavalry can get upgrades or have decent trample. And I think that specialism is a seperate calculation (not subject to attack) because if it was, look at how terrible it would be. As it is, it is doesn't seem worthwhile.

[sum1won]

I had some skirmishers trample some elephants once. I think those were Marcus's elephants. I have a screenshot somewhere, but it isnt very good.

I find specialism only good for really weak opponents. Seeing a veteran die to a skirmishers dagger is definitely worth it.

However, it may be good for romans against celts, as it might make up for their lack of concuss. Somebody try that, tell me how it goes. Load up on anti and protection from.

[lcjr]

OK in that case I don't(or can't) see where Anti does anything. After 219 kills even at a 5% chance you should see some effect.

[honvedseg]

The rare occasion where you get an instant kill in melee is depicted by a sword icon. I've gotten a fair number of them with a couple of my Auxilia that were given various "Anti-" skills and other odd promotions in an earlier campaign. They don't seem to be as effective as many of the other skills, though, so I didn't use them in the VH campaign I'm currently going through.

[fatetriarrii]

Alright, I have modded my demo of Legion Arena (because I don't want the full version mess it up, and I am to lazy to create a back up) to find out :

• 1 What symbol (if any) is used for Anti- skill instant kills
  2 If the Anti- skills are subject to hit chance

To test this, I went into the files and made the Anti-Infantry skill a 100, meaning 100% chance I believe. The results (you can try it) are:

1) Because my enemies did NOT die on contact, I assume instant kills from Anti- sills are subject to hit chance. I do not know if it is dodge-able.

2) Because all damage was still shown in the normal format of ones and zeros I believe that instant kill does NOT have its own symbol.



Alright, I have two (2) requests for a future patch. Very small (I think). One is personal, one I think everyone will appreciate.

• 1) Could a symbol be made for Anti- skill instant kills? (it would allow the player to know which enemies had anti- skills though...)
  
  2) Could squad names be listed next to unit type in combat? I often fight with multiple legionaries and one has missile protection while the other anti- infantry and I want to know which one is retreating, expecially because the shields are invisible during combat. Besides, when my legionaries fight their warriors or whatever, I don't which "heavy infantry" it says is about to flee

That is all.

[spedius01]

Ave fatetriarri,

Could you please explain to me in VERY simple English, what does "modded" mean and how does altering the text files change the dynamics of the game? I would really like to know!!!

Thank you.

Vale

M. Spedius Corbulo

PS. "Modded" = modified??? Yes or no???

[fatetriarrii]

O, yes!

I am sorry, but I have read about modifying other games, and they are always called mods (the end-products) and the process is called modding (approximately the same number if letters, but the ones in "modding" are closer together and therefore easire to type ).

Anyway. I got over my fear, and I modifyed the files for the full game so:

Spearmen were given 100% hit chance

Peasants and militia were given a 100% dodge chance

Using a save of mission 3, I gave my spearmen endurance and Anti Infantry. I went to battle, and every wave of the spear hit and every stroke killed!

It was scary, trust me , I only had to survive for 100 seconds, I put the spearmen in the center. 10 seconds reaching the middle peasants. 10 - 20 seconds killing them. 20 - 30 seconds reaching everyone else (who was behind me now), and finally 10 - 20 seconds killing them, with 9 seconds left on the clock! like I said, scary

I therefore present a theory that anti-skills are NOT affected by dodge. Protection is still up for grabs, but I doubt it.

[fatetriarrii]

Hahaha! I have the full game now, so nothing can stop me from checking the value of skills, based on the real numbers!

First, I have seen a claim that the anti ~ skills are worthless, so I am going to compare them to the other availible skills at various levels. This will be hard because of the sheer number of pathways that the unit can take, so I will start small. I will use the following equation (the underlines are just to highlight the variables):

((Damage_if_a_Hit Were_Scored / Possibility_to_Hit) * 10 - Enemy_Health) - ((Enemy_Damage_if_a_Hit Were_Scored / Enemy_Possibility_to_Hit) * 10 - Health)

The "x100" is just to make the numbers bigger (meaning, not negative). Ok, Peasant against various infantry, level 2.

The possible upgrades are:

Dodge
Endurance
Swordsman
Officers

and at level 2 the following is added:

Drill
Anti Infantry Specialist

I will ignore drill and Officers, as they do not effect combat directly and the impacts of it are very (incredibly) hard to place numbers on. So, peasant vs peasant, the normal stats are:

Damage_if_a_Hit_Were_Scored = (7 Damage - 1 Armor + 1 Concuss) = 7

Chance_to_Hit = 3/50 Attack Chance * 99/100 Inverse of Opponent's Dodge Chance = 297 / 5,000

7 * 297 =

2,079 / 5,000 =

0.4158 * 100 =

41.58 - 25 = 16.58 damage

The peasants, of course, are an even 16.58 - 16.58 right now, but lets try adding upgrades:

Dodge:

3/50 enemy attack chance * 47/50 inverse of allied dodge chance = 141 / 2,500 (or 282 / 5,000)

7 * 282 / 5,000 * 100 =

39.48 - 26 (increased health) = 13.48

Ok, 16.58 - 13.48 = 3.1 greater damage. Not too bad. Now for Endurance:

41.58 - 31 (greatly increased health) = 10.58!

So, 16.58 - 10.58 = 6, making Endurance almost twice as good a first choice in Peasant v Peasant as Dodge! Now for Swordsman:

9 / 100 Improved Attack * 99 / 100 = 891 / 10,000 (445.5 / 5,000)

7 * 445.5 / 5,000 * 100 = 62.37

62.37 - 25 = 47.37

So swordsman first upgrade comes out, 47.37 - 16.58 = 30.79, making it an incredible increase over everything else. So, first upgrade, go swords.

I will spare the reader the equations this time, but will produce some if you want proof. Here are the combinations and their difference. The Anti - Skill's instant kill will be represented as a percentage of enemy health (because, if there are 20 legionaries, and one insant-dies, that is 1/20th the total health).

Dodge + Endurance = 9.1

Dodge + Swordsman = 33.89

Dodge + Anti-Infatry = 5.35

Endurance + Swordsman = 36.79

Endurance + Anti Infantry = 8.25

Swordsman + Anti Infatry = 33.04

So, at least in Peasant v peasant at level 2, anti infantry is NOT worth it, the worst combo is Dodge + Anti Infantry (guesses at what the corresponding worst first 2 upgrades are?) and the best combo is endurance + swordsman. I will get around to more units later.


*NOTE* All above numbers have been rounded up by my calculator, and so might not be the EXACT one.

Update! I forgot I had multiplied damages by 100! that means anti infantry doesn't do attack * chance of instant kill * health (0.075)! There is a times 100 in there, so it is 7.5. still not too good, but better than dodge.