F3 Strong/Average/Weak

[BigFurryMonster]

• From Test 6:
  1 Hoplite = 2.06 Warrior.

Hypothesis adjusted to:

Unit Value = 1 + 0.60 * (Attack Value - 1) + 0.53 * (Defense Value - 1)
(with some rounding errors)

(updated) Formula correction below.

[BigFurryMonster]

• From Test 7:
  1 Bowman = 2.08 Warrior.

So... a Bowman and a Hoplite would almost be of the same strength...!

The formula is therefore not correct.

(update) Value updated below.

[DaveMcW]

Some more data points:

10-attack-Archer = 6.5 or 6.6 Warriors
50-attack-Archer = 30.5 or 30.6 Warriors

[BigFurryMonster]

Applying my formula, I'd get 6.4 and 30.4 respectively.

I assume you created (A-D) 10-1 and 50-1 units.

If we assume the difference is due to rounding errors, we can confirm that the unit value increases linearly with the attack value, given that the defense value remains at 1.

[DaveMcW]

10-defense-Spearman = 4.6 or 4.7 Warriors
50-defense-Spearman = 20.6 or 20.7 Warriors

This works out to the simple formula:
0.6 * Attack + 0.4 * Defense

Can you run your spearman test with more units to see if the original is accurate? Placing units in the editor lets you work with much bigger numbers than placing them in debug mode.

[bongo]

Wow, you're doing some impressive research here. How do you find the time?

Will you add mobility to the research list?

[BigFurryMonster]

Not so fast, DaveMcW! I found the following interesting fact:

• 18 Warriors -vs- 7 Immortals: Weak
• 18 Warriors -vs- 7 Artificially Created "4-2" Units: Average

Apparently, the unit value is dependent on a factor we do not know yet.

Oh, and:

• 1 Immortal = 3.23 Warrior
• 1 "4-2" Unit = 3.20 Warrior
• 1 Legionary = 3.00 Warrior
• 1 Numidian Mercenary = 2.51 Warrior
• 1 Veteran Numidian Mercenary = 3.34 Warrior

I set the "4-2"'s cost to 30 shields, to rule out that factor.

[FrustratedPoet]

Originally posted by BigFurryMonster

• 18 Warriors -vs- 7 Immortals: Weak
• 18 Warriors -vs- 7 Artificially Created "4-2" Units: Average

Apparently, the unit value is dependent on a factor we do not know yet.

Time to throw some ideas out and see what sticks....

Maybe the unit value includes such variables as "unique unit" and "resource required". A civ that has Immortals must have access to Iron (whereas a generic 4.2 unit would be missing this flag), which implies strength and the ability to produce more powerful units in the future (although I find it hard to believe that 'potential strength' would be included)

Also, because the Immortal has the ability to put the Persians in their GA they could be valued more highly. Again, the generic 4.2 unit wouldn't have this potential. Try running the test again using a Persian Civ that has already used up its GA and whether this changes things.

[BigFurryMonster]

I already thought of this, and set the flags for the "4-2" unit to exactly match the flags for the Immortal:

• Can trigger GA
• Available to one civ only
• Upgrade abilities
• Resource required

(update) The CivSpecific Ability causes this effect. See below.

[FrustratedPoet]

Ah, OK then. Good thinking.

[BigFurryMonster]

Finally found something! I was testing under Despotism and Monarchy. Here, it actually makes a difference how many cities you have. The number of cities determines the Army Support Cost.

For example:

• 13 Vet Warriors -vs- 15 Warriors: Strong (3 cities for the Vet party = 2 gpt* support cost)
• 13 Vet Warriors -vs- 15 Warriors: Average (1 city for the Vet party = 10 gpt* support cost)

* It also supported a worker.

To rule this effect out, I should be testing under equal circumstances, with zero support cost, for instance.

• (update) 1 Vet Warrior = 1.33 Warrior (matches the result found above for NumMercs)
• 1 Elite Warrior = 1.66 Warrior

[BigFurryMonster]

Using the knowledge obtained above, I had to run most tests again.

I got the following:

• 1 Archer = 1.60 Warrior
• 1 Spearman = 1.40 Warrior
• 1 Bowman = 2.02 Warrior
• 1 Hoplite = 1.82 Warrior
• 1 Immortal = 3.23 Warrior
• 1 NumMerc = 2.42 Warrior
• Veterans = 1.33 Regular
• Elite = 1.66 Regular

...leading to the following formula: (updated)

Unit Strength = (Hitpoints / 3) * (0.6 * Attack Value + 0.4 * Defense Value) * (1.01 if UU and CivSpecificAbilitiesOn)

Army Strength = Sum (Unit Strengths) * (Factor depending on ArmySupportCost)

...I haven't tested that last factor.

[DaveMcW]

Great detective work!

One minor detail: ArmySupportCost should be factored in to the final calculation, not the one for individual units.

[BigFurryMonster]

Absolutely right. Edited above.

[nbarclay]

Is it times the support cost factor, or minus the support cost factor? That, too, needs to be investigated before the formula can be considered pinned down completely.