Unit Cost Equation

[The_Tauren13]

Im moving this to a new thread so I quit hogging Scott Heberts excellent thread on Commander costs...

Heres my current formula for caulculating the cost of a unit based on (and only on) its physical stats:
sqrt(((HP*(10.0+Prot)*Def*MR)/1000.0)*((Str*Att)/10.0))*((3.0+Move)/5.0)*((40.0+AP)/50.0)*(9.0/(6.0+Enc))*((Mor^log10(7))/7.0)
Comments, anyone? Suggestions? Flames? Donations?

So, back to the morale buisiness:
Perhaps just a chart is the way to go, then.
I hate making morale 0-5 cost exactly the same, because there is a change, however small and imperceptable
Besides, there arent any troops with under 7 morale, are there? Theyd be useless, and Illwinter knows it
Code:

---

Morale   Cost

   0     0.38

   1     0.39

   2     0.40

   3     0.41

   4     0.43

   5     0.46

   6     0.50

   7     0.55

   8     0.65

   9     0.80

  10     1.00

  11     1.40

  12     1.70

  13     1.90

  14     2.00

  15     2.09

  16     2.17

  17     2.24

  18     2.30

  19     2.35

  20     2.39

  21     2.42

  22     2.44

  23     2.45

  24     2.46

  25     2.47

  26     2.48

  27     2.49

  28     2.50

  29     2.51

  30     2.52

---

Now, the question is, if I do get this chart accurate, should it stay as just a multiplier to what the cost would be otherwise?

[The_Tauren13]

Heres a quick graph of the data in the chart.

[Saber Cherry]

The_Tauren13 said:
I hate making morale 0-5 cost exactly the same, because there is a change, however small and imperceptable
Besides, there arent any troops with under 7 morale, are there?

Just starving units

That looks pretty accurate. As far as multiplier-or-not goes...

On commanders, morale is (AFAIK) unimportant except for repel attempts. So it should not be applied to commanders.

On normal units, it sort of depends. High morale is worth more on cheap units than expensive units, because you get lots of them. Maybe it should have an additive AND multiplicative effect? In other words, if the unit's value (aside from morale) is "X", with morale ("MV", value of morale from the chart) it might be:

(X+X*MV+K*X^2*MV)

The first X considers units in huge groups, or boosted by a priest casting Sermon of Courage, or with "Berserkers" cast, or patrolling, or waiting as targets forn Fires from Afar, or as bodyguards where morale is not relevant, or as arrow targets / lance fodder where morale is meaningless.

The second term considers normal groups with no morale support, in normal melee battles.

The third term (with an unknown constant, K) is the usefulness of high-morale units in keeping low-morale groups from fleeing, preventing complete routs (so mages can do their business), when the enemy is using units with Fear or casting Terror and Panic, and other cases where high morale is crucial.



... then again, I never stop playing with a formula until it is so complex I can no longer understand it, so maybe you should ignore everything I just said. Probably, in fact. Actually, I order you to banish it from your mind . Your current formula seems fine; it looks good to me, anyway 2.5 seems a little high as an upper asymptote, though; 2.0 might be high enough for a purely multiplicative term. I wouldn't pay 2.5 times as much for units with infinite morale as for 10 morale - the max would be, maybe, 2.0 times, at which point I'd only buy a few of them.

[The_Tauren13]

Ok, new chart
(can you tell I dont have a life)

Code:

---

Morale   Cost

   0     0.450

   1     0.460

   2     0.480

   3     0.510

   4     0.550

   5     0.600

   6     0.660

   7     0.730

   8     0.810

   9     0.900

  10     1.000

  11     1.100

  12     1.195

  13     1.285

  14     1.370

  15     1.450

  16     1.525

  17     1.595

  18     1.660

  19     1.720

  20     1.775

  21     1.825

  22     1.870

  23     1.910

  24     1.945

  25     1.975

  26     2.000

  27     2.020

  28     2.035

  29     2.045

  30     2.050

---

Attatched is another graph of the data.
Its a much smoother spread, too However, the change close to 10 is less severe...

[Saber Cherry]

Hmmm.......

Yeah, it has better endpoints. Is it possible to increase the slope around 10 while keeping the endpoints and the smoother line?

[The_Tauren13]

Saber Cherry said:Is it possible to increase the slope around 10 while keeping the endpoints and the smoother line?

Probably. Lemme give it a go...

And why is the spacing all wacked out in the 2nd chart?

[Saber Cherry]

The_Tauren13 said:

Probably. Lemme give it a go...

And why is the spacing all wacked out in the 2nd chart?

Editing always messes up (code)(/code) sections. Forum bug.

[The_Tauren13]

Code:

---

Morale   Cost

   0     0.500

   1     0.510

   2     0.523

   3     0.541

   4     0.564

   5     0.596

   6     0.638

   7     0.694

   8     0.768

   9     0.868

  10     1.000

  11     1.251

  12     1.439

  13     1.580

  14     1.686

  15     1.765

  16     1.824

  17     1.869

  18     1.903

  19     1.928

  20     1.947

  21     1.961

  22     1.971

  23     1.979

  24     1.985

  25     1.990

  26     1.993

  27     1.995

  28     1.997

  29     1.999

  30     2.000

---

[Saber Cherry]

Perfect!

[sushiboat]

Here is a quick and dirty formula based on a multiple linear regression that
included only units with morale below 30. (AFAIK, the 30 and 50 morale
numbers are only symbolic and represent a qualitatively different state.) I
didn't include movement because the spreadsheet I have needs work to
adjust those numbers into a useable format. (Plenty of other boring
qualifiers omitted.)

Cost = -386.0 + (11.9 * Size) + (2.3 * HP) + (-2.0 * Prot) + (11.0 * Morale) +
(21.8 * MagicRes) + (1.4 * Enc) + (-4.8 * Str) + (2.8 * Att) + (.7 * Def) +
(4.0 * Prec)

The adjusted multiple R-squared is .70, so about 70% of the variance in cost
is explained by the predictors. How does that compare to the formula in the
first post?

In case you are not familiar with multiple regression, don't be fooled by the
size of the coefficients. There is some collinearity -- some of the stats used
as predictors are correlated with each other, so their unique predictive
contribution is affected. For example, strength has a zero-order correlation
of .24 with cost, but in the multiple regression, its coefficient is negative.

Edit: Commander vs. non-commander makes a difference, so here are the
formulae after splitting the two groups.

Non-commander formula (adjusted R-squared = .81):

Cost = -60.1 + (12.3 * Size) + (2.9 * HP) + (.8 * Prot) + (5.3 * Morale) +
(4.1 * MagicRes) + (-1.9 * Encumb) + (-8.0 * Str) + (1.5 * Att) + (.5 * Def) +
(-1.9 * Prec)

Commander formula (adjusted R-squared = .71):

Cost = -459.7 + (16.8 * Size) + (.3 * HP) + (-2.5 * Prot) + (11.0 * Morale) +
(25.4 * MagicRes) + (5.0 * Encumb) + (.8 * Str) + (-1.1 * Att) + (6.2 * Def) +
(-.1 * Prec)