Unit Cost Equation
 

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? http://forum.shrapnelgames.com/images/smilies/wink.gif

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 http://forum.shrapnelgames.com/images/smilies/happy.gif
Besides, there arent any troops with under 7 morale, are there? Theyd be useless, and Illwinter knows it http://forum.shrapnelgames.com/image...es/biggrin.gif
<font class="small">Code:</font><hr /><pre>
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
</pre><hr />
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?

Re: Unit Cost Equation
 

Heres a quick graph of the data in the chart.

Re: Unit Cost Equation
 

Just starving units http://forum.shrapnelgames.com/images/smilies/happy.gif

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 http://forum.shrapnelgames.com/images/smilies/happy.gif. Your current formula seems fine; it looks good to me, anyway http://forum.shrapnelgames.com/images/smilies/happy.gif 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.

Re: Unit Cost Equation
 

Ok, new chart http://forum.shrapnelgames.com/images/smilies/happy.gif
(can you tell I dont have a life)

<font class="small">Code:</font><hr /><pre>
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
</pre><hr />

Attatched is another graph of the data.
Its a much smoother spread, too http://forum.shrapnelgames.com/images/smilies/happy.gif However, the change close to 10 is less severe...

Re: Unit Cost Equation
 

Hmmm.......

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

Re: Unit Cost Equation
 

Probably. Lemme give it a go...

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

Re: Unit Cost Equation
 

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

Re: Unit Cost Equation
 

<font class="small">Code:</font><hr /><pre>
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
</pre><hr />

Re: Unit Cost Equation
 

Perfect!

Re: Unit Cost Equation
 

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)