Totally bonkers bribery mechanics

[alpaca]

Ok, after deciding to settle for some qualitative results, I decided to test what determines the cost on a successful bribery attempt. I found out it only depends on the bribee's loyalty attribute and all the modifiers don't seem to affect the cost, only the chance. I did my tests with a single spearmen unit (stat-wise very similar to the levy spearmen from vanilla) with 0 and with 6 xp

However, there's a problem: The function isn't monotonous!



Exact data:

Spoiler Alert, click show to read: 

Loyalty	Cost (0 XP)	Cost (6 XP)	Ratio (0xp / 6xp)
-3	3115	4603	0,68
-2	4239	5727	0,74
-1	6490	7978	0,81
0	8740	10228	0,85
1	14039	15676	0,9
2	20688	22474	0,92
3	26867	30621	0,88
4	11636	13719	0,85
5	11235	13467	0,83
6	10384	12765	0,81
7	9083	11613	0,78
8	8607	11285	0,76
9	9293	12120	0,77
10	9980	12956	0,77

Not bad enough that the cost shows a sudden severe drop at a loyalty of 4, the cost doesn't even seem to scale uniformly with army quality so it could well be there's some hidden inversions there, too.

This is so seriously screwed and insane that I believe there must have been some kind of oversight at work. At first I presumed it was some integer number overflow (i.e. the game wrapping the number around after reaching 2^15 or 2^16) but that doesn't fit either.

Some number crunching using gnuplot to fit:

f(x) = b*x + c (values -2 to 0)
g(x) = g1*x^2 + g2*x + g3 (values 0 to 3)
h(x) = h1*x^2 + h2*x + h3 (values 4 to 7)
i(x) = i1*x + i2 (values 8 to 10)

Spoiler Alert, click show to read: 

*******************************************************************************
Fri Oct 12 23:55:07 2007


FIT: data read from "bribery.txt"
x range restricted to [-2.00000 : 0.000000]
#datapoints = 3
residuals are weighted equally (unit weight)

function used for fitting: f(x)
fitted parameters initialized with current variable values



Iteration 0
WSSR : 1.23565e+006 delta(WSSR)/WSSR : 0
delta(WSSR) : 0 limit for stopping : 1e-005
lambda : 1.1547

initial set of free parameter values

b = 1700.4
c = 10136.5

After 4 iterations the fit converged.
final sum of squares of residuals : 0.166667
rel. change during last iteration : -1.84833e-006

degrees of freedom (FIT_NDF) : 1
rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.408248
variance of residuals (reduced chisquare) = WSSR/ndf : 0.166667

Final set of parameters Asymptotic Standard Error
======================= ==========================

b = 2250.5 +/- 0.2887 (0.01283%)
c = 10228.2 +/- 0.3727 (0.003644%)


correlation matrix of the fit parameters:

b c
b 1.000
c 0.775 1.000

*******************************************************************************
Fri Oct 12 23:56:37 2007


FIT: data read from "bribery.txt"
x range restricted to [0.000000 : 3.00000]
#datapoints = 4
residuals are weighted equally (unit weight)

function used for fitting: g(x)
fitted parameters initialized with current variable values



Iteration 0
WSSR : 7.05427e+007 delta(WSSR)/WSSR : 0
delta(WSSR) : 0 limit for stopping : 1e-005
lambda : 3.10913

initial set of free parameter values

g1 = -3096.5
g2 = 14578.7
g3 = 7965.2

After 5 iterations the fit converged.
final sum of squares of residuals : 0.05
rel. change during last iteration : -3.22514e-007

degrees of freedom (FIT_NDF) : 1
rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.223607
variance of residuals (reduced chisquare) = WSSR/ndf : 0.05

Final set of parameters Asymptotic Standard Error
======================= ==========================

g1 = 674.75 +/- 0.1118 (0.01657%)
g2 = 4773.45 +/- 0.35 (0.007332%)
g3 = 10227.9 +/- 0.2179 (0.002131%)


correlation matrix of the fit parameters:

g1 g2 g3
g1 1.000
g2 -0.958 1.000
g3 0.513 -0.688 1.000


*******************************************************************************
Fri Oct 12 23:59:43 2007


FIT: data read from "bribery.txt"
x range restricted to [4.00000 : 7.00000]
#datapoints = 4
residuals are weighted equally (unit weight)

function used for fitting: h(x)
fitted parameters initialized with current variable values



Iteration 0
WSSR : 6.63552e+008 delta(WSSR)/WSSR : 0
delta(WSSR) : 0 limit for stopping : 1e-005
lambda : 19.8074

initial set of free parameter values

h1 = 1
h2 = 1
h3 = 1

After 8 iterations the fit converged.
final sum of squares of residuals : 0
abs. change during last iteration : -3.30872e-024


Hmmmm.... Sum of squared residuals is zero. Can't compute errors.

Final set of parameters
=======================

h1 = -225
h2 = 1773
h3 = 10227


*******************************************************************************
Sat Oct 13 00:01:58 2007


FIT: data read from "bribery.txt"
x range restricted to [8.00000 : 10.0000]
#datapoints = 3
residuals are weighted equally (unit weight)

function used for fitting: i(x)
fitted parameters initialized with current variable values



Iteration 0
WSSR : 4.41373e+008 delta(WSSR)/WSSR : 0
delta(WSSR) : 0 limit for stopping : 1e-005
lambda : 6.4291

initial set of free parameter values

i1 = 1
i2 = 1

After 6 iterations the fit converged.
final sum of squares of residuals : 0.166667
rel. change during last iteration : -5.05772e-011

degrees of freedom (FIT_NDF) : 1
rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.408248
variance of residuals (reduced chisquare) = WSSR/ndf : 0.166667

Final set of parameters Asymptotic Standard Error
======================= ==========================

i1 = 835.5 +/- 0.2887 (0.03455%)
i2 = 4600.83 +/- 2.609 (0.0567%)


correlation matrix of the fit parameters:

i1 i2
i1 1.000
i2 -0.996 1.000

At -3 this seems to be capped so I didn't include that point.
What's interesting is that h(x) actually gives a very good fit for all except the last three values (it hits the three values it was fit to perfectly and seems to do the same for the -2 and 0 values; -3 is hit almost exactly, too). However the whole thing remains a mystery and I wonder what CA did to generate those values. It's simply totally insane (I think they just included it to see if somebody actually notices - or they smoked some really bad **** that evening)

For the 0xp test things change slightly. The first 4 points follow the same proportionality, but now the second differentiation has a negative value at loyalty 3 and also differs at 4 and 5, while the rest is similar again.


--------------------------------------------------------------------------

See what I tried before at the org: http://forums.totalwar.org/vb/showthread.php?t=93070

[Mersk]

How did you change the XP of the unit? Made sure none of the factors that would touch anything below stayed the same for each test?

   <bribery>
      <bribe_to_family_tree bool="false"/>
      <base_character_chance float="0.4"/>
      <religion_modifier float="0.66"/>
      <combined_attribute_modifier float="0.2"/>
      <briber_attribute_divisor float="3.0"/>
      <bribee_attribute_divisor float="3.0"/>
      <army_size_modifier float="0.035"/>
      <base_settlement_chance float="0.8"/>
      <settlement_loyalty_modifier float="0.01"/>
      <settlement_population_modifier float="0.0001"/>
      <faction_standing_divisor float="10.0"/>
      <max_bribe_chance float="100.0"/>
      <min_bribe_chance float="1.0"/>
      <bribe_chance_modifier float="1.0"/>
   </bribery>

excerpt from descr_campaign_db

[alpaca]

How did you change the XP of the unit? Made sure none of the factors that would touch anything below stayed the same for each test?

   <bribery>
      <bribe_to_family_tree bool="false"/>
      <base_character_chance float="0.4"/>
      <religion_modifier float="0.66"/>
      <combined_attribute_modifier float="0.2"/>
      <briber_attribute_divisor float="3.0"/>
      <bribee_attribute_divisor float="3.0"/>
      <army_size_modifier float="0.035"/>
      <base_settlement_chance float="0.8"/>
      <settlement_loyalty_modifier float="0.01"/>
      <settlement_population_modifier float="0.0001"/>
      <faction_standing_divisor float="10.0"/>
      <max_bribe_chance float="100.0"/>
      <min_bribe_chance float="1.0"/>
      <bribe_chance_modifier float="1.0"/>
   </bribery>

excerpt from descr_campaign_db

I spawn the unit using the spawn_army command.
And no, I didn't change anything in the campaign db in between. I tested these separately with the same character/unit combination and they didn't seem to have an effect on the cost at any rate.