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Chas

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This supplements the 1.08 FAQ
EDIT 24/11/04: Updated for November beta.

Beta Tech Costs
=============
1. Derivation of Tech Costs
--------------------------
The formula is similar to 1.08, but has more factors; some of the factors also use different values. Any that are different are shown below in italics:
Code:
Section            Component
----------     ---------------
1.1             [I]BV: Base Value[/I]                    (Different values)
1.2             [I]x ATM: Ahead of Time Multiplier[/I]   (Different values and dates)
                    x TSM: Tech Speed Multiplier
                            Religion modifier
                            + Cities modifier
1.3.1                       + [I]Vassals modifier[/I]        (New factor)
1.3.2                       + [I]HRE modifier[/I]            (New factor)
                            + No Contact  modifier
                            + Whiteman modifier
                    x TGM: Tech Group Multiplier
                    x DPM: Domestic Policy Multiplier
                    x DFM: Defender of Faith Multiplier
                    x Inflation
1.1 BV: Base Value
------------------
This can be looked up in the following table.
Code:
  Level    Infrastructure       Trade
   to      -------------- ----------------
 research   BV       ATD      BV      ATD
---------  --------------  ---------------
   1        141.5           141.5
   2        858             858
   3       3712.5          7725
   4       7155     1440   4000     1465
   5       6720     1485   6760     1490
   6      11895     1525  10980     1530
   7       7680     1590   7680     1590
   8      12360     1630  12360     1630
   9      10850     1690  10850     1690
   10     24000     1740  24000     1740


                              Land and Naval
-----------------------------------------------------------------------------
  Level                      Level                      Level
   to                         to                         to
 research   BV       ATD    research  BV      ATD     research  BV      ATD
-------------------------   -----------------------    ----------------------
   1        141.5            21      1875     1600       41     866     1733
   2       1440              22       942.5   1610       42     651     1737
   3       3118.5   1419     23      2101     1615       43    1092.5   1740
   4       2280     1440     24      1544     1626       44    1097.5   1745
   5       1545     1455     25      2150.5   1634       45    1102.5   1750
   6       1565     1465     26       982.5   1645       46    1107.5   1755
   7       1590     1475     27      3000     1650       47    1115     1760
   8        319     1485     28      3052.5   1665       48    1120     1765
   9        159.5   1487     29      2060     1680       49    1125     1770
   10       642     1488     30      1872     1690       50    1132.5   1775
   11       972     1492     31      1045     1699       51     226.5   1780
   12      1640     1498     32      1050     1704       52     227     1781
   13      2004     1508     33       844     1709       53     682.5   1782
   14      1690     1520     34       423     1713       54     684     1785
   15       852.5   1530     35       424     1715       55     687     1788
   16       857.5   1535     36       637.5   1717       56     918     1791
   17      2625     1540     37       426     1720       57     922     1795
   18      3590     1555     38       640.5   1722       58     694.5   1799
   19      2745     1575     39       428     1725       59     231.5   1802
   20      1850     1590     40      1293     1727       60     464     1803
Note 1: The price per year, used to calculate these BV's, is different (bigger) to base 1.08, correspondingly increasing the BV's for all techs. The increase varies depending on the year the level is due, decreasing progressively.
Code:
Examples of Price per year
         1.08           Beta        Inc
         ----           ----        ---
1450     136            148.5        9%
1750     204.5          217          6%
Note 2: From the November beta onwards, infra.csv and trade.csv are different for levels 6 and above, giving substantial increases in BV relative to earlier betas.
Code:
Examples of increase in economic techs due to November beta

Tech         Level      Pre-Nov   Nov      % inc
-----        -----       ------  ----      -----
Infra          6          6160   11895      93%
Trade          6          5280   10980     108%
Infra/Trade    7          5490    7680      40%
Infra/Trade    8          7680   12360      61%
Infra/Trade    9         12360   10850     -12%
Infra/Trade   10         10850   24000     121%
1.2 ATM: Ahead of Time multiplier
---------------------------------
If current date is ATD (see table above) or later, then ATM = 1
Else ATM = 2.5 + (ATD – Current Date) x 0.1

Note 1:
The ATD is 10 years before start date (compared to 5 years for 1.08)
1.08 uses 1.5 as the first constant in the formula.

The effect is that you can afford to be 5 years earlier before the ATM cuts in, but after that the penalty is worse.

e.g. years before 'scheduled' Start Year:
Code:
                  9              10
1.08 ATM         x1.9          x2.0
Beta ATM         x1.0          x2.6
Note 2:
The November beta changes to infra.csv and trade.csv, for levels 6 and above, changed the ATD's (later). The effect is that the ATM is applicable at dates that previously would not have incurred the penalty, for levels 7 and above.
Code:
Examples of the effect on ATD of November beta

Tech         Level      Pre-Nov   Nov     Change
-----        -----       ------  ----      -----
Infra          6          1525    1525      -
Trade          6          1530    1530      -
Infra/Trade    7          1560    1590     +30
Infra/Trade    8          1590    1630     +40
Infra/Trade    9          1630    1690     +60
Infra/Trade   10          1690    1740     +50
Note 3: The overall effect of the November beta changes, on economic tech costs.
Code:
Example for researching Infra 8 in 1610:
                        BV     ATM     Combined
                        --     ---     ---------
Pre-November betas :   7680    x1        7680
November beta:        12360    x4.5     55620
1.3 TSM: Tech Speed Multiplier
------------------------------
The capping rule is the same: TSM not less than x1

1.3.1 Vassals modifier
---------------------
If you have at least one vassal, you get a basic modifier to the TSM of -0.02.
This modifier is reduced the more Centralised you are.
How much the Centralisation affects the modifier, depends on whether the vassal is on the same continent as you.
In either case, once you are fully Centralised, you get no benefit
Code:
Centralisation     Same      Different
  Setting         Continent  Continent
    0             -0.02        -0.02
    1             -0.02        -0.02
    2             -0.02        -0.02
    3             -0.02        -0.02
    4             -0.02        -0.02
    5             -0.02        -0.02
    6             -0.02        -0.016
    7             -0.02        -0.012
    8             -0.016       -0.008
    9             -0.008       -0.004
    10              0            0
‘Same continent’ means the continents of the capital provinces, as defined in country.csv. Land connections, islands etc. make no difference.

If you have 2 vassals or more, at least one on the same continent, at least one on a different continent, you get the better benefit applicable to the same continent vassal.

Note that the beta release notes say that you get a benefit per vassal.
This is not the case, you get the same benefit whether you have 1 or vassal or several. Given that the full benefit is small by comparison with many other modifiers/multipliers, and that centralisation makes the benefit even smaller, it’s possible that this is a bug. Or possibly the release notes are wrong, and only mean the other vassal benefits (income etc.) are per vassal.

1.3.2 HRE modifier
-----------------
If you are HRE, you get -0.02 modifier, per elector that has relations >=100.

Electors are as defined in country.csv. Countries with 2 votes only give the same benefit as single vote countries.

If the HRE is an elector, he does not give himself a benefit (so if there are 25 electors, and you are one of them, and you have good relations with all of them, the best you will get will be -0.48).

This benefit makes the HRE a good proposition, especially at the beginning of the game when there are still plenty of electors. Hungary starts in 1419 with -0.5 from the 25 electors, which effectively wipes out the penalty from 4 of its 8 cities. The modifier for 25 electors is equivalent to the Cities penalty for 5 cities – conspiracy theorists may note that Austria starts the game with 5 cities – somehow Austria always seems to come out best with the HRE.

1.3.3 Modifier capping
---------------------
In 1.08 there are 4 modifiers
– 2 of them are capped to +3.0 – the sum of Religion and Cities
– 2 of them are uncapped, No Contact and Whiteman

In the beta there are 6 modifiers
- 4 are capped to +3.0 – the sum of Religion, Cities, Vassals and HRE
- 2 are still uncapped, No Contact and Whiteman
 
Last edited:

unmerged(36024)

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Nov 11, 2004
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About base value

When researching level X+1 base value is
(round down ((DD(X)-1400)*5/11)/2+137.5)*(DD(X)-DD(X-1)),
where DD(X) - discovery year for tech X in land/naval/trade/infra.csv.

Example:
Researching 3 trade tech
X=2, ГО(X)=1475, ГО(Х-1)=1425

BV= (round down((1475-1400)*5/11)/2 +137.5)*(1475-1425) = (round down (75*5/11)/2 +137.5)*(50) = 7725

P.S.: In extensive testing seems (round down((DD(X)-1400)*5/11)/2+137.5) can be 0.5 less or more.
So 5/11 - no exact multiplier, but close enough for me.
 

Chas

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minusa said:
When researching level X+1 base value is
(round down ((DD(X)-1400)*5/11)/2+137.5)*(DD(X)-DD(X-1)),
where DD(X) - discovery year for tech X in land/naval/trade/infra.csv.

Example:
Researching 3 trade tech
X=2, ГО(X)=1475, ГО(Х-1)=1425

BV= (round down((1475-1400)*5/11)/2 +137.5)*(1475-1425) = (round down (75*5/11)/2 +137.5)*(50) = 7725

P.S.: In extensive testing seems (round down((DD(X)-1400)*5/11)/2+137.5) can be 0.5 less or more.
So 5/11 - no exact multiplier, but close enough for me.
Well, before I go and check against my test DB, thanks for taking up the challenge.

I did try the odd scheme with 1400 as the constant of subtraction, but your particular combination of constants and rounding is not one I have tried.

You've posted in this thread, so I assume you have been using the beta - fair enough - my instinct is that the only difference between base 1.08 and the betas is that the contant of subtraction has been changed, so if we can get it for the beta, it will probably be obvious what it is for base 1.08.

I'll be back to you. :)
 

Chas

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minusa said:
When researching level X+1 base value is
(round down ((DD(X)-1400)*5/11)/2+137.5)*(DD(X)-DD(X-1)),
where DD(X) - discovery year for tech X in land/naval/trade/infra.csv.

Example:
Researching 3 trade tech
X=2, ГО(X)=1475, ГО(Х-1)=1425

BV= (round down((1475-1400)*5/11)/2 +137.5)*(1475-1425) = (round down (75*5/11)/2 +137.5)*(50) = 7725

P.S.: In extensive testing seems (round down((DD(X)-1400)*5/11)/2+137.5) can be 0.5 less or more.
So 5/11 - no exact multiplier, but close enough for me.
Hmm. Well, close, but no coconut :)

As you say, this formula fails by 0.5d (on the 'price'; this is multiplied by the number of years for the level, of course) for several cases. e.g.:
- Land/Naval 28, 30, 35, 53
- Infra 7 and Trade 6, using the new November beta .csv files.

As I said in the other thread, I have managed to find whole-integer constants (like yours) that get nearly all of the answers right. In fact somewhere I think I have one that produces all the actual values used in the game - but this one failed when the .csv files were edited to have different years.

Anyway, like me, I guess you think that there really must be some answer similar to yours that the program uses - rather than the 798.8 and 0.22831 that I currently use.
 
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I just wanted to say thank you for a brilliant analysis and a very nice exposition - I almost understood everything at the first reading :)

Hopefully it can reach perfection after minusa's eventual findings has been implemented.

----

I missed this post when it was first posted. Must be because noone responded to it. Were everyone so stunned that they simply dropped their pencils to the floor!

Thanks Iron for bringing it to life again (in the BUG forum were minusa apparently found it).