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Argandios

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Jun 10, 2020
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Hi all,

a few months ago, I found the 'almost' exact formula for the research times in HoI2, I wanted to post it in the HoI2 wiki, but I was unable to modify the wiki. Asking in the forums, Altruist told me to post the formula in this forums, because several of you would find it very interesting. So there I go.

I did this several months ago already, so I do not remember all the details (in fact, I had to look at the formula into an excel spreadsheet I did with it and reworked it from there), and this might be a formula which had not the right modifiers for the rocket and nuclear research facilities, but I think this is the good one.

First of all, each research is divided into 5 'parts', this formula gives you the research time of each of those parts, in order to get the total research time, you need to add the 5 partial times. Second, this formula gives a fractional number, you will need to use the next whole integer in order to get the right number of days for each part, except if the difference with the previous integer is less than 0.01 (not sure if this one is the right difference, but I think it was this one), then you willl use the previous integer (this has to do with the limitation in the number of decimals the game can handle). Last, in the parts with double effort (or double level), mainly those which requires to build prototypes, you need to put the real lelvel of that part, not the one which shows up in the research pannel, but half of it.

Now comes a bit of 'what the hell means each thing':

T = research Time of that part of the research.
D = Double time, 2 if it is one of those parts which require of double time (or double effort, or whatever you want to call it), 1 if it is not.
Nr = Number of rocket or nuclear research facilities you have, if that part of the research is related to either rocket or nuclear science projects, if that part is not related with any of those, this number is 0.
Er = Extra research efficiency due to industrial research for tabualte and computing machines, if any.
Tl = Research team level.
Em = Extra research efficiency due to any minister, if any.
Dr = Dificulty level of that part of the research.
MF = Main Field research, 1 if it is NOT a Main Field research for the team, 0.5 if it is.
B = Blueprints, 1 if if u do NOT have a blueprint, 0.5 if you do have a blueprint.

And now comes the formula:

T = 100*D / [1.65*Nr + {(100+Er)*3*(6.1+Tl)} / {(100-Em)*(4+2*Dr)*MF*B}]

Hope you enjoy it, and hope to have put this post in the right place, xD.

Wanted to attach the spreadsheet with the formula, but is an xls, so I cannot
 
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Very interesting!
I don't have time to check it now, so I'm waiting feedback from all other players, how good this formula works in practice.
I also always wanted to have such a formula, but my low mathematical skill and incredible lazyness not allowed me to do it :rolleyes:
All these 15 years I had to rely only on intuition and experience.
If someone finally created a working formula, it's fine, although it makes life really too easy for noobs. :D

So, hey, people! Don't be silent!
Write, has anyone already tested this formula in practice?

P.S.
Although it seems to be for a full maximum, one more coefficient is missing - "ahead/behind the year of technology" coefficient.
 
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Altruist told me to post the formula in this forums
And thanks a lot for it (the suggestions and improvement part of the forum might be not the best place but, I guess, we are happy to have this formula to crunch over: bookmarked, and, perhaps, a moderator might want to move this topic to the general DH forum).

Ok, my math abilities are limited, so I am a good example (*grin) when trying to use this formula:

From my present game:
# 17th April 1940
# researching Assembly Line Experimentation (1940)

I have no ministers modifying research, I am playing the mod Edge of Darkness and misc.txt says: Research Modifier: 0.3. In the tech overview research speed is stated as 51%. I take it that's my present Research modifier, the result of the 0.3 starting research modifier plus the techs/events improving it to now 51%.

The tech is researched by Ford Motors, no blue print. It is year 1940, the tech is from 1940, so there should be no further boni or mali due to ahead/behind tech research:

research_1940-04-17.png


So, we have a tech team level 6 researching a matched tech of level 7: Platform Development. Should be easy enough to fill out the formula (if I manage to grasp its meaning):

T = 100*D / [1.65*Nr + {(100+Er)*3*(6.1+Tl)} / {(100-Em)*(4+2*Dr)*MF*B}]

D: 1 (no double time)
Nr: 0 (not rocket related)
100 + Er: 51 (mmh, not sure about it but I guess 100 is implying research speed=100 which it is neither for EoD nor DH full, so I am starting with using the shown reseach speed instead - edit: probably a correct approach)
TI: 6 (tech team level)
100-Em: 51 (as unsure about it as for 100+Er above... let's see - edit: that was wrong, correct would had been to keep it as 100-Em)
Dr: 7 (tech level)
MF: 0.5 (it is a matched tech field)
B: 1 (no blueprint)

Now, let's fill this out:
Code:
T = 100*D / [1.65*Nr + {(100+Er)*3*(6.1+Tl)} / {(100-Em)*(4+2*Dr)*MF *B}]
T = 100*1 / (1.65*0  + (  (51)  *3*(6.1+6))  / (  (51)  *(4+2*7) *0.5*1))
T = 100   / (  0     + (     153  *  12.1 )  / (   51   *  18    *0.5  ))
T = 100   / (                   1851.3       /            459           )
T = 100   /                               4.0333
T = 24.79
T = 25 rounded up
Platform Development is 20% of the whole tech and for this part our calculation says we'll need 25 days which means 20%/25days = 0.8% advance per day plus/minus some rounding which usually happens at the start and end of a tech part. Seems reasonable which encourages me that my slight change of how to use Er and Em might be correct (edit: it was wrong, but only partly, see below).

I'll come back to this after a few game days have passed... but first for a late dinner...
 
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Mmh, the result was off but I have an idea...

As a recap, without the exact formula, so far we were using an approach developed for HoI2.
What Argandios graciously has been posting above is no less than, let's call it, the unified research formula.

After (not enough) comparisons with real research time, I'd suggest the following small change. I am leaving out rocket science *grin* and for now also ahead/before modifier. Darkest Hour and most of its mods work with a slowed research speed of 0.4 (lowered from 1 in HoI2) as defined in misc.txt, line 954. To include this I would suggest to change the expression:
100+Er
to
Rm
with Rm simply being the research speed as shown in the tech overview (which seems to consist of the base as given in misc.txt plus improvments via the computer techs and perhaps events). Which gives us the following formula:

T = 100*D / (Rm*3*(6.1+Tl)) / ((100-Em)*(4+2*Dr)*Mf*B)

T = research Time of that part of the research.
D = Double time, 2 if it is one of those parts which require of double time (or double effort, or whatever you want to call it), 1 if it is not.
Rm = Research modifier (as shown in the tech overview)
Tl = Research team level.
Em = Extra research efficiency due to any minister, if any.
Dr = Dificulty level of that part of the research.
Mf = Matched Field research, 1 if it is NOT a Matched Field research for the team, 0.5 if it is.
B = Blueprints, 1 if if u do NOT have a blueprint, 0.5 if you do have a blueprint.

Questions:
1) The pre- and post-historical mali or boni for research in Darkest Hour Full are defined in misc.txt in the lines 1028 and 1030. So, where would we include those into the formula?
Code:
# Blueprint Bonus
    2.0
# Pre-Historical Date Mod (value * days prior to historical date. Lower limit for the total is -0.9. )
    -0.0022
# Post-Historical Date Mod ( 1 + value * days post historical year). The Highest possible value is equal to Blueprint Bonus. Doesn't apply to Nuclear and Rocketry researches
    0.000925 #0.0 #full bonus after 3 years post historical

2) The double time bits of the research. Do I understand it correctly that you would use only the halved values of the difficulty level? For example Improved Computing Machine (1940) ends with a level 14 (or doubled) tech part. So it would be: D=2 but Dr=7 or Dr=14?
 
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