Research Maths... Or why AIs are more important than ETs...

Research – Energy vs AI

The basics of research are simple, and in the FAQ.

Every time you research you get an amount of stats as a proportion of the product of your energy & research at the time you hit the button.

The exact equation is:

Stats = Research x Energy / [random number 900 – 2000]

When you research you use all your energy (unless you choose not to, but there is no real reason to do that) and twice as much research as you spend energy. If you have less than twice your energy in available research you still gain the same amount, the numbers when you click the button are what count, not your maximum possible, nor what you have left afterwards.

Research regenerates at 1 point per minute, and 5% energy per level (both increase by 50% if you are notorious – research comes back as 1 point at the start of even minutes and 2 points at the start of odd minutes, and energy at 7.5% per minute).

You get energy from:
Energy Technologies ( +1 or +3 per slot equipped )
Levels ( +1 per level, starting with 10 at level 1, so 9 +1/level )
Energy Max Protocol ( +1 can be found in the Ascension mission )
C.O.A.L. ( 30 minute consumable giving +3 energy )

You get research from:
Bigger Ship ( +10 per ship size increase )
Levels ( +1 per level )
AI Equipment ( +1, +4, +6 per slot equipped )
Science Fact Protocol ( +20 can be found in the Ascension mission )

At first glance it looks as though you do better with energy boosts. Most people have considerably more research than energy, and boosting the smaller number makes a bigger difference to the product. However the catch to this is that the recharge time is also related to the energy you spend. When the maths is done energy cancels out of the equation and makes no difference in the long term to active research rate.

What this means is that if you are playing actively and want to research most efficiently then you should use AI and SFP equipment, and as big a ship as you can, to boost your research and be willing to sit for a few minutes in your labcoat waiting for this extra research to fill up.

The time to use energy techs is when you are preparing to leave for a time long enough to completely recharge your research bar. At that point it is worth spending all your research with as much energy as you can muster.

The Maths:

This is assuming that Research > 2 * Energy. This assumption holds until player level of at least 250 once you have a ship of any real size.

I'm using '=' to mean is proportional to throughout rather than factoring in the 900-2000 and exact recovery rates. The exact numbers really don't matter

Stats = Research * Energy

Recharge Time = Energy * 2

Energy * 2 is the amount of research used, and Research regenerates more slowly than Energy so is the limiting factor.

This gives the result that:

Stats/Time = Research * Energy / Energy * 2 = Research / 2

If you are not online much, then you can find that using energy tech is more efficient. But by the time you have 60 energy you will be researching once every 2 hours (80 minutes if notorious) and the time in which the research over energy strategy works in your favour gets longer.

Addenda: Yes, I know I could remove the '/ 2' from the equation as it is all proportionality so the constant doesn't matter, but it is amazing how that seems to confuse people more

That's what I thought, I just didn't do the math. Thanks for doing it for me.

I'll try to go over those numbers later tonight. Are you sure the range is 900-2000?

Yes, it is 900-2000 (actually to be more specific "This is actually 20 times a random integer between 45 and 100.")

See the Forum FAQ Page - [You must be registered and logged in to see this link.]

That post claims that the equation is:
Energy Used * Research Available / [NUMBER]

Its important to know the difference between
Research Used and Research Available, does anyone know which one it is?

Nachos, the wording in that formula is correct.

If you use 50 energy with 200 research in the bank you will earn twice (statistically) what you would earn by using 50 energy with 100 energy in the bank. In both cases you will burn 100 research, but your odds are much better with a higher research available.

This is why people advise you to wait to research until your research bar is full.

It might behoove you to use a diffrerent variable for research points and research output.

Two quick points:

Although the range is 900 to 2000, the average is around 1300, not 1450. If you wonder why you get more low rolls than high roles, this is the reason.

Energy and Research each increase by 1 in a sunspot.

Bridgeburners

Bridgeburners wrote:
Although the range is 900 to 2000, the average is around 1300, not 1450. If you wonder why you get more low rolls than high roles, this is the reason.
Bridgeburners

Doesn't a lower divisor would equal a higher average result?

I took some time to do the maths... it is another counter-intuitive result...

Value Reciprocal
900.00 0.001111111
920.00 0.001086957
940.00 0.00106383
960.00 0.001041667
980.00 0.001020408
1000.00 0.001
1020.00 0.000980392
1040.00 0.000961538
1060.00 0.000943396
1080.00 0.000925926
1100.00 0.000909091
1120.00 0.000892857
1140.00 0.000877193
1160.00 0.000862069
1180.00 0.000847458
1200.00 0.000833333
1220.00 0.000819672
1240.00 0.000806452
1260.00 0.000793651
1280.00 0.00078125
1300.00 0.000769231
1320.00 0.000757576
1340.00 0.000746269
1360.00 0.000735294
------------------ <--- average value of reciprocal
1380.00 0.000724638
1400.00 0.000714286
1420.00 0.000704225
1440.00 0.000694444
------------ <--- arithmetic mean
1460.00 0.000684932
1480.00 0.000675676
1500.00 0.000666667
1520.00 0.000657895
1540.00 0.000649351
1560.00 0.000641026
1580.00 0.000632911
1600.00 0.000625
1620.00 0.000617284
1640.00 0.000609756
1660.00 0.00060241
1680.00 0.000595238
1700.00 0.000588235
1720.00 0.000581395
1740.00 0.000574713
1760.00 0.000568182
1780.00 0.000561798
1800.00 0.000555556
1820.00 0.000549451
1840.00 0.000543478
1860.00 0.000537634
1880.00 0.000531915
1900.00 0.000526316
1920.00 0.000520833
1940.00 0.000515464
1960.00 0.000510204
1980.00 0.000505051
2000.00 0.0005
------------------------------
81200.00 0.040732581 <- Total
1450.00 0.000727368 <- Average
1374.820803 <- Reciprocal

So there are 24 above average rolls, and 32 below average rolls... The long term average result is higher than you might expect from the arithmetic mean, but it is occasional really good rolls that get you there.

Hope this makes some sense, if it doesn't then it doesn't affect the conclusion that AI > ET, merely the exact numbers you might get

Also your original assumption is the most efficient if you disregard time, I would like to run the numbers for researching every 20 minutes (which is much more time efficient, but delivers diminishing returns)

PapaNachos wrote:Also your original assumption is the most efficient if you disregard time, I would like to run the numbers for researching every 20 minutes (which is much more time efficient, but delivers diminishing returns)

You could spend 1 energy every 2 minutes for the same effect as all your energy every ( energy * 2 ) minutes. But you wouldn't get much leveling done then. (Adjust those numbers accordingly if you are notorious).

I disregarded the exact time as everything is 50% faster if you are notorious, but the end result is the same.

CrispyTina wrote:It might behoove you to use a diffrerent variable for research points and research output.

Good point, edit made. Now calling points gained 'stats' not 'research'.