PLEASE NOTE WHILE MUCH OF THE INFORMATION IN HERE IS MORE OR LESS CORRECT, THERE IS A NEW, MUCH MORE ACCURATE FORMULA EXPAINED HERE: https://www.torn.com/forums.php#/p=threads&f=61&t=16182535&b=0&a=0

THIS POST IS NO LONGER MAINTAINED.


The Calculator can be found: HERE
Explanation of the new formula can be found: HERE

NOTE (As of 5/27/2020)

In coordination with the Journal of Torn Sciences, specifically Kivou, Prezze, Pyrit and Proxima (not to leave anyone out!), I have been working on a new formula. I have added this new estimate alongside my old estimate. At this time I will not be publishing the formula or giving any explanation as we are not ready for that yet, BUT, please let me know if the you ever get an estimated SINGLE train value outside of the shown margin of acceptable error.

I did my best to give an estimate for multiple trains but these will never be perfect as happy loss is slightly random.

Thanks.

For the rest of you math nerds that wants to understand how training gains actually works, continue reading:

In an attempt to explain how I believe gains are determined, I'll break it down into the components that go into it. Training is affected by several things:

Which stat you train

The statistic that you are training matters for two reasons:

• Most gyms have different multipliers (Gym Dots) for different stats
• Different Stats will normally have different totals, which is one of the primary factors in determining how much you gain

The total of the stat you are about to train

There is a linear relationship between the total of the statistic being trained and the amount you will gain. This has the general format seen below:

Gain = X * (Stat Total) + Y

As will be explained below both the variable part of this formula (X) and the "constant" part of the formula (Y) are both actually determined (in part) by your happiness level (which will be explained below). The general result of this is that at low statistic levels, a doubling of your statistic total will have only a very small effect on your total gains, where as at higher stat levels, a doubling of the statistic will roughly double your gains.

It is important to note that your overall stat total, or the total of the stats that you are not training, do not appear to have any effect whatsoever on your training total (i.e. if all of your stats are at 100k, a strength train will be identical to someone who has 100k strength and 50m in everything else, all else held constant).

Also (this is important as well!) there is a "stat cap" that occurs at 50 million in a given statistic. This does not mean that you can't gain statistics past 50 million, it just means that gains after 50 million in a given statistic will be constant (assuming all other variables are held constant). In other words - even if you have 1 billion in a statistic, the formula still uses 50 million.

Happiness

Happiness is the other primary variable in determining training gains. The first way happiness affects your gains is by modifying the multiplier. Again, the basic formula is:

Gain = X * (Stat Total) + Y

Happiness affects the value of X (and Y - more on that below). It does this in such a way that at very low values of happy, increases will have a large effect on the multiplier, while at higher levels of happy, the same increase will have a much smaller effect. This is because the formula for this portion is logarithmic, of the form a*ln(HAPPY+b)+c, where a, b & c are random constants (read about natural logs here, for the math inclined). The "b" constant is added in because otherwise this part of the formula goes negative if happy is less than 1. At any rate - if you're ever still reading this after all that math mumbo jumbo, due to the logarithmic nature of the formula, increases in happiness have diminishing returns. If you increase your happiness from 1000 to 2000, this will have a much larger effect than increasing your happiness from 21000 to 22000.

Some people will tell you that the effect of happiness is the same at low stats as it is at high stats - that it is a constant. THIS IS NOT TRUE. The more stats you have (up to the cap), the more happiness will benefit you in absolute terms, but as a percentage increase, it will be less and less due to the next part of the equation, which is the "constant" Y in the formula above.

The format of this constant portion of the formula is actually d*(HAPPY+b) + e, again where d & e are random constants and b is the same "adder" to happy as in the other portion of the formula. This is the part of the formula that doesn't care what statistic levels you have - here happiness has the same effect at 50 million as it does at 380, and because of this, happiness totally dominates the formula at low statistics levels. The end result?

• At low stat levels (lets call it <100k), increases in stats have a fairly minimal affect on your gains. At these levels a doubling of your statistic might only give you 10% more gains, or less. Increases in happy, however, have a HUGE effect (an increase from 100 to 5000 happy might give you 10 times or more improvements)
  
• At higher stat levels, a doubling of stats will approximately double your gains. Increases in happy will help, but the effect is much smaller (increasing from 100 to 5000 happy at 1 million in a stat is about a 30% increase in gains
  

The Gym You Train In

When you go to look at a gym, you will see that each statistic has a bar next to it. The value of this bar is what some people call the "Gym Dots". There are two ways to determine what exactly this value is - one is you can right click on the bar and "Inspect Element" and see what percentage it says (i.e. 36% of 10 bars = 0.36*10 = 3.6 dots). The other is to use www.tornstats.com/ and click on the "update your goals" - you can then pick your gym and see how many dots the gym has for each of a given statistic on the right side.

The important thing to know about these values is that it is a direct multiplier on the formula per energy trained, NOT per train. If you train once in a gym that has 4.2 dots and takes 10 energy vs. twice in a gym that has 4 dots and takes 5 energy per train, your gains will approximately 4.2/4 = 1.05 times better, because you spent 10 energy at each gym, and the one gym had a gym dot value that was 5% higher.

It is important to note that training in a 6 dot 10 energy gym will not result in exactly twice the gains of a 3 dot 5 energy gym, for two reasons - one, each train removes some happiness, which then effects the next train, and two, each train adds statistics, which then effects the next train - however these effects are typically so small than the next result will be very close to proportional with the gym dots (in this example, twice as much).

So in summary, it multiplies the basic formula as follows:

(Gym Dots) * (Energy per Train) * (Unmodified Gains) = Total Gains (before other modifications)

Training Multipliers

There are various training bonuses that you can get from your faction, from education, from items, and from your property. They directly multiply what your training would be if you had no bonuses. These can be found under your "personal perks" in your home/index page. As far as I can tell, these bonuses are multiplicative - in other words, you multiply each category of benefit to get your overall bonus. For example:

Property: +2% to all gym gains

Faction: +10% to strength gym gains

Education: +2% to strength gym gains

Book: +30% to strength gym gains

Total = (1.02)*(1.10)*(1.02)*(1.30)= 1.487, or an overall bonus of (1.487-1)*100 = 48.7%

Note that (again, best I can tell), you do NOT add them together. If you did, in the above case, the total would be 44% (and the formula would underestimate your true gains).

So, you take what your gains would be if you had no training multipliers, and (in this case), you would increase it by 48.7%:

Total Gains = 1.487 * (Training gains if you had no multipliers)

Training One at a Time vs. All your energy at once

Contrary to what some people will tell you, there is no difference at all in clicking trains one at a time to spend all your energy (such as 5 energy trains 30 times) or spending all your energy at once (150 energy in one go, for example). This has been confirmed by Chedburn in the following thread:

https://www.torn.com/forums.php#!p=threads&f=19&t=15961663

So unless you enjoy clicking train a lot more than you need to... go ahead and train it all at once.

Formula Summary

In summary, the general format of the training formula is as follows:

(Modifiers)*(Gym Dots)*(Energy Per Train)*[ (a*ln(Happy+b)+c) * (Stat Total) + d*(Happy+b) + e ]

Where a,b,c & d are constants, estimated values below:

a = 3.480061091 x 10^-7

b = 250

c = 3.091619094 x 10^-6

d = 6.82775184551527 x 10^-5

e = -0.0301431777

Example Data - How Happiness Changes Gains at Varying Stat Levels

Happy	Stat Gain @ 1k stats	Stat Gain @ 10k stats	Stat Gain @ 100k stats	Stat Gain @ 1M stats	Stat Gain @ 50M Stats
1	1	2	24	247	12356
200	1	3.5	33	325	16237
1000	4	7	39	356	17645
5000	21	25	59	404	19187
25000	107	110	148	523	20931
99999	429	432	473	876	22795

Happy	Percent Gain Over 1 Happy @ 1k stats	Percent Gain Over 1 Happy @ 10k stats	Percent Gain Over 1 Happy @ 100k stats	Percent Gain Over 1 Happy @ 1M stats	Percent Gain Over 1 Happy @ 50M Stats
200	0.00%	75.00%	37.50%	31.58%	31.41%
1000	300.00%	250.00%	62.50%	44.13%	42.81%
5000	2000.00%	1150.00%	145.83%	63.56%	55.28%
25000	10600.00%	5400.00%	516.67%	111.74%	69.40%
99999	42800.00%	21500.00%	1870.83%	254.66%	84.49%

Other Cool Charts

Using this formula, you can do cool things, like figure out the point at which premium training isn't worth it anymore... Which as it turns out is around 400k stat total (although it probably stops being worth the money much earlier than that, for all us non-restarts/multis, anyway)





Or you can figure out whether it's more beneficial to use an LSD or a Ecstasy when your starting out and don't have the money for xanax - it looks like below approximately 125k, your gains will be better using an ecstasy (note also that ecstasy has a lower cooldown, which makes it doubly good to take at low stat levels)







Or you can show just how much worse it sucks to be drug free:



TL;DR

Training gains increase in a linear fashion with totals in a give statistic.

Happy has both a constant portion that is the same no matter your stats and a variable portion that does increase with stats.

Increasing happiness has diminishing returns the higher the happy level gets

Happiness dominates your stat gains at very low stat levels and has a much more subdued effect at high stat levels.

Yes, SSL really is that much worse for stat gains than using Xanax.

You should stop doing premium trains before 400k in a given stat.

Try this spreadsheet HERE to figure out what your gains will be

If you want a better idea of how to actually APPLY all of this, check out one of the other great tutorials in this forum, such as Throe's guide to getting started strong here.

[i][color=#333333][size=12][color=#333333][size=12][b]NOTE: If you're wondering why your happy jumps aren't as productive anymore, it's because I noticed an error in how they were working and reported it here and here. Chedburn corrected it per this update. He said "Fixed minor discrepancy training stats multiple times at once", but it was really a fairly major error! Sorry!

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