Probability of Getting a New Scientist Each Tick?

[MyNameIsMatija]

Was this posted somewhere?

If not, this is what I came up with...
x = 2500 (number of tries = assumed average number of ticks per age)
r = 82 (most probable number of successes in the given distribution = starting amount of scientists subtracted from the average number of scientists per age declared by Bishop = 100-18)

p = r / x (probability of getting a new scientist each tick)
The formula is explained by the end of this video (if anyone cares):

This puts p at 3.28%.

The formula and the logic should be sound, what I don't know is what kind of distribution parameters the developers actually used to calc. it (for example 2500 being the average number of ticks per age they used to calc. this is just a somewhat educated guess on my part, could have taken it to be 2400 or in other words 100 days or anything similar).

[drkzeraga]

I hope they used something more like Dota's presudeo random number generator:
http://dota2.gamepedia.com/Pseudo-random_distribution

IE you are more likely to get a scientist if you haven't gotten one and the chance reset once you get it.

[MyNameIsMatija]

Doesn't seem that way so far to me, it seems "truly random".

[MyNameIsMatija]

If we assume the calc. correct (should be roughly correct in theory) it's easy to calc. some other stuff like:

Chance of NOT getting a new scientist each real day (24 ticks): 45%
Chance of getting at least one scientist each real day (24 ticks): 55%

So yeah, if you haven't gotten a new scientist during protection, don't lose your mind over it, according to this almost a half of the players will not (or is protection 25 ticks? Well you get what I mean).

[CannaWhoopazz]

That video is a very silly way to calculate out the odds. Or, the explanation is much more complex than it needs to be IMO.

.calc 82/2500 (total scientists/total ticks) = 0.0328

Percent chance to get a scientist each tick: 3.28%


Edit: In fact, it was so unnecessarily complex of an explanation I didn't even realize my formula was the exact same as the formula they were explaining.

[MyNameIsMatija]

You just repeated it... I don't understand. It does seem trivial but I wasn't sure that's how it works before checking how the distribution actually works... It's not actually the number of scientists you will get, it's the most likely outcome...

[drkzeraga]

Well I got some good news guys.
I wrote a program that calculate the number of scientists everyone is going to get.

Using the following variables:
- Number of players: 3600
- Number of ticks: 2500
- Spawn chance: 3.28%

I got the following results:
- Mean: 99
- Median: 100
- Standard Deviation: 9.6898
- 5th Percentile: 84
- 95th Percentile: 116

So basically nearly everyone is going to get at least 80 scientist, with the majority falling between the 90 - 108 range.
The codes are here if you wish to tweak the values and test yourself: http://dumptext.com/KwlORMwP

[MyNameIsMatija]

Yeah thanks for that, just keep in mind 3.28% is a result for unconfirmed parameters.

[CannaWhoopazz]

I think 3.28% is an ugly percent, and I would expect them to have used 3.5% instead, assuming a ~14 week age (comes out to 3.48% at exactly 14 weeks)

[MyNameIsMatija]

Yeah makes sense, don't know why I used 2500, 2350 or so makes more sense, so does 3.5%.

[MyNameIsMatija]

That video is a very silly way to calculate out the odds. Or, the explanation is much more complex than it needs to be IMO.

.calc 82/2500 (total scientists/total ticks) = 0.0328

Percent chance to get a scientist each tick: 3.28%


Edit: In fact, it was so unnecessarily complex of an explanation I didn't even realize my formula was the exact same as the formula they were explaining.

It's maths. It's not "your formula". You just got the same result by dividing two numbers. That video is actually really simplified since it doesn't prove the expressions used, in other words it doesn't get to them by any means of mathematical deduction, there's nothing that proves your calculus to be correct without this background, it's just dividing two numbers essentially and the result happens to be correct since, you said it yourself, you don't actually understand the distribution well.

Using a formula that the video explains you can get the actual variance with some simple calculus and you don't have to run a program to "bruteforce" the result.

[tiggis]

There is no such thing as random.
It does not exist in reality.

the 3.28% is most likely very close.

[Caelum]

There is no such thing as random.
It does not exist in reality.

Oh stop it.

[MyNameIsMatija]

I plotted the distribution curve in WolframAlpha:

Image:
https://www.photobox.co.uk/my/photo/...id=21298955082
WolframAlpha:
https://www.wolframalpha.com/input/?...3D1500+to+3500

x-axis represents a number of ticks and y-axis is the probability of reaching 100 scientists in the given amount of ticks at 3.5% tickly spawn probability


As you can see some lucky people will likely be at 100 scientists by tick 1700 while some might need 3000 ticks for that (that's higher than the usual age duration) at 3.5% probability. This is without taking other mods in account of course (buildings, abductions etc.)

[MyNameIsMatija]

Here's a full 25 prov KD-wide version of the curve, it's less volatile than a single prov version one:
https://www.wolframalpha.com/input/?...50000+to+67500

A large majority of the results fall into the 2150-2550 ticks range, in other words it would very likely take all full KDs this many ticks to reach 2500 scientists if we disregard other game dynamics. Some provs will end up on more than 100 scientists, maybe even breaking the cap, while some will be left a little behind.