Probability of Getting a New Scientist Each Tick?

[MyNameIsMatija]

So the thing that gives you more scientists also stops them from being taken, that's broken.

Good, good, forget I've said anything :D

[Goodwitch]

in the old system you could calculate how much gold was needed to reach the science goal you set for yourself or for the kingdom. If you couldn't reach your goal with gold you could supplement with occasional learns. TMs generally produce more gold so they could more easily reach their goals by investing, while attackers have less gold so attacked for science.
With the new system you have no control over when or if scientists arrive and as far as science goes attackers have a clear advantage because they have the opportunity to hit for scientists while tms cannot. The new system pretty much forces mages and thieves to play hybrid making them weaker as far as magic and thievery goes. coincidentally the strongest weapon they used to have against bottomfeeding slimebags. Or they can stay true tms and be sitting ducks.

I totally understand why kingdoms such as FS like this new science system. But I think for the average kingdom with average logs of 2 a day or less with no specific interest for the race to the top(so about 3/4 of the server) it has only disadvantages. And no rose colored glasses will fix that. I tried to find positive effects and there are a couple but none that even come close to evening out the drawbacks.

[Andurilas]

The old system favored top kingdoms significantly more than the new one does.

Its flaws now are primarily psychological. It could be remedied by weakening the effect per scientists but making them a little easier to acquire or the like.

[Persain]

Okay everyone has been guessing at the spawn rate. Im going to take my kd and only those people whose science is <12 hours old. Anyway given our current science then

1.28 2.27 3.26 4.26 5.26 6.25 7.25 8.25 9.25 10.25 11.24 12.24 13.24 14.23 15.22 16.21 17.21 18.21 19.21 20.20 21.20 22.20
Sum: 519

519-18*22=123 scientists gained.

For reference: however, we had 10 of those 22 do learns before the game was "Fixed" and they got reset to 23. This means that 50 of those "gained scientists" were actually gained during our oop wave. For a grand total of 73 gained scientists since the age began.

We did one fort stance of 72 hours, and since our science is <12 hours old im going to use Game start till Feb 12 yr 1 and determine that we've had 8.5 days of game time. This gives me a total of 8.5*24-72=132 game ticks.

22 provs with 132 game ticks gives us 2904 chances to gain scientist.

73/2904 =0.0251= 2.5% scientists spawn rate.

With nearly 3,000 observations the "randomness" should be washed out. If that rate holds steady we'll be looking at have only gained 60 sciencets per province in a 14 week age. Seems low, and unfortunately its been to long since i did my statistics to show how horribly unlikely this is if the research rate is supposed to be 3.5%.
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For what its worth the only way i can explain why our values are so low is that we learned oop and have 123 scientists gained. 123/2904=4.2%.....if scientists spawn rates per tick are lowered/raised compared to the expected value we are doing really well, would make sense since we got WAY ahead oop with learns.


edit......based on the learns my kd has done too the MAX possible learn rate is 3.5%. Which means a prov needs 29 scientists before abduct works (58 on a sage). Which means abduct is worthless for the first 18 days oop (2.5 weeks) on a normal prov and 66 days oop on a sage (or year 9 lol)

[Azureflames]

I've had 72 ticks of fort this age and have received 6 scientists naturally. No labs or rev. Puts me around 4.2% I believe? 9*24-2-72= 143 6/142 =~4.2%

For reference: however, we had 10 of those 22 do learns before the game was "Fixed" and they got reset to 23. This means that 50 of those "gained scientists" were actually gained during our oop wave. For a grand total of 73 gained scientists since the age began.

Assuming those 10 players only had 18 scientists each prior to abducting and did not generate any afterwards, before the adjustment. Seems unlikely.

[jmiedema]

Yea, bishop said we would have 80 total with no modifiers. 60 gained by eoa + 18 starting scientists is pretty close to your guesstimation, so it seems that it is currently working as designed.

[Persain]

I've had 72 ticks of fort this age and have received 6 scientists naturally. No labs or rev. Puts me around 4.2% I believe? 9*24-2-72= 143 6/142 =~4.2%

strip 5 scientist off the top 10 in my kd and you have a spread of 20-24 scientists. your results would be among the best we've seen. as for

Assuming those 10 players only had 18 scientists each prior to abducting and did not generate any afterwards, before the adjustment. Seems unlikely.

i'm personally on 0 gained all age expect the oop abducts, and as far as i know none of them gained any scientists before the "Fix." Even if they did its going to be a 3-4 scientists change and could be just as off as me saying 10 of them did learns and all landed on 23 (we had 19 people doing learns early age, 14 were before the fix, 1 of those was a guy who hit oor for 0 and one guy got up to 50+ scientists so he might have been "Fixed" to 24)

The POINT of what i posted was to show ~3000 data points to get a rate. if you personally are on 6 gained congrats thats 142 data point to add to the set. However 2904>>142 and over time i'd expect your results to come in line with mine. It looks as though the base rate is 2.5%. Unless there are "other" factors.

[MyNameIsMatija]

Nice to see someone is gathering data, thank you for your contribution. That said ~3000 ticks is not a big enough sample at all to draw conclusions with such certainty (we can say the spawn rate is probably not 1% or 5% but calling it exactly 2.5% over some other relatively close number is a bit of a stretch). That is something similar to one and a half unlucky provinces at EoA which can certainly happen (it will probably happen, there should be more KDs with higher results if the spawn rate is indeed higher though - we simply lack that data at the moment). Just look at the graphs for one province at EoA, your KD might have simply landed on a lower end of the graph just like my province ended up on the lower end of a shorter term distribution while someone else in my KD might be at a higher end. The lower the chance is the higher the sample size needs to be to draw any meaningful conclusions and for a ~3% probability your sample is relatively small or rather the results still vary quite a bit from the expected median. The larger the sample the closer we get to the median - this is a basic rule of mathematical probability, I'm not making this stuff up. Try flipping a fair coin and track the result for each toss. Compare the median after 5, 10, 20, 50, 100, 200... tosses (this is a really simple experiment that anyone with too much time on their hands can do).

[Azureflames]

The POINT of what i posted was to show ~3000 data points to get a rate. if you personally are on 6 gained congrats thats 142 data point to add to the set. However 2904>>142 and over time i'd expect your results to come in line with mine. It looks as though the base rate is 2.5%. Unless there are "other" factors.

Hm, well I have 2689 ticks with 83 scientists I could give you, but I can't confirm lab %s unfortunately so it is tainted. Probably 2300+ of the ticks had 0 labs. No rev though. My own province data is included in that. Still puts us under 3.1%, with possible overestimation of the base rate due to labs.

[Chanain]

Nice to see someone is gathering data, thank you for your contribution. That said ~3000 ticks is not a big enough sample at all to draw conclusions with such certainty (we can say the spawn rate is probably not 1% or 5% but calling it exactly 2.5% over some other relatively close number is a bit of a stretch). That is something similar to one and a half unlucky provinces at EoA which can certainly happen (it will probably happen, there should be more KDs with higher results if the spawn rate is indeed higher though - we simply lack that data at the moment). Just look at the graphs for one province at EoA, your KD might have simply landed on a lower end of the graph just like my province ended up on the lower end of a shorter term distribution while someone else in my KD might be at a higher end. The lower the chance is the higher the sample size needs to be to draw any meaningful conclusions and for a ~3% probability your sample is relatively small or rather the results still vary quite a bit from the expected median. The larger the sample the closer we get to the median - this is a basic rule of mathematical probability, I'm not making this stuff up. Try flipping a fair coin and track the result for each toss. Compare the median after 5, 10, 20, 50, 100, 200... tosses (this is a really simple experiment that anyone with too much time on their hands can do).

A 3000 sample actually isn't TOO bad.

I had been working on an assumption that the base was 3.5% or maybe 3%, but if Persain's numbers are right, those figures look pretty unlikely. At 3.5%, getting 73 or fewer spawns over that period would have a probability of about 0.15%. That's sufficiently remote that, if we believe Persain's figures, we can probably rule out 3.5% as a base.

3% is harder to rule out, though. At that base, there'd be more like a 6.6% chance of achieving Persain's results or fewer - significant enough that we really can't discount the possibility that Persain's experience is just 'unlucky'.

[Bart of Sparta]

What is this science stuff people speak so much of?

[MyNameIsMatija]

A 3000 sample actually isn't TOO bad.

I had been working on an assumption that the base was 3.5% or maybe 3%, but if Persain's numbers are right, those figures look pretty unlikely. At 3.5%, getting 73 or fewer spawns over that period would have a probability of about 0.15%. That's sufficiently remote that, if we believe Persain's figures, we can probably rule out 3.5% as a base.

3% is harder to rule out, though. At that base, there'd be more like a 6.6% chance of achieving Persain's results or fewer - significant enough that we really can't discount the possibility that Persain's experience is just 'unlucky'.

3.5%:
https://www.wolframalpha.com/input/?...5D+x%3D0+to+73
3%:
https://www.wolframalpha.com/input/?...5D+x%3D0+to+73
2.5%:
https://www.wolframalpha.com/input/?...5D+x%3D0+to+73

My apologies Persain, this is what happens when you just talk without running the math, still anything is possible.

[Azureflames]

3.5%:
https://www.wolframalpha.com/input/?...5D+x%3D0+to+73
3%:
https://www.wolframalpha.com/input/?...5D+x%3D0+to+73
2.5%:
https://www.wolframalpha.com/input/?...5D+x%3D0+to+73

My apologies Persain, this is what happens when you just talk without running the math, still anything is possible.

Are all 3 of those links the same?

[MyNameIsMatija]

Are all 3 of those links the same?

Not anymore.

[Azureflames]

i'm personally on 0 gained all age expect the oop abducts, and as far as i know none of them gained any scientists before the "Fix." Even if they did its going to be a 3-4 scientists change and could be just as off as me saying 10 of them did learns and all landed on 23 (we had 19 people doing learns early age, 14 were before the fix, 1 of those was a guy who hit oor for 0 and one guy got up to 50+ scientists so he might have been "Fixed" to 24)

Well, it might only be 3-4 for 10 people. But it could be more. For example, I got one on Jan11 and another on Jan16 during protection. My 3rd was on February 11th, right after the fix I think? I had multiple kd members who got 1-2 in protection and others who only recently got their first scientist. Anyway, my point is assuming your kingdom mates got 0 during protection could have an impact on your calculations. Or it could have none at all, but it's better to account for the scientists or exclude those ticks altogether.

From 19 people I have 7 gaining 9 scientists in protection. From 19 people I have 7 gaining 8 scientists from Feb1-Feb9(I'm not sure what date the 23adjustment happened but this one might be close), 3 of which gained 1 or more scientists in January. Anyway, my point is it's not unreasonable for you to be off by 10 or even 20 scientists.

I think it could be fair to say that 3% seems more probable than 3.5% but I'm not ready to believe 2.5% with the information presented.

Also, my +6 is tied for 2nd in my kingdom. The winner has +8 natural scientists with no rev or labs in the same time period of 142ticks.