Page 2 of 4 FirstFirst 1234 LastLast
Results 16 to 30 of 47

Thread: Science diminishing returns

  1. #16
    Forum Addict RattleHead's Avatar
    Join Date
    Feb 2013
    Posts
    1,144
    Quote Originally Posted by Dvorak View Post
    which formula is accurate up to 180 skill points?
    They diverge a lot at 180. (90 professors). one shows about 50% effect and the other 34%.

    I repeat, are you sure these are correct? I didn't do any math last age but I thought I was seeing a drop of 50% effectiveness as early as the 10th professor. That contrasts sharply with the formulas you've posted.
    The second one, where it mentions the 180 in the post along with the formula(I've edited my original post). I definitely can confirm 10 profs over does not result 50% effect. I made direct observations from my province, and KD mates at/around 30 profs over the cap, and the categories come out at about 70% of what they would be if those professors were giving full effects.

    @Wilmington I did not try to use the other in-game examples of diminishing gains, like you suggests, so its entirely possible.

    I'm just using simple excel trendline to make the curve... I would imagine its a cubic function... around the 180 point it has more or less leveled out, I expect with info that went beyond there we would see the rate of diminish pick up again.

    @yootohpeega I am not sure what you mean... every 2X = 1 Professor

  2. #17
    Post Fiend
    Join Date
    Jan 2015
    Posts
    184
    Yes, pleas share some data. One question I have that would clear a lot of things up is the 31st scientist in tools. The hard cap used to be 20, truncating the last scientist. If 31 profs is now more than 20, but lees than 20.46 it's figured on effect not scientists
    Last edited by Wilmington; 05-11-2017 at 05:06.

  3. #18
    Post Fiend
    Join Date
    Jan 2015
    Posts
    184
    I didn't even understand that the way I wrote it. 31 profs in tools would be 20.46 without the cap. Diminishing returns based on the number of scientists would have the 31st at full strength making the bonus 20.46. If it's based on the ratio of overage (what it would be/soft cap), it would be slightly less. Unfortunately, we don't get that accurate of info unless it diminishes enough to drop it below 20.45 and that's doubtful.

  4. #19
    Member
    Join Date
    Apr 2016
    Posts
    43
    Quote Originally Posted by RattleHead View Post
    @yootohpeega I am not sure what you mean...

    @RattleHead
    What I mean is, would you be kind enough to share with us your raw data?

  5. #20
    Member
    Join Date
    Nov 2008
    Posts
    40
    Thanks Rattlehead. You really... rattled... my conception of the science diminishing returns and I was definitely playing it wrong last age! Thanks for the works you've done on this. And thanks also for the work on the power rankings sheet. It's a very tricky and subjective thing to attempt, and the category breakdown is very instructive.

  6. #21
    Veteran
    Join Date
    Aug 2008
    Posts
    621
    Quote Originally Posted by RattleHead View Post

    @yootohpeega I am not sure what you mean... every 2X = 1 Professor

    You are using different X's. Yootohpeega's X is the professor where the additional benefit of that prof is 50% the full amount. Your X is the amount of skill points over the cap you are.

    It would be great if someone could translate the formula into something like a rule of thumb (which is what I think Yootohpeega was trying to get at). ie I need to decide how far over the cap to go. How many extra skill points can I have before the gain drops to (a) 75% of normal for that extra skill point (b) 50%, (c) 25% (d) 10%. Or something like that. A chart from 90% down to 10% at 10% intervals would be even more wonderful ;)

  7. #22
    Forum Addict RattleHead's Avatar
    Join Date
    Feb 2013
    Posts
    1,144
    I am not using # of scientists at all... and if you check this thread out; http://forums.utopia-game.com/showth...e-Skill-Points

    You can see where the caps actually are, and that they aren't necessarily related to "# Profs" ... such as Thievery the exact soft cap of which cannot be landed on with any combination of scientists, Or channeling which needs at least 1 Graduate because it has a decimal figure.

    @Wilmington the other thing is that the first couple points after the soft caps, effects are actually INCREASED for the first 3-4 points beyond that cap, and then start to diminish after that... You will see that my graphs start just above 100%!

    I think something like y = -1E-7 (x-175)^3+0.5 would be a rough approximation of the curve I am expecting to see.

    Here are some graphical representations, first my data with the trendline, and then one that shows a comparison of the trendline I've come to, and my approximation, just above here.



    The trendline based on my data is shown here, in green. You can see, in red, an example of what I am expecting to see if I had more data (I pulled the red function out of thin air more or less, there is no data supporting it)


    If someone wants my actual data, I prefer you to DM me so I can send it that way- I'm not just going to post a large series of numbers in this thread.
    Last edited by RattleHead; 05-11-2017 at 15:52.

  8. #23
    Veteran
    Join Date
    Aug 2008
    Posts
    621
    Thanks. This is incredibly useful.

    What are the axis? y axis I am guessing is the % (or fraction in 2nd graph) of the full amount of benefit received by each additional SP. X is the number of skill points you have over the number of SP needed to cap?

    Does this one curve apply to every category, even though they need a different number of skill points to soft cap?

    So If i am understanding all this correctly, you can go a very long way above the soft cap (something like 160-200 SP above the soft cap) and still be getting 50% of the normal benefit for each additional SP?
    Last edited by Chris121; 05-11-2017 at 16:23. Reason: sci system is too complicated to write about clearly without edits

  9. #24
    Forum Addict RattleHead's Avatar
    Join Date
    Feb 2013
    Posts
    1,144
    Yes, X is the number of SP over the required cap for a given category, and Y is the effectiveness of the category in question (not all your science). It also appears to me that, yes, one curve applies to all categories, but each category's diminish is calculated individually.

    I wouldn't look much beyond that 160-180 range where it gets flat, maybe it even stays flat beyond there but I don't have info... I think your understanding is a bit off on the value per additional SP, explanation below.

    I'll pull out a few numbers here;

    20 SP (10 Profs) over the cap - That category works at ~90% of what it would be, if science continued to accumulate at base rates
    40 SP (20 Profs) over the cap - ~80%
    60 SP (30 Profs) over the cap - ~70%
    90 SP (45 Profs) over the cap - ~60%
    150 SP (75 Profs) over the cap - ~50%

    It starts out much much like Wilmington has postulated, but you start to see the curve once you exceed ~30 profs over (I would call that roughly ~2x the cap).

    So, you hit soft cap for Alch, 60SP = +30% Income

    If you got up to 210SP (150 over the cap in Alch), the base would be;

    210SP * 0.5 Alch multiplier = 105 = +105% Income

    But your actual effect(according to my curve) would be ~+52.5% Income... So you have the first 60 SP giving you +30%, and then the next 150 SP only gives you +22.5%

    The base rate for Alchemy is 0.5 per SP, by the time you reach 150 SP, you are getting only (22.5/150=0.15) 0.15 effect per SP, which is actually 30% effect for each additional SP at that point.
    Last edited by RattleHead; 05-11-2017 at 16:44.

  10. #25
    Veteran
    Join Date
    Aug 2008
    Posts
    621
    Ah - so the y axis is showing me the % benefit of the category as a whole as compared to if there were no caps and it continued in a linear way. I had thought it was showing the % of the normal benefit from each additional SP beyond the cap), hence why

    So alchemy at 20 SP over the cap, according to your graph is about 85% of non-capped benefit. So non-capped would be +40% income, but capped is +34%, so an extra 0.2 benefit per SP (on average), as compared to the normal 0.5, ie only 40% of the normal benefit.

    So when Dvorak said "I was seeing a drop of 50% effectiveness as early as the 10th professor. That contrasts sharply with the formulas you've posted.", then this would be correct (and in fact underestimate the speed of drop off) if Dvorak's reference to 50% was to the effectiveness of each additional prof/SP rather than the category as a whole.

    Am I understanding this right now or still missing the point?

    If I've got it right, I think it would be helpful to have a graph that shows the % of normal benefit of each SP over the soft cap on the y axis (rather than the % of the benefit the whole category is giving). I have no idea how to do it but it must be possible to draw that graph from the data /formula we already have.

  11. #26
    Forum Addict RattleHead's Avatar
    Join Date
    Feb 2013
    Posts
    1,144
    Yep, I think you are onto it now!

    Ya I should be able to pull that info, it will be different for each category... but I do try to disclaim my laziness as often as I can :P

  12. #27
    Forum Addict RattleHead's Avatar
    Join Date
    Feb 2013
    Posts
    1,144
    So what I've come up with is this;

    Alchemy, Tools, Production, follow the same pattern (they have the same SP cap)...

    20 SP (10 Profs) over the cap - each SP is worth 60% of base
    40 SP (20 Profs) over the cap - each SP is worth 50% of base
    60 SP (30 Profs) over the cap - each SP is worth 40% of base
    90 SP (45 Profs) over the cap - each SP is worth 33% of base
    150 SP (75 Profs) over the cap - each additional SP is worth 30% of base

    Crime and Channeling are very similar to the above, within 1%, but they are not the same, even as each other, because their SP cap differs.

    Housing and Military you get this;

    20 SP (10 Profs) over the cap - each SP is worth 52.5% of base
    40 SP (20 Profs) over the cap - each SP is worth 42.5% of base
    60 SP (30 Profs) over the cap - each SP is worth 32.5% of base
    90 SP (45 Profs) over the cap - each SP is worth 26.7% of base
    150 SP (75 Profs) over the cap - each additional SP is worth 25% of base

    This table plots Alchemy, Tools, Production, Crime, and Channeling as the blue dots, and Housing and Military as the orange dots.

    X axis = # of SP over the cap
    Y axis = % effect of your SP in addition to the cap... roughly this tells you what your 'next' SP will be worth as a percent of the base SP in that category.



    These numbers are rough, as they are based on my rounded estimates in post #24

  13. #28
    Member
    Join Date
    Nov 2008
    Posts
    40
    Thank you Chris for digging deeper. This distinction is really important.

    Rattlehead and I were obviously were talking about different things and I misunderstood the formula. I was talking exactly as you say, % effect for the next professor, or you could say "marginal scientist effect".

    I wonder then, if you did a curve-fit would the curve come out to a more... simple formula? if the final "y" variable was marginal scientist effectiveness instead of total effectiveness of all scientists?

  14. #29
    Post Fiend
    Join Date
    Jan 2015
    Posts
    184
    y=(x-1)/(x+1) +1 x>1

    y*cap=effect
    x= raw total/cap (effect, not scientists)

    This would give a limit of 2 times the cap

    yx=(x-1)/(x+1) +1 would give your curve

    Actually, I'm thinking it might be just (x-1)/x +1
    Last edited by Wilmington; 05-11-2017 at 22:04.

  15. #30
    Forum Addict RattleHead's Avatar
    Join Date
    Feb 2013
    Posts
    1,144
    should be negative, I think?

    y = -[(x-1)/(x+1)]+1 (oic urs is yx= :P nvvvm)

    or ya your final option looks like the right shape as well... im not sure if this lines up quite with my observations though, its quite possible I'm missing something in your description though, my mind is currently in an altered state
    Last edited by RattleHead; 05-11-2017 at 22:14. Reason: yx

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •