Charis
Realms Beyond
Thanks for all your work running this game, cracker!
Good job to Jaxom and the others who finished the race - I think we'll all learn some nice tips from those reports - tnx Zenga for those links, I look forward to reading them
I was glad to see the Excel spreadsheet available, there was some analysis I was quite interested in doing. I primarily wanted to test to see how close the QSC points were to a pure exponential function. To my surprise, VERY close. I took all the scores, took their logs, then did linear regressions. I was expecting it to be a "straight line" plot vs the turn number, but a much better fit was obtained using the actual year. (Firaxis did a nice job with the decreasing years per turn, at least in this regard )
A second thing I wanted to check was the settler effect. (Cracker's 3400BC pop). I figured one of three things would happen: i) his curve alone would fail to be a straight line, but rather one that decreased with time, ii) he would have a slope very similar to all of ours, with a shift in the intercept, iii) there would still be a straight line, with an increased slope. Does that make sense? I know math junkies are following me...
Here's the plot, of Log(QSC score) vs Year
The result was #3, not really what I expected
If you extrapolate cracker's "terminal" slope back to the origin, it hits 4000BC +/- 50 years. Also, there is a "bump" in his score post-3400BC, but in fact the terminal slope is quite strong, and not monotonically decreasing. How much of an increase from the settler is hard to tell, without cracker replaying w/o it, or by assuming his score would have been 'average' - a poor assumption)
Regarding the games in general, the slopes are as follows:
(These use final year log-QSC and starting point, not full linear regressions - time was short)
(Overall is (ln(qsc_170)-ln(qsc_4000)) / (4000-170) * 1000 -- avg was 1.096
The terminal one uses 1525BC to 170BC instead)
Conclusions -
i) the QSC score may be accurately represented by a monoexponential in year
ii) an early settler pop increases your growth coefficient
iii) a good player can sustain this higher growth rate
(Corollary A - cracker played extremely well and took great
advantage of his good start - no surprise there)
iv) some of the choices for opening strategy don't show an
increase in growth rate until much later, nearly 0AD
(These show up as lines on the plot that start to shoot up at the end, and as higher 'terminal' slopes)
I'll post my final launch story and report tonight - I can't for the life of me remember the year!
Charis
Good job to Jaxom and the others who finished the race - I think we'll all learn some nice tips from those reports - tnx Zenga for those links, I look forward to reading them
I was glad to see the Excel spreadsheet available, there was some analysis I was quite interested in doing. I primarily wanted to test to see how close the QSC points were to a pure exponential function. To my surprise, VERY close. I took all the scores, took their logs, then did linear regressions. I was expecting it to be a "straight line" plot vs the turn number, but a much better fit was obtained using the actual year. (Firaxis did a nice job with the decreasing years per turn, at least in this regard )
A second thing I wanted to check was the settler effect. (Cracker's 3400BC pop). I figured one of three things would happen: i) his curve alone would fail to be a straight line, but rather one that decreased with time, ii) he would have a slope very similar to all of ours, with a shift in the intercept, iii) there would still be a straight line, with an increased slope. Does that make sense? I know math junkies are following me...
Here's the plot, of Log(QSC score) vs Year
The result was #3, not really what I expected
If you extrapolate cracker's "terminal" slope back to the origin, it hits 4000BC +/- 50 years. Also, there is a "bump" in his score post-3400BC, but in fact the terminal slope is quite strong, and not monotonically decreasing. How much of an increase from the settler is hard to tell, without cracker replaying w/o it, or by assuming his score would have been 'average' - a poor assumption)
Regarding the games in general, the slopes are as follows:
(These use final year log-QSC and starting point, not full linear regressions - time was short)
Code:
Player Overall Terminal
cracker 1.230 1.154
charis 1.115 1.300
zenga 1.124 1.318
lee 1.093 1.144
meldor 1.047 1.193
jaxom 1.132 1.295
steve 1.084 1.121
borea 1.091 1.258
sjf 1.173 1.421
hotrod 1.105 1.190
stwils 0.822 0.869
swift 1.151 1.192
theos 1.081 1.403
The terminal one uses 1525BC to 170BC instead)
Conclusions -
i) the QSC score may be accurately represented by a monoexponential in year
ii) an early settler pop increases your growth coefficient
iii) a good player can sustain this higher growth rate
(Corollary A - cracker played extremely well and took great
advantage of his good start - no surprise there)
iv) some of the choices for opening strategy don't show an
increase in growth rate until much later, nearly 0AD
(These show up as lines on the plot that start to shoot up at the end, and as higher 'terminal' slopes)
I'll post my final launch story and report tonight - I can't for the life of me remember the year!
Charis