You've brought up a good point though, and I should go ahead and make an attempt to test if it truly does happen 25% of the time, each turn.
well, despite the sour taste that's worked its way into this thread, i'd thought about doing this myself. thankfully i have a firm enough grasp on statistics to offer some insight. 200 is generally considered statistically valid sample (standard error of 5%), at least in population studies . since we're only trying to figure out how frequently creativity works, this means we can test 200 game turns (or just under 4 game years), rather than 200 games.
to establish a better sense of the correlation between luck bonus and the frequency it triggers, it'd be best to test it at multiple bonus levels, i.e. a 200-turn game with a 0% creativity bonus (to establish a base line for comparison), a 200-turn game with a 25% creativity bonus, a 200-turn game with a 50% bonus, etc.
if we assume that there's no other factors involved in the creativity tigger other than your actual bonus, then there would be no need to impose other controls on the experiment. does the game actually tell you when creativity has worked? (even when i have played with it, i've never noticed; i usually just ignore most pop-ups in the game if i can't disable them). continuing on the assumption that creativity works
in vacuo, and we have a reliable method to tell when it's been triggered, the only data we'd need to collect is the game date each time creativity triggers.
however, i'm not sure any of us know for sure that creativity in fact does work
in vacuo. it could possibly be tied to other variables in the game, which is why if i were going ot set this test up myself, i'd probably create a custom map to do it (thus you'd have the same starting conditions in every game. i'd also probably play in cheat mode, just to better control any pesky AI who'd want to kill me. game events could present an annoyance; ideally i'd run these tests through without re-loading the game at all, but i'd probably err on the side of re-loading if an event occured that could potentially interfere with results (even with mega events disabled, some of those minor events could potentially have an effect).
if the creativity trigger is tied to another game variable, it seems to me most likely that it'd be tied to research. i'd want to play 6 games in total: three games at 0/25/50% creativity with X amount of research being done every turn, and a three games at 0/25/50% with 2x research being done (which could be accomplished relatively easy running in cheat mode).
perhaps the best way to monitor the effect of creativity without recording lots of data every turn would be under these conditions:
create a custom map with 1 planet for yourself. quality doesn't matter. on your first turn, fill that planet with some sort of research center and complete them in that turn by using the ctrl+J cheat. it's probably a good idea to leave 3 tiles empty (you're likely to get research bonus tiles in at least one of the various test games - best to simply leave them empty).
create a custom mod with a unique tech tree. delete every tech in the game, and replace them with a linear tech sequence called "test bed tech X" where X is the number in the sequence. make them all cost the same thing. i think this would provide the easiest way to keep track of how many techs get completed. i'd still write down the game date every time a tech was completed. i'd also probably delete the various ship modules in this set up, so that the AI couldn't build anything.
disable all victory conditions. since the AI won't be able to build anything, you can basically play the game for as long as you have techs.
...some of that might not make sense if you lack a background in statistics. considering that it's new year's eve, i'm not about to jump into a set of tests like this, and i probably won't (as i already said, i don't have a problem out-teching the AI... the best way to complete techs quickly is to build more research labs--the all-labs approach is great for this).
but if you really want to be certain of how creativity works, this would be the most comprehensive way to get hard data, and possibly even regress its algorithm.
(PS: in case anyone questions my background is statistics or research design, i'm trained as a sociologist. i've conducted both demographies and ethnographies, and research design was a significant topic i focused on while i was a student).