This is a live data image from my current game (via google docs), so the chart will update as I play each turn. Just hit refresh to see the current situation.



Colored horizontal bars show how much RP each Tech Level costs

Shaded RP Sum #1 is the accumulated total RP for game #1

RP/Turn is for each game (#1, #2)









I created a mathematical model to predict RP/Turn, but too many factors can change the rate. Access to colonizable worlds, developing research technology, harvesting research bonus resources. The scores rapidly become chaotic and unpredictable.



My model of research point accumulation was that for any given turn number t, your research points/turn will be approximately:



Rp/turn = 0.00156951 t^3 -0.112558 t^2+3.27027 t +3.77175



Actual vs Predicted shows how the RP/turn diverge in unpredictable ways. The red dataset was used to generate the model, and the blue dataset represents a completely unrelated game, and thus the efficacy of the model's predictive power.





Conclusion

It's reasonable to say this data is not amenable to a polynomial fit. This is not a bad thing, because it means strategy and luck are more important than progress.

Notes:

On turn 19, I added +3 Wit to a hero. On turn 20 he was contributing 0.4 Research to the planet. If we consider rounding error, it may be that Wit is only 1/10 of a research point.



On turn 21, I added another +3 Wit to a hero. This took him from 12 to 15 Wit. Initially he was contributing 2.6 RP, but the additional wit bumped him to 3.3 RP from hero. So the initial guess of a direct relationship to RPs was incorrect.



As a second guess, it might be a contribution per population point. That planet has a population of 4. I'll recheck at next population increase.



Turn 23, lowered tax rate to 25% to boost population growth. It changed the current RP income from 29 to 34. Happy workers are productive workers.



Turn 25, population increased from 4 to 5 on Homeworld. The Hero bonus (Wit:15) also increased to 3.9. This seems to confirm a per population bonus for Wit. Testing this theory: 3.9/15=0.26 RP/pop. If this is the way it is, then the next population increase (around turn 35) should make the hero bonus about 4.1.



Turn 31, launching a colony ship reduced population from 5 back down to 4. But the Hero bonus has gone up, from 3.9 to 5.1. So I'm flummoxed. The only difference I see is that I just did an in-system colonization, so perhaps the redistribution of population had some effect.



Turn 41, civilization infected by the Rapt0r virus, decimating my population. Major drop in productivity.



Turn 48, There seem to be turn-to-turn fluctuations in the RP income. It might have to do with population in transit in colony ships.



Turn 64, Tech buildings starting to complete, and jump up RP production.



Turn 66, War with an adjacent neighbor (Hissho) has turned all my efforts to a war machine. With only two main production planets, I'm fighting a holding action until I get a better economy.



Turn 107, Colonization phase is concluded, all surrounding worlds colonized. On to Forcible Colonization/Repurposement.



Turn 130, I have taken a clear lead over all empires, and will win this game easily. Unless there's a lose condition for being too far in the red financially. Score is: Me-5490, Sophon-4498, United Empire-4295, Cravers-3825, Horatio-3367, Hishio-1702.



Turn 150, begun terraforming operations.



Turn 158, Wiped out Hisshio.

Wit provides a multiplicative bonus to the research output of the system to which the hero is assigned. What I'm not entirely clear on is the way in which multiple multiplicative bonuses are applied (I believe they are additive, but some seem to be multiplied).

...And game over. Evidently someone else won by economic victory.







[Whineyloserrant]

My balance was about minus 45k at game end, because I was losing 4k dust/turn to some mysterious diplomatic reason that I don't understand.[/rant]

Started a second game. Skipped one start, because it was long strings and one homeworld. Second start had four medium strings and three homeworld planets, so I took it. I toyed with the idea of disabling assorted victory conditions, but thought that would be cheating. So the only change to starting conditions from default is using the Disc galaxy instead of the 2-arm spiral.



Turn 1, started as United Empire vs one of every other race. Began in forth place points wise. Jacked the tax up to hire a Hero next turn.



Turn 7, Spiked tax again, to hire a second hero as soon as my colonizer lands.



Turn 8, Reduced taxes to increase birth rates on both systems. Third hero isn't a planetary improvement guy, so I'll hold off on that for now.



Turn 9, After examining the food mouseover, I surmise that there is no need for more food than your system consumes. Population seems to consume 2 food/pop. Don't know if food is exported to other systems. Switching build order to industrial.



Turn 18, population on homeworld maxed out, so I increased the tax rate until just before my other planet's pop growth slowed. Discovered along the way that the most money I could get in tax was not at one end or the other, but a balance point in between (currently 45%).



Turn 20, my first hero finally leveled up enough to opt for the Administrator's Civil Engineering option. +25 production? Best perk ever. Bee-line for that every time. Also modified colonizer blueprint to include the starting +2 engine, and began construction.



Turn 21, began construction of a Suicide Scout, with the express mission of getting in a tangle with the nearby Cravers, so I can find out if they are going missile tech or sticking with guns. If they have missiles then they have Tritanium-70.



Turn 23, ongoing tax tweaking to maintain max population growth and yet remain in the black. Currently ranked last place score-wise; I wish I could see some details on that.



Turn 25, damn pirates ganked my colonizer en route, and then blockaded my homeworld; damn you, pirates, damn you to hell! Constructing modified defender.



Turn 29, Colonized a Titatium-70 world, and a couple things came up. First, it was not connected by a chain of colonized planets back to Homeworld, and yet I was able to queue up a missile ship on homeworld. Not only that, but homeworld was blockaded by pirates at the time, so that also does not apply. So the definition of the "linked systems" requirement may be limited to areas not cut off by other race's planets. Also, deployed defender and rid myself of those pesky pirates.



Turn 30, my Suicide Scout has provided the intel it was built for. The Cravers have gone Guns/Flak, which means they don't have Titanium-70 yet. Good for me. My next research project, Beam/Deflector Destroyers.



Turn 31, lost another colonizer to pirates. New SOP: Station a defender before sending a colonizer. Had to fire the Director of Colonization Efforts for his obvious lack of foresight. The people must be protected.



Turn 39, new tax balancing metric necessary; two planets are cranking out colonizers, and my objective now is to make sure the population grows faster than colonizers are produced. Also High priority is securing the Pullox system, because I need Hyperium for lasers. I'm currently ranked first place, although I don't know why.



Turn 46, the border regions between my empire and the two neighboring empires is heavily populated with systems that are exclusively Lava/Barren. Tech for colonizing that is still a dozen turns off, but I've put aside further weapon research in order to tech up and race for those worlds.



Turn 49, pirates lingering over my solitary Titanium-70 mine, prevented constructions across my empire. Fortunately I had ships en route, and dispatched them with extreme prejudice. Also, some of my new colonies have yet to fill up their best planet, and would take 5+ turns to generate a warship, so I've set them to mine dust.



Turn 53, the dust mining is paying off, I've been able to reduce tax to 25% for a fervent 81% happiness. Most systems have growth rates of 4 turns or less. But all is not well in the Endless Space; I hold the lead with a score of 525 but the Cravers are breathing down my neck with a score of 508. I will have to beat them down soon.



Turn 63, cruiser tech and fleet cap 7, let the invasion begin. I'm really beginning to feel the squeeze of being boxed in on all sides. It's cramping my style.



Turn 75, first Craver outpost (6 pop) has fallen, bringing our scores to a much more comfortable 1235 to 732.



Turn 81, after taking another Craver outpost (8 pop) they finally declared war. Good for them! I've been itching for them to open their borders to my invasion fleets. Incoming.



Turn 90, the slowly crumbling Craver empire is bringing me a much needed boost to my FIDS. Their big mistake was long range expansion with no police force to protect them.



Turn 96, Homeworld's population is maxxed, so began pumping out colonizers to redistribute population to the various systems that still have colonizable worlds.



Turn 101, In a desperate bid for survival, the Cravers launch a stream of colonists to very distant stars, 4+ jumps away. (Or maybe it's just their way). But I send military taskmaster fleets to follow them and subjugate the new colonies as soon as they settle. Hey, free population points.



Turn 111, Cravers eliminated. New target:Hisshio, for which I've been building troops up along their borders. Long range exploration reveals there is a huge swath of well-connected completely empty systems -- 8~12 of them -- on the far side of Hisshio. Why they haven't been colonized by now is anyone's guess.



...Aaaannnd game over, due to bug where the game just hangs in "standby" mode. I'm done with this. [sometimelater] ...Wow, Someone told me how to edit save files to prevent economic victory, so I did that to this game, and now the Carvers aren't listed as dead (even though there aren't any Carvers) and the game is working again.



Turn 114, mapped half the galaxy



Turn 125, a discovery: Ships in the hanger are lost if you lose the star system, and then retake it later. Makes sense.



Turn 134, researched Personal Shielding, which gave me monopoly of Mundane Artifacts, providing a huge research bump of about 30%.