estimating the final score in milking phase -- the N-factor

[Karl_t_great]

My milking lesson is giving me strange results. I started following my per turn score after comparing my result so far with Bartleby, and realizing that I was going to get a far better score than expected.

Score calculation

The scoring works by averaging your per-turn scores throughout the game. For each turn a (hidden) per-turn score is calculated as:

(Territory + HappyCitizens*2 + ContentCitizens + Specialists) * Difficulty

The total of all your per-turn scores is divided by the number of turns played so far to get your actual game score. I.e. your actual score is the average of your per-turn scores.

According to this TurnScoreDelta*TurnNumber should give me an approximation of the internal per-turn score (iPTSa).
Besides fuctuations caused by rounding/truncation this figure should remain pretty much the same when in milking phase, rigth ?

The final score could be estimated:
Score= CurrentScore+ iPTSa* Sum(1/N)
where N is turn number, and the sum is taken over remaining turns.


To get rid of the fluctuation I calculated 10 turn averages of iPTSa getting:
turn#, iPTSa
350 54915
360 55376 (I reached full pop around here)
370 55208
380 55086
390 54103
400 52887
410 51538
420 50095
430 48830
440 47686
450 46680

So the iPTSa is declining on rate of about 100/turn, or 2,5 % /10 turns. The only viable conclusion is that the N-factor is more progressive than 1/N, maybe based on years instead of turn number.

Now fellow HOFfers, is this old news, enyone got the right formula for the N -factor ?

Karl (Still 70 turns to milk)

 

[Bartleby]

The score is better estimated:

[(CurrentScore*TurnsElapsed)+(InternalScore*TurnsLeft)]/540

Apologies if this re-hashes your formula, maths is one of my blind spots.

Also you can use SirPleb's score calculator: http://forums.civfanatics.com/showthread.php?t=17550
It is very accurate once your population is maxed.

edit: I dunno why it put a space in the middle of "left"

 

[sanabas]

According to this TurnScoreDelta*TurnNumber should give me an approximation of the internal per-turn score (iPTSa).
Besides fuctuations caused by rounding/truncation this figure should remain pretty much the same when in milking phase, rigth ?

The final score could be estimated:
Score= CurrentScore+ iPTSa* Sum(1/N)
where N is turn number, and the sum is taken over remaining turns.

The actual per-turn score does remain pretty similar. TurnscoreDelta*TurnNumber gives you an approximation of how far above your current score your per-turn score is, so as your current score gets higher, the difference between your per-turn score and current score will drop. Your actual per-turn score isn't dropping though.

You can work out your per-turn score exactly if you want. [CurrentScore*CurrentTurnNumber-PreviousScore*PreviousTurnNumber]/[currentTurnNumber-PreviousTurnNumber]

i.e. If your score after 400 turns is 40000, and it has increased to 41000 at turn 410, your average per-turn score is
[41000*410-40000*400]/[410-400]
=[16,810,000-16,000,000]/10
=81,000

If you assume you'll maintain that 81,000 per turn, you can work out your score after any number of turns. Just add however many multiples of 81,000 to your current total score of 16,810,000, and divide that total by the new turn number. So your approximate final total score would be 16,810,000 + 81,000*130 = 27,340,000 and to get your final score divide that total by 540, giving you 50,629

So the iPTSa is declining on rate of about 100/turn, or 2,5 % /10 turns. The only viable conclusion is that the N-factor is more progressive than 1/N, maybe based on years instead of turn number.

Now fellow HOFfers, is this old news, enyone got the right formula for the N -factor ?

Karl (Still 70 turns to milk)

The other viable conclusion is your approximation isn't accurate, which gives the wrong N-factor. If you're having trouble still, post a couple of firaxis scores after however many turns, and I'm sure one of us will give you your per-turn score and a reasonably accurate final score prediction.

 

[Karl_t_great]

Thanks once again,
I must have been too stubborn to notice that in addition to 1/N on the "new" score the "old" score is actually diluted by N factor too by the average operation (exatly as expressed in SirPlebs text I quoted). The idea of getting some point and then giving them "back" was just too much for me to gasp.

BTW , this means that if You are enough low on terratory and have very few citizen You can actually have negative PTS, and Your score will decrease every turn.

So my (correct) iPTSa of 79180 and turn 390 score of 25947 gives me an estimate of 40734 and turn 502 score predicts 40754 final, well within round off limits.

Sorry for the fussy incorrect math -- though It has been a good mental exercise while waiting for the milk to run.

 

[sanabas]

BTW , this means that if You are enough low on terratory and have very few citizen You can actually have negative PTS, and Your score will decrease every turn.

Sorry, I have to be pedantic one more time. It's not possible to have a negative per-turn score, it is possible (but difficult) to have a per-turn score lower than your current firaxis score, in which case your firaxis score will decrease each turn.

What level are you getting 40k on?

 

[Karl_t_great]

Sorry, I have to be pedantic one more time. It's not possible to have a negative per-turn score, it is possible (but difficult) to have a per-turn score lower than your current firaxis score, in which case your firaxis score will decrease each turn.

What level are you getting 40k on?

You are rigth, I was referring to the visible per turn score, not the internal one ( iPTS). The decreasing score can be observed on the last AI civ when milking.

It is a huge demigod continets-3825 dl.