How do I improve my normalized score?

Population score is based on the amount of base food on the map (not counting improvements like farms, plantations, windmills) and how much population you get relative to that base amount. So if you want a big pop score, get lots of cities with food improvable tiles (and biology) and farm/windmill everything, get rid of all your cottages before growing pop to max (don't worry about unhappiness) before winnning.
 
I got over 30k from a Chieftain game because I used a Chukonu Rush. Can't remember how early I finished but my opponents had barely Classical Age.
 
An early AP diplomatic win gave me my only win over 100K. Finished way back in the 1200s. It seems to me the type of victory has the biggest bearing.

All my Domination wins scored higher than my space wins. Domination wins force you to have the high pop and land, and encourage getting it done early, rather than deal with tougher defenses and higher war weariness. UN diplomatic wins can be all over the place.

I find cultural wins to be pretty low since you don't need a large number of cities and population for them. I suppose they can be quite a bit higher if you pull them off early.

Space wins just seem to lack the high scoring because it takes so long to tech that much.

40K on Diplomatic victory just now (Chieftain), Hammurabi didn't even need to take out any civs to do it (though Sitting Bull was throwing a lot of spies my way and bombing my mines and I was building a lot of stuff to wipe him out with) and I lost a lot of ground to more expansive leaders like Cyrus.

What helped was that I got a RE which converted one of the "New World" civs to Buddhism (my religion and that of the AP) which meant that along with Cyrus in the Old World and me and the other three civs strongly Buddhist, a bit of strategic gifting of technology was all I had to do to win.

Settler is enjoyable to try for a peaceful or non-conquest orientated victory because you progress faster technologically and can get the relevant techs much earlier, though still not much before the 1700s. If Hamm hadn't been Grand Lama of the Known and Unknown Worlds I probably would have abandoned the game because otherwise I would have gone under or had to maintain a small civ in a packed world...it is more interesting when you stretch from one end of the map to the other and are regularly eroding the borders of the other civs without even having to lift a musket to do so.

What I would suggest is play the right kind of person on the right kind of map. Play an Organised person on Highlands and your civ spills out like water over a tabletop. Play Financial on a continental/archipelago map and watch your finances swell nicely (don't forget to choose a civ with fishing to make sure you progress better towards Sailing, Optics and Astronomy for the ships you'll need). And so on. That's not exactly the way to increase the score, but it's partly a contribution towards a game you can be sure of winning on.

(And don't forget to take wonders like the Pyramids even if you don't need them. If you can get them get them to hate out other people - I normally don't bother with the Pyramids if I can learn Monarchy, but that leaves them open for everyone else. Wonders I assume also count towards your score so they are worth it for that instance as well.)
 
I'll also say the easiest way is through force, and winning early. Virusmonster got 500k that way, with his quecha fun.

My personal best is 125k. I achieved this by getting a 1705 AD domination win on a normal Pangaea map (monarch difficulty). Pangaea and Terra maps are good for domination and conquest, especially because you can go on rolling vassalizations (vassalize one nation, then you have half their power/score added, so each successive civ capitulates more easily/readily/quickly, kind of like a snowball rolling down a hill in a cartoon).
 
terra isn't that good for dom if you plan to finish before astronomy.

virusmonsters 500k were with praets not quechuas.
 
Well killercane got 700K with immortals.. Though i am not sure if that game is in the hof...
 
I think killercanes game will show up next HOF update (tomorrow probably), assuming he submitted it and it is accepted of course ;)
 
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