For me it always was how many wars your alliance win/lose earlier
sometimes grows during the war, and I do not understand it … 
A big part of the war score is the heroes owned by the people opted in. It will change if players gain a powerful new hero, level up a hero, feed away a high level hero or either opt in or opt out of wars. So yes it does change often 
Or it can be a way to just get another chest rearward.
War - what is it good for? Absolutely nothing. 
Say it again…!!!
Wars are another way to fill chests for those ascension materials! Also helps with raids and defense setups forcing you to focus on getting at least 30 maxed heroes. Just like how the raid tournaments are shifting people to lvl some 3* or less popular slow mana heroes.
For me, wars are a great way to bond with your alliance members, so long as you’re in an active alliance and communicating regarding war strategy.
Many people feel the added pressure of war attacks because you don’t want to disappoint your mates who can all see your war attack outcome.
On the flip side, there’s few moments in the game as pleasant as when you do well in war and help your alliance win.
One of my fondest memories was when we were down by 90 pts, I was fairly new but used my last 3 flags to help us win by a few points.
This helpful posts from Kerridoc summarizes and explains what we know about the effects of past performance on War Score:
it’s very useful, thank you 
Here are exact maths based on my personal experience, of which I’ve kept meticulous charts and such (not really).
You win war: your team +2000 war score, opponent -2000 war score.
You lose war: your team -2000 war score, opponent +2000 war score.
That is 100% accurate (+/- 50% margin of error) based on several months of semi-verifiable but mostly anecdotal evidence from one very trusted and highly respected researcher (myself).
On what basis is war force calculated now? There are big changes 
I think “past performance of the Alliance” could also mean how the alliance performs as a whole in war, titans & even cups maybe.
Here’s why I think that.
Our war score was 49663 when matching started.
-Yesterday 4:56am matching started
-Yesterday 6:53am We were matched with another with the same score 49663
-Yesterday 4pm titan escaped after we were matched. Titan escaped -escaping is negative performance as a whole alliance.
At 7:40pm Our War score dropped to 47775
No new members came, No one left alliance no one un checked their war participation box.
In fact I was the only member online
-Last night 11pm
Before war starts a member left the alliance he was level 29 in the game. So not our big hitters but also not our new little guys.
Early this morning 2 am
war score dropped again to 46603!
So within 7am yesterday and 7am today our war score dropped twice.
from 49663 to 47775 then again to 46603.