| Because its not taking: final $ - initial $ / number of turns. Its averaging your income for each game turn. This means you had a lot of turns with negative income. |
(final$ - initial$) / #turns = average = (Turn1$ + Turn2$ Turn3$ ...+TurnN$)/ nturns
horay for math.
Average is path independant operation. (kind of like gravity and work, and not like friction and work).
So you can take individual points along the path and add them together then divide or just doing it final- initial value.
Since the integral of time Vs income graph is given in units of $ since income is $/turn and time is messure in turn.
Then we can take the ine integral of the function from a to b divided by b-a which is the number of turns.
Also you can take the intial and final values of $ and divide by turns.
Both of these should be =.
But that is only true if there is no outside factors in the $ value.
Such as donations, anomlies with cash, or small civs. paying you off..
If you take that out then they should be equal.
So what this means is that
Initial$ + AverageIcnome(numberofturns)+gifts/anomolies/payoffs = Final$
so if average income < 0, and final >intial then gift >0