Mathematical problem

[President Punxsutawney Phil]

So just now I was making a gerrymander of GA trying to make every seat match the statewide margin of Biden+0.2, but once I had drawn 13 seats with that margin, there was a hiccup.
The last seat turned out to have a margin of Biden+1.2, way bigger than I was anticipating. And every seat was within +/-1000 as well...
What exactly causes this sort of thing?

[muon2]

It could be as simple as rounding error. GA 2020 was won by a margin of 0.23% which rounds to 0.2%. For example, suppose the 13 districts actually had margins of +0.155% which also rounds to 0.2%. That shortfall of 13 times 0.075% is 0.975%. That would be added to the 14th district bring it to 1.205%.

There are more complicated (and more likely) answers that can also explain the result, such as non-uniform turnout and non-uniform third party votes. When the the population and votes are not always in the same proportion then the average can easily shift.