Sorry, I can't give you the math because I'm so bored after reading three plodding articles about voting.
The gist is that fptp voting like the US or Canada has is inferior to ranked choice voting, which means your preferences are always considered even if your first choice doesn't win.
I think it's not a first past the post criticism but a single member districts criticism.
An example of what I mean: you have a body made up of 100 representatives. You can divide the body into 100 voting districts. In each one, the winner gets the seat. Even if you have something like RCV, you can have 49% of people vote for party a and 51% vote for party b. If the voting districts are pretty much the same, then party b will have all the seats and 49% of people won't have someone they voted for in power. With proportional representation and multiple member districts, in the case where roughly 50% of people like party a and 50% like party b, the representatives will be roughly 50% party a and 50% party b.
And it can get worse if the districts are different. If you pack voters strategically, it's possible for a majority government to form with only slightly over 25% of the popular vote. (Or lower, with more than two parties)