What? Preposterous.
Say a set to 11 ends up 11-1. If it was winner breaks, player 1 broke 10 or 11 times (depending on who won the lag). If it was alternate breaks, player 1 broke 6 times.
10 or 11 is not the same as 6.
Say player 1 is up 10-5, and both players are pros. It's player 2's break. In winner breaks, the number of opportunities player 1 is guaranteed to run out for the match is 0. He might not get back to the table. In alternate breaks, The number of opportunities player 1 is guaranteed to break and run for the match is at least 3, regardless of how player 2 plays.
0 is not the same as 3.
"Mathematically", this makes no sense.
-Andrew
In each format, they play 21 racks (potentially, unless someone gets to 11 early), and the lag winner breaks 11 times out of those 21. Winner break versus alternate breaks only changes the order the racks are played.
Of course, if one guy gets to 11 before 21 racks are played, then they don't play the rest of the racks because the outcome of the match won't change. So in your 11-1 example, all of the unplayed racks would belong to the loser's break. But there's no point in playing them, because the loser can only get to 10 even if he wins them all.
In order to win, in either format, if you win the lag you have to win either 11 on your on break, or 10 on your break and 1 on the other guy's, or 9 and 2, or 8 and 3 and so on. Winner or alternate breaks, same deal.
As for your second example. If player 1 is up 10-5, in winner breaks, that means that he has already had either 10 or 11 breaks, depending on who won the lag. If player 2 is breaking, that means that the 6 remaining breaks belong to player 2, so it will come out to 11 breaks for the lag winner and 10 for the other guy if it goes the distance. Again, if player 2 loses one of these last 6 games, they don't play the rest of it it out, because it would be pointless, the winner is already determined.
In alternating breaks, at 10-5, with player 2 breaking, player 1 has had 8 breaks and player 2 7 so far. They alternate and again the lag winner gets 11 out of the 21 potential breaks, but again all the games might not be played out.
Being up 10-5 in winner breaks is a different thing than being up 10-5 in alternate breaks. That's true. But winning a race to 11 (or any number) is mathematically the same either way.