How to calculate win probability for each team in a Round of 16 knockout tournament

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Let's say there are 16 teams in a standard Round of 16 bracket. The initial matchups are known (A plays B, C plays D, etc.). We know the probability for each possible matchup (A has a 54% chance of beating B, 58% chance of beating C, etc.) So is there a formula to determine the win% for each team?

By the time you get through 5 rounds, there are so many possible conflagrations, so I couldn't figure out a reasonable way to make a grid or spreadsheet of every possible combination of results. So I have been just running a simulator that randomizes each game and plays out the whole tournament thousands of times. But I feel like there should be some more precise formula to get a more direct answer. I just don't know how to build it.