Probably less than you think.
We hold a final table championship for our yearly league; the top eight players in points qualify with starting stacks that reflect their accumulated points (typically 20k to 55k, averaging about 34k).
In 17 seasons, the final table's big stack has won exactly
once. The majority of winners have come from the 4th-largest starting stack position (second-highest number of winners came from the 2nd-largest stack position).
A bunch of chips don't guarantee a win.