Following BrooklynGuy's method, I used cFIREsim to compare the performance of taking out a 30-year fixed-rate mortgage, investing the proceeds of that mortgage, and using only that mortgage-derived portfolio to pay your mortgage. This ignores the transaction costs of getting a mortgage, and may not equal exactly how your portfolio would be modeled because cFIREsim pulls a year's worth of spending all at once. This is based on a $100k mortgage (initial portfolio), uses a 0.05 ER, and the spending rate is not inflation adjusted (because your mortgage payments won't be either).
I thought the 30-year mortgage example would be a good way to model this because the term is sufficiently large to capture the expected long-term market returns, and if continuing to hold your mortgage and invest instead is a superior strategy, you'd want to maximize your ability to do that by refinancing right before you quit your job (and make getting a mortgage much harder). But obviously if by the time you are ready to FIRE you have 15 years left on a 3% loan and the market only offers 6% on a 30 year loan, it may not make sense to refi at that time.
The table headers don't line up exactly but I was too lazy to put it into the table code.
100% stock
Interest rate Monthly Annual Success Rate Lowest Portfolio Median Portfolio Highest Portfolio
3% 422 5064 98% ($82,039.73) $564,271.49 $2,385,890.76
4% 477 5724 95% ($103,240.05) $422,969.72 $2,212,153.09
5% 537 6444 88% ($127,727.13) $283,518.02 $2,022,621.13
6% 600 7200 66% ($152,246.38) $171,800.36 $1,823,612.79
7% 665 7980 54% ($179,631.18) $31,882.02 $1,618,286.93
8% 734 8808 39% ($205,557.97) ($60,733.21) $1,400,325.52
75% stock
Interest rate Monthly Annual Success Rate Lowest Portfolio Median Portfolio Highest Portfolio
3% 422 5064 98% ($51,919.39) $388,154.91 $1,735,055.52
4% 477 5724 96% ($82,050.56) $290,397.43 $1,567,618.08
5% 537 6444 82% ($107,102.73) $183,596.70 $1,384,959.01
6% 600 7200 63% ($132,364.73) $78,870.69 $1,193,167.15
7% 665 7980 46% ($159,006.49) ($23,592.30) $995,286.50
8% 734 8808 28% ($186,045.61) ($85,508.41) $812,400.14
There's probably some correlation between prevailing market interest rates at the time you FIRE and future market returns. Obviously the methodology I used here does not take this into account.