In 25,000 simulations of tomorrow’s final round, Dustin Johnson’s scores ranged from 61 to 89 (!).
Remember, 25k is a big number — weird things can and will happen in that many trips around Augusta National.
The plot below displays Dustin Johnson’s win probability as a function of his (possible) final round scores:
DJ's win probability conditional on what he shoots tomorrow
These probabilities reflect the uncertainty around the specific scores shot by the other golfers in the field.
To virtually guarantee a victory tomorrow, Johnson needs to shoot 68
better (we expect him to win more than 99% of the time in these cases). Conversely,
if Johnson shoots 77 or worse we expect a win less than 2.5% of the time.
It’s important to note that part of the uncertainty here lies in how difficult Augusta National plays tomorrow:
our expectation is a field scoring average of around 72.5, but we allow for the possibility of
easier or harder
average conditions. For example, if we know DJ shot a 77, this
increases the likelihood that the course played difficult (and therefore
also increases the likelihood that DJ’s pursuers shot a higher score).
This partly explains why his win probability is not lower for a final round score of 77.
If we wanted to ignore course difficulty, we could repeat this exercise but just
focus on Johnson’s strokes-gained relative to the field. In this case, the
relevant numbers would be +4 SG (greater than 99% win probability) and -4 SG (less than
0.5% win probability).