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
EXP FIELD AVG.
DJ EXP SCORE
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 or
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).