The largest course history adjustment we are making this week
strokes and belongs to Adam Scott,
who in his
at TPC Sawgrass has performed 0.77 strokes above
expectation (i.e. what we would expect based on his performance at other courses and
his course fit at Sawgrass). Si Woo Kim has an incredible, albeit shorter, history
at TPC Sawgrass: Kim has performed 2.03 strokes above expectation in 17 rounds
here. Our model's adjustment for Kim based off this history is just +0.15.
It's worth thinking a bit more deeply about the differences in these adjustments,
as it's not obvious why one would be higher than the other.
First, suppose that both
Scott and Kim actually don't
have higher skill levels at TPC Sawgrass; how likely
would it be to observe their histories? For Scott, the answer is around 1.6%, and for Kim
it's 0.2%. This is interesting because it shows that Kim's history
actually provides stronger evidence
that he has a different skill level at Sawgrass than Scott's does.
However, next suppose that their true skill levels were +0.25 strokes better at
Sawgrass; now the probability of observing Scott's history is 7.4% (4.6 times
more likely than if his true skill was 0)
and for Kim it is 0.5% (2.5 times more likely).
The correct way to think about this is that we want to choose the skill adjustment
that best explains a player's course history while also respecting the fact that
we know players' skill levels don't vary that
much across courses. In Si Woo's case,
there isn't any reasonably-sized adjustment that is going to explain his history well, which
keeps his adjustment (slightly) closer to zero. However in Scott's case, a 0.25 skill adjustment
does a much better job of rationalizing his history. Even though 0.25 strokes is
a large course-specific skill bump, because it does a much better job explaining the
observed data it can be justified.