Expected Value

Expected value is a general statistics and decision-theory concept, not a golf-specific one: multiply each possible outcome by its probability and add the results together. In golf, it explains why a shot that fails more often than it succeeds can still be the smarter play, when the reward on the good outcomes outweighs the cost of the bad ones — and why a shot that usually works can still be a poor decision if its rare failure is expensive enough.

Expected strokes is expected value applied to one specific input: the average strokes needed to finish a hole from a given starting position, averaged across every way the rest of the hole could unfold from there. Strokes gained then compares expected value before and after a shot to price what that single shot was worth.

Evaluating expected value for a real decision — go for a green over water, or lay up short of it — depends on knowing a golfer's own dispersion. The same aggressive line carries very different expected value for a tight ball-striker than for a wild one, because the two golfers reach the costly outcomes at very different rates.