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In a previous entry I demonstrated one simple way to estimate an exponent for the Pythagorean win expectation . Another nice consequence of a Pythagorean win expectation formula is that it also makes it simple to estimate the run value of a win in baseball, the point value of a win in basketball, the goal value of a win in hockey etc. Let our Pythagorean win expectation formula be w=PePe+1, where w is the win fraction expectation, P is runs/allowed (or similar) and e is the Pythagorean exponent. How do we get an estimate for the run value of a win? The expected number of games won in a season with g games is W=g⋅w=g⋅PePe+1, so for one estimate we only need to compute the value of the partial derivative ∂W∂P at P=1. Note that W=g(1−1Pe+1), and so ∂W∂P=gePe−1(Pe+1)2 and it follows \[ \frac{\partial W}{\partial P}(P=1) ...