Pythagoras - 2025 Penn Bowl - BU

Question

A portmanteau between this mathematician and Clay Davenport names a value used to exponentiate runs scored and allowed in another formula. For 10 points each:

[10e] Give this mathematician who names an “expectation” in baseball analytics that resembles a ubiquitous geometric result generalized by the law of cosines.

ANSWER: Pythagoras [or Pythagoras of Samos; accept Pythagorean theorem or Pythagorean expectation; prompt on Pythagenport formula]

[10m] In 2003, Hein Hundal related the exponent in Pythagorean expectation to the standard deviation of this function of the runs distribution. In MLE, the score is defined as the gradient of this function of likelihood.

ANSWER: natural logarithm [or log x and equivalents; or ln x and equivalents; accept log-likelihood]

[10h] In 2006, Steven J. Miller derived the Pythagorean expectation exactly by modeling runs scored and allowed with this distribution equivalent to a generalized gamma distribution with equal shape parameters.

ANSWER: Weibull distribution

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Summary


2025 Penn Bowl - BU	11/01/25	Y	4	17.50	100%	75%	0%
2025 Penn Bowl - CWRU	11/01/25	Y	2	0.00	0%	0%	0%
2025 Penn Bowl - Mainsite (UPenn)	11/01/25	Y	5	2.00	0%	20%	0%
2025 Penn Bowl - Murray State	11/08/25	Y	1	0.00	0%	0%	0%
2025 Penn Bowl - Northwestern	10/25/25	Y	3	6.67	33%	33%	0%
2025 Penn Bowl - Online	11/08/25	Y	2	0.00	0%	0%	0%
2025 Penn Bowl - Ottawa	11/01/25	Y	4	15.00	75%	50%	25%
2025 Penn Bowl - Stanford	10/25/25	Y	3	13.33	100%	33%	0%
2025 Penn Bowl - UK	11/01/25	Y	5	8.00	20%	60%	0%
2025 Penn Bowl - UNC	11/01/25	Y	1	10.00	100%	0%	0%
2025 Penn Bowl - WashU	11/01/25	Y	2	15.00	50%	100%	0%

Data


MIT A	Brown	10	10	20
Harvard	I've been running into you in my lead plumbocene what could have benzene	10	0	10
MIT B	Yale	10	10	20
RIT	Brandeis	10	10	20