The traditional Pythagorean developed by Bill James used an…

The traditional Pythagorean developed by Bill James used an exponent of 2 for baseball and we’ll use this exponent. In the 2024 season, the Guardians scored 708 runs and allowed 621 runs.  Let’s assume the lineup as constructed would repeat this output next year. Suppose the Guardians had their choice of 2 players: 1) Juan Soto: accounted for 58 more runs than an average player due to his batting and baserunning and ALLOWED the opponent to score 6 more runs than an average fielder would have (i.e., he increases runs scored by 58.4 and INCREASES runs allowed by 6) 2) Blake Snell: allowed 14 fewer runs than an average pitcher and has no effect on the batting as the pitcher spot doesn’t hit.   What would the Pythagorean predict as the win% for the Guardians if they replace an average player with Snell? Report your answer as a decimal to 4 places: i.e., 20.34% should be entered as .2034

In class we discussed lactase persistence, a human trait tha…

In class we discussed lactase persistence, a human trait that recently evolved by natural selection.  In class, you drew a graph showing how lactase persistence changed through time, in areas with access to milk from cows.  Below, I gave you the basic graph framework you used in class.  1.  Sketch this graph, drawing a line to represent the frequency of lactase persistence over time.  (2 points) 2.  List 3 steps of natural selection, and briefly explain how each is represented in the graph.  (3 points)