Solves the fivethirtyeight Riddler Express from March 22, 2019
| # -*- coding: utf-8 -*- | |
| """ | |
| Solves the fivethirtyeight Riddler problem from March 22, 2019 | |
| Each inning is represnted by an object called "Inning", that is comprised of | |
| strikes, outs, and runner positions, e.g. Inning(0, 1, (0,1,0)) for 0 strikes, | |
| 1 out, and a runner on second base. | |
| There are 11 unique game actions that can occur. Each is represented by a | |
| function that takes an inning state as input and returns a tuple of the new | |
| inning state after the action and the number of runs that were scored as a | |
| result of the action. | |
| """ | |
| import numpy as np | |
| from collections import namedtuple | |
| # define a container for the current state of an inning | |
| Inning = namedtuple('Inning', ['strikes', 'outs', 'runners']) | |
| # all possible game actions, handled with functions below | |
| __actions__ = [ | |
| ('strike', 4), | |
| ('out_at_first', 4), | |
| ('fly_out', 3), | |
| ('single', 3), | |
| ('base_on_error', 1), | |
| ('double', 1), | |
| ('double_play', 1), | |
| ('foul_out', 1), | |
| ('homerun', 1), | |
| ('triple', 1), | |
| ('walk', 1) | |
| ] | |
| ACTIONS = [a[0] for a in __actions__] | |
| WEIGHTS = [float(a[1]) for a in __actions__] | |
| WEIGHTS = [w / sum(WEIGHTS) for w in WEIGHTS] | |
| def single_inning(verbose=True): | |
| """ | |
| Simulate a single inning until three outs are recorded. Return the number | |
| of runs scored during the inning. If verbose=True, print a "play-by-play" | |
| summary of the inning for each action. If verbose=False, just return runs | |
| """ | |
| state, score = Inning(0, 0, (0,0,0)), 0 | |
| while state.outs < 3: | |
| action = np.random.choice(ACTIONS, p=WEIGHTS) | |
| state, runs = globals()[action](state) | |
| score += runs | |
| if verbose: | |
| print(f'{action:15}: {state}, {score} total runs scored') | |
| return score | |
| def simulate_innings(trials): | |
| """Simulate a large number of innings and return the total runs scored""" | |
| return np.array([single_inning(verbose=False) for _ in range(trials)]) | |
| def base_on_error(inning): | |
| """ | |
| Update the inning for a base on error | |
| * batter and runners advance one base each | |
| """ | |
| if inning.runners == (0,0,0): runners, runs = (1,0,0), 0 | |
| elif inning.runners == (1,0,0): runners, runs = (1,1,0), 0 | |
| elif inning.runners == (0,1,0): runners, runs = (1,0,1), 0 | |
| elif inning.runners == (0,0,1): runners, runs = (1,0,0), 1 | |
| elif inning.runners == (1,1,0): runners, runs = (1,1,1), 0 | |
| elif inning.runners == (1,0,1): runners, runs = (1,1,0), 1 | |
| elif inning.runners == (0,1,1): runners, runs = (1,0,1), 1 | |
| elif inning.runners == (1,1,1): runners, runs = (1,1,1), 1 | |
| return Inning(0, inning.outs, runners), runs | |
| def double(inning): | |
| """ | |
| Update the inning for a double | |
| * all runners score; batter advances to second | |
| NOTE: in reality about 50% of runners on first score on a double | |
| """ | |
| return Inning(0, inning.outs, (0,1,0)), sum(inning.runners) | |
| def double_play(inning): | |
| """ | |
| Update the inning for a double play | |
| * if the bases are empty this is treated like a single out; otherwise | |
| it's assumed the two runners farthest advanced are picked off. | |
| """ | |
| if inning.runners == (0,0,0): | |
| # only one out available | |
| runners = (0,0,0) | |
| outs = inning.outs + 1 | |
| if inning.runners in [(1,0,0), (0,1,0), (0,0,1)]: | |
| runners = (0,0,0) | |
| outs = inning.outs + 2 | |
| elif inning.runners in [(1,1,0), (1,0,1), (0,1,1)]: | |
| runners = (1,0,0) | |
| outs = inning.outs + 2 | |
| elif inning.runners == (1,1,1): | |
| runners = (1,1,0) | |
| outs = inning.outs + 2 | |
| else: | |
| runners = (0,0,0) | |
| if outs > 2: | |
| return Inning(0, 3, (0,0,0)), 0 | |
| else: | |
| return Inning(0, outs, runners), 0 | |
| def fly_out(inning): | |
| """ | |
| Update the inning for a fly out | |
| * runner on third scores unless it's the third out | |
| """ | |
| outs = inning.outs + 1 | |
| if inning.runners == (0,0,1): runners, runs = (0,0,0), 1 | |
| elif inning.runners == (1,0,1): runners, runs = (1,0,0), 1 | |
| elif inning.runners == (0,1,1): runners, runs = (0,1,0), 1 | |
| elif inning.runners == (1,1,1): runners, runs = (1,1,0), 1 | |
| else: runners, runs = inning.runners, 0 | |
| if outs > 2: | |
| return Inning(0, 3, (0,0,0)), 0 | |
| else: | |
| return Inning(0, outs, runners), runs | |
| def foul_out(inning): | |
| """ | |
| Update the inning for a foul out | |
| * runners stay where they are | |
| """ | |
| if inning.outs > 1: | |
| return Inning(0, 3, (0,0,0)), 0 | |
| else: | |
| return Inning(0, inning.outs + 1, inning.runners), 0 | |
| def out_at_first(inning): | |
| """ | |
| Update the inning for an out at first | |
| * runners advance one base | |
| """ | |
| outs = inning.outs + 1 | |
| if inning.runners == (0,0,0): runners, runs = (0,0,0), 0 | |
| elif inning.runners == (1,0,0): runners, runs = (0,1,0), 0 | |
| elif inning.runners == (0,1,0): runners, runs = (0,0,1), 0 | |
| elif inning.runners == (0,0,1): runners, runs = (0,0,0), 1 | |
| elif inning.runners == (1,1,0): runners, runs = (0,1,1), 0 | |
| elif inning.runners == (1,0,1): runners, runs = (0,1,0), 1 | |
| elif inning.runners == (0,1,1): runners, runs = (0,0,1), 1 | |
| elif inning.runners == (1,1,1): runners, runs = (0,1,1), 1 | |
| if outs > 2: | |
| return Inning(0, 3, (0,0,0)), 0 | |
| else: | |
| return Inning(0, outs, runners), runs | |
| def single(inning): | |
| """ | |
| Update the inning for a single | |
| * runners advance two bases; batter advances to first | |
| """ | |
| if inning.runners == (0,0,0): runners, runs = (1,0,0), 0 | |
| elif inning.runners == (1,0,0): runners, runs = (1,0,1), 0 | |
| elif inning.runners == (0,1,0): runners, runs = (1,0,0), 1 | |
| elif inning.runners == (0,0,1): runners, runs = (1,0,0), 1 | |
| elif inning.runners == (1,1,0): runners, runs = (1,0,1), 1 | |
| elif inning.runners == (1,0,1): runners, runs = (1,0,1), 1 | |
| elif inning.runners == (0,1,1): runners, runs = (1,0,0), 2 | |
| elif inning.runners == (1,1,1): runners, runs = (1,0,1), 2 | |
| return Inning(0, inning.outs, runners), runs | |
| def strike(inning): | |
| """ | |
| Update the inning state for a strike | |
| Returns a new Inning object and the number of runs scored | |
| """ | |
| strikes = inning.strikes + 1 | |
| if strikes > 2: | |
| strikes, outs = 0, inning.outs + 1 | |
| if outs < 3: | |
| return Inning(strikes, outs, inning.runners), 0 | |
| else: | |
| return Inning(0, 3, (0,0,0)), 0 | |
| else: | |
| return Inning(strikes, inning.outs, inning.runners), 0 | |
| def triple(inning): | |
| """ | |
| Update the inning for a triple | |
| * all runners score; batter advances to third | |
| """ | |
| return Inning(0, inning.outs, (0,0,1)), sum(inning.runners) | |
| def homerun(inning): | |
| """ | |
| Update the inning for a triple | |
| * all runners and the batter score | |
| """ | |
| return Inning(0, inning.outs, (0,0,0)), sum(inning.runners) + 1 | |
| def walk(inning): | |
| """ | |
| Update the inning for a walk | |
| * batter advances to first; runners advance if forced | |
| """ | |
| if inning.runners == (0,0,0): | |
| runners, runs = (1,0,0), 0 | |
| elif inning.runners in [(1,0,0), (0,1,0)]: | |
| runners, runs = (1,1,0), 0 | |
| elif inning.runners == (0,0,1): | |
| runners, runs = (1,0,1), 0 | |
| elif inning.runners in [(1,1,0), (1,0,1), (0,1,1)]: | |
| runners, runs = (1,1,1), 0 | |
| elif inning.runners == (1,1,1): | |
| runners, runs = (1,1,1), 1 | |
| return Inning(0, inning.outs, runners), runs | |
| if __name__ == '__main__': | |
| trials = 100000 | |
| results = simulate_innings(trials) | |
| print(f'Average score from {trials:,.0f} innings: {results.mean():,.2f}') |
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