This week the #puzzle is: How Lucky Can a Baseball Team Get? #probabilities #counting #montecarlo #coding
| The Fiddler Baseball League consists of exactly two teams of equal skill: the Algebraists and the Geometers. Over the course of a season, these two teams play each other 162 times. Each team has an equal chance of winning each game, and the results of games are independent of one another. |
| At the end of the season, on average, how many games would you expect the team with the better record to have won? (If the teams have the same record, then you should include one of them in your calculation.) |
And for extra credit:
| After some expansion, the Fiddler Baseball League now boasts 30 teams. Over the course of a season, each team plays each other team five times. (Thus, each team plays a total of 145 games.) As before, each team has an equal chance of winning each game, and the results of games are independent of one another. |
| At the end of the season, on average, how many games would you expect the team with the best record to have won? (If more than one team has the same best record, then you should include one of them in your calculation.) |

How Lucky Can a Baseball Team Get? ![]()
Solution, possibly incorrect:
Method 1: Monte Carlo. Play through a tournament of 162 games. Do this in a loop a lot of times. Run the program a few times to find a stable result.
Method 2: Calculate the average directly. E.g., with 82 wins, there’s a probability of of this situation arising. Multiply by 82. Sum over all win options, 0-162. Note that 82 wins and 80 wins both produce “winner won 82 times” situations.
Result: 86.06988.
And for extra credit:
Method 1: Definitely Monte Carlo.
Result: .







