Tuesday, September 27, 2016

The 100-Win Cubs and Competitive Balance in MLB

In today's article on ESPN about the 100-win Cubs, David Schoenfield writes, "(W)e’ve had more parity in the past decade, making 95- and 100-win seasons increasingly rare." He measures this by comparing the number of teams with 95+ wins since MLB expanded to 30 teams in 1998:

1998-2006: 44 teams with 95-plus wins
2007-2016: 33 teams with 95-plus wins

I sought to see if a more mathematical calculation of competitive balance (CB) backs this up. I've looked at CB in the NBA in the past, and I applied this same technique to MLB (since 1998) by calculating the Noll-Scully Measure (NSM), which is the ratio of the actual standard deviation in each to season to the "ideal" standard deviation for that season. The lower the NSM, the greater CB there is in the league, with a perfectly balanced league having a ratio of 1.
In the two periods Schoenfiled indicated, there is indeed a difference in the NSM: it is much higher from 1998-2006, which implies less competitive balance.

1998-2006: 1.95 average NSM
2007-2016: 1.72 average NSM

For perspective, this season it is currently 1.724, which is right in line with the last decade, an era of more parity.

Thursday, September 22, 2016

"What are the odds?" That a Survey with 27 Choices and 1000 Participants Will End in a Tie

"We have a survey of 27 choices. There will be approximately 1,000 people voting, and they can only vote once and only make one choice each. What are the chances of a tie?"

Even without doing any math, it's obvious the number of combinations over 27 choices and 1,000 votes makes it very unlikely that there will be a tie. However, we can determine this probability indirectly using simulation.

I assumed that exactly 1,000 people will vote, and that each choice has an equal 1/27 chance of being chosen (this is obviously not likely true, but for simplicity this is the most basic assumption we can make).

I wrote a simulator in Python, and ran 10,000 simulations and tallied how often the survey resulted in a tie for first place: 14.34%.