How often does the best team win?

How often does the best team win?

Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer
http://bit.ly/2gHCI0C
Fields Institute, May 25, 2018

You might remember this…

You might not remember this…

(https://www.mlb.com/news/elvis-andrus-has-two-key-errors-in-alds-game-5/c-154487546)

You probably remember this…

Using statistics to assess luck in sports

• The best team does not always win.

• How often does the best team win in each sport?

• How to untangle luck from skill?

• Luck —> parity

What parity looks like

What parity does not look like

Parity checklist

1. Equality at a fixed time
2. Postseason tournament
3. Within season equality
4. Between season equality

Prior work

• Extend Glickman and Stern, 1998

Challenges

The model: definitions

• \(p_{(q,s,k)ij} =\) probability that team \(i\) will beat team \(j\) in season \(s\) during week \(k\) of sports league \(q\), for \(q \in \{MLB, NBA, NFL, NHL\}\).
• \(\alpha_{q_{0}}\) be the league-wide home advantage (HA) in \(q\)
• \(\alpha_{(q) i^{\star}}\) be the extra effect (+ or -) for team \(i\) when playing at home
• \(\theta_{(q,s,k) i}\) and \(\theta_{(q, s, k) j}\) be season-week team strength parameters

The model & assumptions

\[ E[\text{logit}(p_{(q,s,k) ij})] = \theta_{(q,s,k) i} - \theta_{(q, s, k) j} + \alpha_{q_0} + \alpha_{(q) i^{\star}} \]

Assumptions:

1. \(\sum_{i=1}^{t_{q}} \theta_{(q,s,k)i} = 0\)
2. \(E[\theta_{(i,q,s+1,1)}] = \gamma_{q, season} \theta_{(i, q,s,k)}\)
3. \(E[\theta_{(i,q,s,k+1)}] = \gamma_{q, week} \theta_{(i, q,s,k)}\)
4. \(\gamma_{q,week}\) and \(\gamma_{q,season}\) week/season level autogressive parameters

Fitting a cross-sport model

• Data
  • 2006–2016 reg. season in MLB, NBA, NFL, NHL (Sports Insights)
• Priors
  • Uniform (variance parameters) and Normal (team strength parameters)
• Software
  • rjags package in R statistical software
• Draws
  • 20k iterations, 2k burn in, thin of 5

Unpredictability at a fixed point in time

How often does the best team win?

GMs need to predict the future

GMs need to strategize

GMs need a longe-term plan

“They have to rethink their whole philosophy”

Mike Milbury on the 2016 Washington Capitals losing to Pittsburgh

• There’s an immense amount of luck involved in hockey. Rethinking your philosophy on a postseason series is ludicrous

Acknowledgements: Greg & Mike

Parity in sports