How often does the best team win?

Benjamin Baumer & Michael Lopez (with Gregory J Matthews)

How often does the best team win?

Michael Lopez, Gregory J Matthews, Benjamin Baumer

An anecdote

What we remember

What we forget

Pitches in the series

That pitch

The truth is…

What we also forget

About that error…


Luck and parity
in sports

Using statistics to assess luck in sports

How to define parity

the state or condition of being equal


What parity looks like

What parity does not look like

Parity checklist

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

A cross-sport model

Prior work



Team Line (\(\ell\)) Probability (\(p\)) Normalized
-127 0.559 0.548
+117 0.461 0.452

\[ p_i(\ell_i) = \begin{cases} \frac{100}{100 + \ell_i} & \text{ if } \ell_i \geq 100 \\ \frac{|\ell_i|}{100 + |\ell_i|} & \text{ if } \ell_i \leq -100 \end{cases} \,. \]


The model: definitions

The model & assumptions

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


  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







Unpredictability at a fixed point in time

How often does the best team win?



Who cares?

GMs need to predict the future

GMs need to strategize

GMs need long term plans

“They have to rethink their whole philosophy”

Mike Milbury to the 2017 Washington Capitals after a playoff series loss to Pittsburgh

Acknowledgements: Greg

Summary: parity in sports

More info: - Paper ( - Github (