Benjamin Baumer & Michael Lopez (with Gregory J Matthews)

Michael Lopez, Gregory J Matthews, Benjamin Baumer

https://github.com/bigfour/competitiveness

- About 80% of pitches taken at this location called a strike (using advanced modeling)
- Walk worth about 12% in win expectency (32% to 44%)
- Red Sox were lucky!

- Jose Iglesias: 98.5% fielding percentage (
*Note*: Statcast data unavailable) - Error worth about 20% in win expectency over out at second (36% to 56%)
- Red Sox were lucky!

- Two huge swings in win probability that were outside the Red Sox control
- Red Sox were lucky!

in sports

- The best team does not always win. Sorry, Detroit

- How to untangle luck from skill?

- How often does the best team win in each sport? Luck —> parity

the state or condition of being equal

**Google**

- Equality at a fixed time
- Within season equality
- Between season equality

- Extend Glickman and Stern, 1998

- Problem 1: wins and losses alone insufficient (noisy)
- Problem 2: point differential non-generalizable
- Solution: if you can’t beat em, use their numbers in a statistical model

Team | Line (\(\ell\)) | Probability (\(p\)) | Normalized |
---|---|---|---|

-127 | 0.559 | 0.548 | |

+117 | 0.461 | 0.452 |

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

- \(p_{(q,s,k)ij} =\) 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

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

Assumptions:

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

- 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

How often does the best team win?

- Our team strengths are better at predicting future W-L

- Patriots rest starters in 2015 against Dolphins
- Home advantage matters in 🏈 and 🏀

“They have to rethink their whole philosophy”

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

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

- Unpredictability at a fixed time: 🏆 (NHL), ⚾
- Within season unpredictability 🏈
- Between season unpredictability 🏆 (NHL)
- Largest home advantage 🏀

More info: - Paper (https://arxiv.org/abs/1701.05976) - Github (https://github.com/bigfour/competitiveness)