Schedule strength in professional sports

Michael Lopez (with Gregory Matthews, Benjamin Baumer

Schedule strength in professional sports

Michael Lopez (with Gregory Matthews and Benjamin Baumer) https://github.com/bigfour/competitiveness.

What we’re told

What we’re told

Traditional approach for understanding wins

Wins = Skill + Luck

Proposed approach for understanding

Wins = Skill + Observable league factors + Unobservable factors

Observable league factors:

Who you play and when you play them

Who you play and when you play them

Where you play

How rested you are

Goals

A cross-sport model

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

A cross-sport model with rest

\[ E[\text{logit}(p_{(q,s,k) ij})] = \theta_{(q,s,k) i} - \theta_{(q, s, k) j} + \alpha_{q_0} + \alpha_{(q) i^{\star}} + \] \[ \beta_{(q,1)}(Rest_i) - \beta_{(q,2)}(Rest_j)\]

Worst rest differences, 2005-2016

Team League Home+ Home- Road+ Road- Net rest
Philadelphia Phillies MLB 30 38 12 32 -28
Los Angeles Lakers NBA 78 17 27 147 -59
Buffalo Bills NFL 9 11 5 11 -8
Columbus Blue Jackets NHL 83 32 21 104 -32

Best rest differences, 2005-2016

Team League Home+ Home- Road+ Road- Net rest
Oakland Athletics MLB 27 27 43 21 22
Milwaukee Bucks NBA 123 26 32 98 31
Carolina Panthers NFL 8 7 9 4 6
Anaheim Ducks NHL 124 24 23 97 26

Dissecting a schedule

\[ E[\text{logit}(p_{(q,s,k) ij})] = \theta_{(q,s,k) i} - \theta_{(q, s, k) j} + \alpha_{q_0} + \alpha_{(q) i^{\star}} + \] \[ \beta_{(q,1)}(Rest_i) - \beta_{(q,2)}(Rest_j)\]

Expected win totals

For team \(i\) in sport \(q\) in season \(s\),

\[ Wins_{(q, s) i}|\theta_{(q,s,k) i}, \theta_{(q,s,k) j }, \alpha_{q_0}, \alpha_{(q) i^{\star}}, \beta_{(q,1)}, \beta_{(q,2)} = \] \[\sum_{g}p_{(q,s,k) ij}*I(Home_{g,i} = 1) + \sum_{g}(1 - p_{(q,s,k) ij})*I(Home_{g,j} = 1)\]

Expected win totals

Wins due to rest =\[ Wins_{(q, s) i}|\theta_{(q,s,k) i}, \theta_{(q,s,k)j }, \alpha_{q_0}, \alpha_{(q) i^{\star}}, \beta_{(q,1)}, \beta_{(q,2)} - \] \[Wins_{(q, s) i}|\theta_{(q,s,k) i}, \theta_{(q,s,k)j }, \alpha_{q_0}, \alpha_{(q) i^{\star}}, \beta_{(q,1)} = 0, \beta_{(q,2)} = 0\]

Expected win totals

Wins due to opponent caliber =\[ Wins_{(q, s) i}|\theta_{(q,s,k) i}, \theta_{(q,s,k)j }, \alpha_{q_0}, \alpha_{(q) i^{\star}}, \beta_{(q,1)}, \beta_{(q,2)} - \] \[Wins_{(q, s) i}|\theta_{(q,s,k) i}, \theta_{(q,s,k)j } = 0, \alpha_{q_0}, \alpha_{(q) i^{\star}}, \beta_{(q,1)}, \beta_{(q,2)}\]

Preliminary results

team season Rest wins Schedule wins
Toronto Blue Jays 2006 -0.06 -1.44
Toronto Blue Jays 2007 -0.02 -2.34
Toronto Blue Jays 2008 -0.02 -2.77
Toronto Blue Jays 2009 0.03 -3.47

Preliminary results

team season Rest wins Schedule wins
Los Angeles Lakers 2006 -0.36 -0.45
Los Angeles Lakers 2007 -0.40 -0.88
Los Angeles Lakers 2008 -0.49 -2.69
Los Angeles Lakers 2009 -0.82 -1.00

Conclusions with respect to rest

Conclusions with respect to opponent strength

Conclusions with respect to opponent strength

Should this team have made the playoffs?

2011 World Series winning Cardinals (90 wins, +3.3 opponent wins)

Summary:

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

References

“How often does the best team win?”, Lopez/Baumer/Matthews

“The Vegas Flu”, Lopez, 2018

“Impact of rest”, McCurdy, 2017

“Scheduling effects in the NBA and NHL…”, Osborne, 2017 NESSIS