Schedule strength in professional sports

What we’re told

What we’re told

Traditional approach for understanding wins

• Behind most strength of schedule metrics
• Behind most approaches for assessing league parity

Proposed approach for understanding

Observable league factors:

1. Who you play and when you play them
2. Where you play
3. How rested you are

Who you play and when you play them

Who you play and when you play them

Where you play

How rested you are

Goals

• Incorporate “observable league factors” into a statistical model
• Understand impact of rest and relative opponent strength
• Derive schedule metrics

A cross-sport model

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

• \(p_{(q,s,k)ij}\) is probability that team \(i\) will beat team \(j\) in season \(s\) during week \(k\) of sports league \(q\), for \(q \in \{MLB, NBA, NFL, NHL\}\).
• \(\alpha_{q_{0}}\) and \(\alpha_{(q) i^{\star}}\) correspond to home advantage
• \(\theta_{(q,s,k) i}\) and \(\theta_{(q, s, k) j}\) be season-week team strength parameters
• See Ben’s talk tomorrow for more detail

A cross-sport model with rest

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

• \(Rest_i\): indicator for team \(i\) having a rest advantage
• \(Rest_j\): indicator for team \(j\) having a rest advantage
• \(\beta_{(q,1)}\): benefit to home team of having rest
• \(\beta_{(q,2)}\): benefit to away team of having rest

Worst rest differences, 2005-2016

Best rest differences, 2005-2016

Dissecting a schedule

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

• \(\theta_{(q,s,k) i}\): skill.
• \(\theta_{(q, s, k) j}\): who you play and when you play them
• \(\alpha_{q_0}, \alpha_{(q) i^{\star}}\): where you play
• \(\beta_{(q,1)}, \beta_{(q,2)}\): how rested you are

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

Preliminary results

Conclusions with respect to rest

• Small but non-negligible differences in rest
• NBA with largest rest impact, MLB with smallest
• Rest differences tend to even out over time
• Part of what’s considered a home advantage may be a rest advantage

Conclusions with respect to opponent strength

• Large differences in schedule strength in NFL and MLB
• Persistent in MLB, more variable in NFL
• Less of a schedule impact in NBA (conference differences aside)
• Small role of schedule in NHL

Conclusions with respect to opponent strength

• St. Louis Cardinals with easiest schedule (+ 2.2 wins a year)
• Baltimore Orioles with most difficult schedule (-2.8 wins a year)

Should this team have made the playoffs?

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

Summary:

• In which sport does rest matter the most? 🏀
• In which sport does opponent strength matter the most? ⚾️, 🏈
• In which sport is there a persistent schedule (dis)advantage? ⚾️

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