STAT 479 Lecture 17

New NFL Overtime Rules

NFL Overtime

• NFL games consist of four 15-minute quarters
• What happens when the score is tied at the end of Q4?
  • Pre-1974: game declared a tie
  • 1974-2010: “sudden death” overtime
  • 2010-2022: modified sudden death
  • 2022-present: both teams get possession

Problems w/ Earlier Formats

• Sudden death: first team to score wins
  • One team can take possession, kick a FG, and win
  • Opposing team never possesses ball
  • Huge advantage to team w/ first possession

• Modified Sudden Death: can’t win with first-possession FG
  • If first team scores TD, game ends
  • If first team kicks FG or doesn’t score: second team gets possession
  • Team w/ first possession still has advantage

Proposed Solution

• Give both teams a chance to possess the ball
• If first team scores a TD, second team has chance to tie/win

• \(\mathbb{P}(\textrm{second team scores TD} \vert \textrm{first team scores TD})\)???
  • If prob. very low, is it reasonable to change the rule?
  • If prob. very high, can change team decision making

Estimating the Probability

• Idea: use empirical estimate
  • Find all drives following opening-drive TDs in OT
  • Compute proportion ending in TD
• Problem: prior to 2022, there were no such drives!

Model-based Simulation

• Starting context: down, distance, yardline, time, etc.
• Theoretically feasible to model play components:
  • Play type (run vs pass) given starting context
  • Yards gained & time elapsed given starting context & play type

• What about penalties???
  • Pre-snap penalty given starting context
  • Play type given starting context & no pre-snap penalty
  • Penalty during play given starting context & no pre-snap penalty
  • Yards gained & time elapsed given startign context, no penalties
  • Post-play penalty given all else…

Re-sampling Based Simulation

• Imagine simulating drive play-by-play
• Given starting context:
  • Find pool of similar existing plays
  • Randomly sample play from that pool
• Repeat until simulated drive ends

Challenges

• Unique decision-making environment
• In OT, trailing by \(<= 8\) points, second team
  • Will never punt or kick of a field goal nor attempt a fake
  • Must score a TD to extend the game
  • Is relatively unconcerned about time
• How to define “similar”??

Plan

1. Build a pool of plays from which to sample
2. Determine dist. of starting positions for second OT drive
3. Write function to sample similar play
4. Simulate & visualize drives

Starting & Ending Context

• Context variables: down and
  • yardline_100: how far to opponents endzone
  • ydstogo: how far to 1st down marker
• nflfastR includes unique drive identifier fixed_drive
  • Numbered consecutively (from 1) in each game

• Plan: group by game_id and fixed_drive
  • Use dplyr::lead() to get next value of context variables
  • For end-of-drive plays, need to set next_*to NA

Building Pool of Plays

• Team is trailing but by \(\leq 8\) points
• Exclude plays in final two-minutes
• Only include running & passing plays
• Must exclude fake punts & FGs

Defining Similar Plays

• Idea 1: Sample a play matching exact down, ydstogo, and yardline_100

• Idea 2: Exactly match ydstogo but allow some “wiggle room” for yardline_100 & down
• When down %in% c(1,2,3): exactly match down
• Second team in new OT will never punt or kick FG
  • Use 3rd and 4th down plays to simulate outcomes when down == 4

Adjusting yardline_100

• Similar outcomes on 1st and 10 from your 47 and from your 49
• Heuristic: sample plays starting from
  • yardline_100 \(\pm 3\): when yardline_100 b/w 90 & 60
  • yardline_100 \(\pm 2\): when yardline_100 b/w 60 & 40
  • yardline_100 \(\pm 1\): when yardline_100 b/w 40 & 10
  • yardline_100: when yardline_100 b/w 10 & 1
  • [90,99]: when yardline_100 b/w 90 & 99