Friday, March 12, 2021

Cake Cutting in Overtime

There's a new proposal out of Baltimore for a new way to handle overtime in National Football League games. This post is about American Football, soccer has its own overtime issues we won't talk about here.

Instead of randomly choosing who gets the ball, which gives an advantage to the team on offense, the Raven's coach John Harbaugh suggests a "spot and choose" rule based on cake cutting. One team picks a starting position and the other team decides whether to be on offense or defense.

Sounds intriguing but there's a problem. In cake cutting, if you cut off a crumb, everyone would definitely choose the rest of the cake. But in football suppose the spotting team chose the offensive's team one-yard line (99 yards needed for a touchdown). For spot and choose to work the one-yard line would have to be an obvious choice for defense. But many teams might still choose starting at the one-year line on offense. There's a chance you can march down the field and if not you can always punt it away. So the team that gets to choose whether to be on offense could get an advantage no matter what the spotting team did.

I still like the idea of "spot and choose". Maybe you let the first team choose not only the yard line but what down to start. Because no one would start at their one yard line at 4th down.

Are there variations for spot and choose in other sports? I like using game theory to figure out how to play actual games. 


  1. When connection games such as Hex, TwixT, or the Shannon switching game are played competitively (e.g., TwixT is played at the Mind Sports Olympiad), the standard procedure is for one player to make an initial move and for the other player to have the option of switching sides. Theoretically, of course, the player who has the option of switching sides has a winning strategy, but in practice, the high computational complexity of determining which side is winning means that the game is approximately balanced.

  2. Interesting idea to bring downs into it. Have you talked to "football people" to ask about preference for offence even on the 1 yard line? The goal would be to have enticement to offer something good enough that the other team would choose to defend, right?

  3. It's fairly well understood what the expected points are from various yard lines, downs, and distances. NFL teams would choose defense every time rather than start on offense at the 1.

    1. I found this analysis and it does only give a 10% chance of scoring from the 1 so I see your point. Nevertheless you can still punt and I'm still not sure how many teams, especially with good offenses, will choose to play defense. Maybe we'll get the chance to see.

  4. I like the spot and choose proposal.

    (btw, the Ravens coach is John Harbaugh. His brother Jim is the coach of the Michigan Wolverines.)