The Marble Game in R

By Alex Spurrier

January 9, 2018

The college football playoff selection process is broken.

The current College Football Playoff (CFP) was created to address the shortcomings of the Bowl Championship Series (BCS). Under the BCS system, a combination of polls and computer rankings were used to select two teams to play for the national championship. It seemed like a good idea, but controversial the results of the BCS system are well-documented. One of the most obvious flaws: several teams finished with an undefeated season and did not have a chance to play for a championship.

In the hope of mitigating BCS-like contoversy, the CFP relies on a selection committee to create a four-team playoff each year to determine the national champion. The selection committee’s ability to apply more subjective criteria was intended to prevent BCS-style controversy, but the past two seasons (2016-2017 and 2017-2018) led to a decent amount of controversy surrounding the selection of playoff teams. In a throwback to the BCS days, the 2017-2018 college football season ended with an undefeated team (Central Florida) that was not allowed to compete in the CFP.

Something needs to change

In response to the flaws of the CFP system, David Burge proposed an easy-to-comprehend alternative approach to determine which NCAA football teams would be invited to the four-team playoff called the “Marble Game.” The motivation behind the Marble Game is clear:

The rules of the Marble Game are simple:

  • Each team starts with a pre-determined amount of marbles.
  • If a team wins a home game, they take 20% of the loser’s marbles.
  • If a team wins a road game, they take 25% of the loser’s marbles.
  • Neutral site games are treated as home wins for the victor (20% marble transfer).
  • At the end of the season, the four teams with the most marbles are invited to participate in the CFP.

Using these rules, I created an R package, marblr, to simulate the results of the Marble Game. The marblr package uses game data scraped from Massey Ratings to simulate the Marble Game using Burge’s rules. Additionally, the marblr package allows for simulations that grant extra weight to teams from the Power Five conferences (ACC, Big 12, Big Ten, Pac-12, SEC, plus Notre Dame). As a default, teams from the Power Five start with 120 marbles, while all other teams start with 100.

Simulating the 2017-2018 Marble Game

The plot above illustrates the outcome of the Marble Game for each NCAA Division I FBS football team1. The first ten weeks of the season are very noisy - it’s hard to discern a clear top tier of teams - but a distinct cohort of competitive teams begins to separate from the pack between weeks 10 and 15. At the end of week 15, conference championships have been played and final bowl and CFP selections are made.

We know that Alabama, Georgia, Clemson, and Oklahoma were selected to play in the CFP for the 2017-2018 season, but which teams would have been invited to the CFP via the Marble Game?

Table 1: Marble Rankings after Week 15
Rank Team Marbles
1 Clemson 425
2 Ohio St 405
3 Oklahoma 405
4 UCF 385
5 Georgia 378
6 USC 353
7 Alabama 327
8 Wisconsin 310
9 Auburn 274
10 Miami FL 256

According to the Marble Game, Ohio State and Central Florida (the lone undefeated team) would have received CFP invites over Georgia and Alabama - teams that both won their first-round CFP games and made the national championship game in 2017-2018. At the same time, both Ohio State and Central Florida won their bowl games. It’s hard to make a definitive case for the groups of four produced by the CFP or the Marble Game.

Ideally, the Marble Game would be used to determine an 8-team playoff. Under this system, each Power Five conference has a strong chance for their champion to make the playoff and undefeated teams from non-Power Five conferences would have a chance too. Conferences with multiple championship-caliber teams could send more than one team to the playoff. Such a playoff would have created the following first-round games in 2017-2018:

  • Clemson (1 seed, ACC) vs. Wisconsin (8 seed, Big Ten)
  • Ohio State (2 seed, Big Ten) vs. Alabama (7 seed, SEC)
  • Oklahoma (3 seed, Big 12) vs. USC (6 seed, Pac-12)
  • UCF (4 seed, AAC) vs. Georgia (5 seed, SEC)

This bracket would resolve the controversy following this year’s selections. Each major conference is represented, stronger conferences (Big Ten and SEC) have multiple contenders, and a non-Power Five team (Central Florida) was able to enter based on the marbles they accumulated through an undefeated regular season.

I’d like to see the first round of the tournament hosted at the higher seed’s home field, with the semifinal and final rounds following the same process the CFP currently uses2.

Moving forward

College football deserves a better process for determining a national champion. There are simply too many seasons with more than four teams with a solid case to compete in a playoff. While the calendar and physical constraints prevent the development of a March Madness-style bracket in college football, expanding the CFP to an 8-team format could mitigate most of the controversy generated under past systems.

The CFP could continue their process of a selection committee, but the Marble Game is an attractive substitute. It places more weight and importance on winning late-season games - games that are either conference championships or rivalry games. It also would discourage programs from scheduling “cupcake” games; scheduling strong opponents would translate to better opportunities to increase a team’s marble count. Most importantly, the criteria for advancing to the playoff would be transparent, consistent, and fair to all teams.

It’ll never happen, but it’s a fun idea to consider.

  1. The only games that count for the purposes of the Marble Game are games between FBS teams - Alabama’s 56-0 drubbing of Mercer provides no useful information about Alabama’s potential to contend for a national title.

  2. The current semifinal games rotate between the following bowl game pairings each year: Rose Bowl and Sugar Bowl; Orange Bowl and Cotton Bowl; and the Fiesta Bowl and Peach Bowl. The site of the championship game is determined through a bidding process.

Posted on:
January 9, 2018
6 minute read, 1069 words
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