Recently, the Rasch listserv (see www.rasch.org/rmt) has been discussing sports scoring and ranking using the Rasch Model. As the faculty coach for our sailing team for the last 6 years, I was interested that the only ranking of sailing teams was a coach's poll in Sailing World Magazine typically issued by 3 coaches. Clearly, the opportunity (and evidence) for bias and was the subject of much debate.
This issue came to a head about a year ago when 2 "at-large" berths were created at the Nationals with little factual information to use as the mechanism to add the last 2 teams to the district eliminations. The last team picked "at-large" won the national championship last year!
Scoring sailing is "as ordinal as you can get." Most contests are regattas with 2 to 4 divisions (A,B,C,D). Usually, one thinks of the A division as the best. The regatta consists of 4 to 36 races in a weekend between each division's competitors representing 4 to 20 teams.
A team's score is their ordinal place in each race added together at the end of the regatta. The lowest total wins, excluding tie-breakers, disqualifications and similar exceptions. No one cares if you win by 2 inches or 200 yards. The number of points doesn't always reflect skill, since strategy between divisions dictates sacrificing some points in a given division to ensure overall victory.
|Rasch measures vs. Coaches' Poll|
Last fall, I entered data on 71 regattas representing 142 teams into a Rasch analysis. Since regatta conditions vary widely by weather, type of boat, level of competition, and unknown factors, each regatta was a FACET you could call "harshness" or "difficulty" which represented the skill needed at that event.
The Figure contrasts the coach's poll and the Rasch measures for November, 2001. Old Dominion, OD,is ranked 2nd by the coaches, and 8th by Rasch. Brown, B, is ranked 13th by the coaches, and 5th by Rasch.
Along the top of the plot are teams unranked by the coaches, such as MIT, M, which is ranked 14th by Rasch. The Rasch results produced quite a conversation on the Internet and we're new collecting data for the spring season.
The Rasch measures are helpful in seeing distance between schools. The Rasch ranking of regattas made good sense to the sailors and they enjoyed that information. The biggest problem was the number of schools without common opponents or enough data to be measurable, such as Hawaii, ranked 8th by the coaches. Most schools were excited that Rasch measures were posted for all 142 teams.
Ranking and Measuring of Sailing Teams. Lang S. 15:4 p. 851
Ranking and Measuring of Sailing Teams Lang S. Rasch Measurement Transactions, 2002, 15:4 p. 851
|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
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