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2012 Bracket Critique

2012 Bracket Critique

The NCAA Selection Committee and the Dominetrics rankings agreed on 33 of the 37 at-large bids given for this year’s post-season tournament.  The four difference of opinion appear in the table below.

Invited by the NCAA but not invited by Dominetrics Invited by Dominetrics but not invited by the NCAA
Notre Dame (Dominetrics Rank:  51) Marshall (Dominetrics Rank:  29)
South Florida (Dominetrics Rank:  54) Northwestern (Dominetrics Rank:  37)
California (Dominetrics Rank:  55) Akron (Dominetrics Rank:  41)
Iona (Dominetrics Rank:  58) Ole Miss (Dominetrics Rank:  46)

Note:  The final at-large invitee in the Dominetrics rankings is Texas, whose Dominetrics rank is 48.

To look for the reasons for these four disagreements between the NCAA Selection Committee and Dominetrics, it’s useful to decompose Dominetrics into its four components.  Recall that Dominetrics removes the subjective cardinal coefficients that the NCAA uses to compute the RPI, but it preserves the importance-ordering over the RPI’s components that is implied by those cardinal coefficients.  That importance-ordering is (1) Opponents’ winning %, (2) Own non-home winning %, (3) Opponents’ opponents’ winning %, and (4) Own home winning %. 

Thus, in the table below, D1 is the Dominetric that would be earned if only category (1) were used, D2 is the Dominetric that would be earned if only categories (1) and (2) – in that order of importance – were used, D3 is the Dominetric that would be earned if only categories (1), (2), and (3) – in that order of importance – were used, and D4 is the full dominetric that was earned using categories (1), (2), (3), and (4) – in that order of importance.  The table below shows this decomposition for the eight teams in the table above as well as a ninth team – Texas – which was the last at-large team selected by Dominetrics.

Team D1 D2 D3 D4 = Dominetric
Marshall 317 264 263 243
Northwestern 305 255 256 224
Akron 223 215 213 215
Ole Miss 251 198 200 202
Texas 317 203 203 200
Notre Dame 261 183 183 193
South Florida 279 185 185 187
California 173 172 173 185
Iona 51 172 173 176

Marshall’s opponents had the 14th highest winning % out of the 344 NCAA Division 1 teams, and Northwestern’s opponents had the 21st highest winning % out of this same group.  Each team’s Dominetric falls off somewhat – to 264 and 255, respectively – when non-home winning % is taken into account, but this leaves both teams well above the cutoff Dominetric of 200 compiled by Texas.

South Florida and Notre Dame played tough schedules, too:  their opponents’ winning percentages ranked 33rd and 42nd, respectively.  Their ensuing poor non-home winning percentages, however, knocked them below the benchmark Dominetric of 200 earned by Texas.  Notre Dame’s non-home winning % tied for 157th place, while South Florida’s non-home winning % tied for 172nd place.  In contrast, Marshall’s non-home winning % tied for 96th best, while Northwestern’s non-home winning % tied for 104th best.

Notice that Akron and California scheduled fairly closely to the strength of their teams.  But Akron played to the level of a tougher schedule while Cal played to the level of a schedule that was not as difficult.

Iona scheduled beneath the strength of their team.  By the time that Iona’s excellent work in non-home games is taken into account, they are on a par with California, but still well short of Texas, on whom they gain little as the final two winning % categories are added to the Dominetric calculations.

The Dominetrics rankings would have produced the following breakdown of invitations by conference:

Big East 7
Big 10 6
Big 12 6
ACC 5
SEC 5
Mountain West 4
Atlantic 10 3
Conference USA 3
West Coast 3
Mid-American 2
Missouri Valley 2
Pacific 12 1

The NCAA Selection Committee gave 26 at-large invitations to the Big 6 power conferences and 11 at-large invitations to the mid-major conferences.  Dominetrics would have given 24 and 13, respectively.

When the NCAA constructed its RPI by using cardinal weights of 0.5 for opponents’ winning %, 0.25 for opponents’ opponents winning %, and 0.25 for “adjusted” own winning %, and then implemented the “adjustment” to the own winning % by weighting road wins by 1.4, neutral wins by 1.0, home wins by 0.6, road losses by 0.6, neutral losses by 1.0, and home losses by 1.4, it generated the importance-ordering already mentioned in this discussion:  (1) Opponents’ winning %, (2) Own non-home winning %, (3) Opponents’ opponents’ winning %, and (4) Own home winning %. 

Thus, the NCAA sends a message to all college coaches and players about what it deems important.  The decisions of the Tournament Selection Committee should remain consistent with this message.  The basic Dominetric critique of the RPI is the cardinal weights of 0.5, 0.25, 1.4, 1.0, and 0.6 are subjective and can be distortionary.  The Dominetric alternative removes these subjective cardinal weights while preserving the importance-ordering over the four key winning percentages, thereby preserving the NCAA’s message and eliminating any distortions caused by the subjective cardinal weights.

When teams such as Marshall, Northwestern, Akron, and Ole Miss heed the message of the NCAA and produce deserving winning percentages in the four categories of performance that the NCAA says it values, these teams should be invited to the tournament.