Here is Princeton's profile:
ARPI Rank: #31
Non-Conference ARPI Rank: #18
Results Against Top 60 Teams Rank: 55
Standing Within the Ivy League: 5
Ivy League Average ARPI: .5376
Ivy League ARPI Rank: 8
Head to Head Results Against Top 50 Teams Score and Rank: -1.67/56
Common Opponent (With Other Top 60 Teams) Results Score and Rank: -0.18/29
Last 8 Games Score: -12
Several of these aspects of the profile are ones I've developed as surrogates for some of the NCAA's at large selection criteria. I developed them in order to be able to create a computer program that will make objective decisions rather than relying on my own or others' subjective decisions.
- Results Against Top 60 Teams assigns values to wins and ties against Top 60 teams, with those teams broken down into subgroups by ARPI rank. The higher the opponent's rank, the higher the score for a win or tie against the opponent. The points awarded are on a geometric scale, so good results against very highly ranked teams are very valuable. Apart from the ARPI, I have found this profile aspect to be the most consistent with the Committee's decisions.
- Head to Head Results assigns values to wins, ties, and losses in head to head games against Top 60 teams. It then averages each team's scores for all head to head games based on the number of those games, to give an average score per head to head game. This factor, unlike the Results Against Top 60 Teams, does not distinguish among the Top 60 teams based on their ranks. A positive score is good and a negative score is bad.
- Common Opponent Results identifies each common opponent a team had with another Top 60 team, compares the two Top 60 teams' results against that opponent, and assigns scores based on the comparison to the two Top 60 teams' results. It then averages each team's scores for all of its common opponent games based on the number of those games, to give an average score per common opponent game. A positive score is good and a negative score is bad.
- Last 8 Games is a surrogate for an NCAA criterion. The NCAA criterion looks at a team's results over the last 8 games. I've found no evidence that the Committee actually uses that criterion, and I'm not sure what it is looking for, but my best guess is it's looking for poor results. Based on that guess, as a surrogate my system looks at poor results over the course of the season, assigning negative values based on how poorly ranked the team is against which the poor result occurred.
When my system evaluates teams, it compares the aspects of their profiles, either as individual factors or as paired factors (such as ARPI rank combined with Top 60 Results rank), to the patterns of the Committee's decisions over the last 9 years. The patterns are a set of "standards":
- A "yes" standard means that over the last 9 years, a team that met that standard always got a "yes" decision from the Committee either for a particular seed or for an at large selection.
- A "no" standard means that over the last 9 years, a team that met that standard always got a "no" decision from the Committee either for a particular seed or for an at large selection.
If a team this year meets both "yes" and "no" standards, what that means is the Committee has not met a team with this one's profile, over the last 9 years. Princeton is in that position this year.
In terms of "yes" standards, the most obvious one for Princeton is ARPI Rank: an ARPI rank of #34 or better is a "yes" standard.
Here are other "yes" standards that Princeton meets:
- ARPI Rank <=35 and ANCRPI >=0.6168
- ARPI Rank <=43 and ANCRPI Rank <=22
- ARPI Rank <=37 and Conference ARPI >=.5322
- ANCRPI Rank <=22 and Conference Standing <=6
- ANCRPI Rank <=19 and Conference Standing <=5.75
- ANCRPI Rank <=19 and Top 60 Common Opponent Score >=-2.21
- ANCRPI Rank <=22 and Top 60 Common Opponent Score >=-2.10
It's important to note that all of Princeton's "yes" standards are based on either the ARPI or the ANCRPI.
In terms of "no" standards, here are the ones Princeton meets:
- Top 60 Head to Head Results Score <=-1.37
- Top 60 Results Rank >=54.5 and Conference Standing >2
- Top 60 Results Rank>=45 and Last 8 Games Score <=-11
- Top 60 Results Rank >=46 and Last 8 Games Score <=-10
- Top 60 Results Rank >=51 and Last 8 Games Score <=-8
- Top 60 Results Rank >=54 and Last 8 Games Score <=-5
- Conference Standing >=3.75 and Top 60 Head to Head Results Score <=1.33
- Top 60 Head to Head Results Score <=-1.25 and Last 8 Games Score <=-4
Based on this evaluation, the Committee could go either way with Princeton. They have the RPI in their favor. Except for that, however, their profile is against them.
This raises the question of how the Committee members look at the RPI. Princeton is an example of a problem the RPI has. When one calculates the Strength-of-Schedule portion of the RPI (effectively weighted at 50% of the RPI itself), the formula gives an effective weight of 80% to the opposing team's winning percentage and only 20% to its opponents' winning percentages. In other words, what Team A contributes to its opponents' strength of schedule is mostly Team A's winning percentage. A result of this is that, if one compares a team's ARPI rank to its rank in terms of what it contributes to an opponent's strength of schedule, those two ranks can be quite different. I ran some calculations this morning, and the ranks of Princeton's opponents in terms of what they contribute to its strength of schedule are roughly 9 positions better, on average, than their ARPI ranks. In other words, Princeton is a beneficiary of this flaw in the RPI formula. I ran some other very crude calculations and came up with an RPI-flaw-corrected rating of #38. I haven't done this for the ANCRPI, but presumably Princeton's ANCRPI rank likewise would be poorer if flaw-corrected. It's thus possible that with corrections Princeton would not meet any "yes" standards. Whether the Committee members understand this RPI flaw, and if they do are willing to take it into account, is something I don't know.
Given all of this, in my Bracket Simulation, I had to make a choice of what I think the Committee will do about the previously unseen profile that Princeton presents. My choice was that the Committee will not give Princeton an at large selection. I most certainly, however, could be wrong.