Social choice theory in 10,000 meters: examining independence and transitivity in the NCAA cross-country championships.
Mixon, Franklin G., Jr. ; King, Ernest W.
I. Introduction and Background
A recent study by Hammond (2007)--one that is built on the
"long ... recognized [result] that our methods for making social
and political choices may violate desirable principles such as
transitivity and the Pareto principle ... (see Arrow, 1963; Sen, 1970;
Schwartz, 1986; Brains and Fishburn, 2002) ..."--delves into
scoring methods in athletic events as a way of illuminating social
choice problems. In that regard, Hammond's study follows a decades
old tradition (see McKay, 1980; Saari, 2001) that examines scoring in
popular Olympic competitions, such as decathlon, track, and figure
skating. Hammond follows and extends Saari (2001) by showing that in a
multi-team high school girls' cross-country (track) meet, which is
a long-distance race that does not take place on a standard oval track,
violations of long-established social choice principles can and do
occur.
As Hammond (2007: 360) explains, a team's score in a
cross-country meet is "based on the sum of the positions in which
some k of the team's runners finished the race." For example,
in the NCAA Division I men's cross-country championships,
participating teams bring seven runners, though k equals the top five
finishers for scoring purposes. Hammond also points out that on occasion
three or more teams will participate in a cross-country meet, yet
officials may score the event as (1) a single three-way meet (i.e., A
versus B versus C), or (2) three separate dual meets (i.e., A versus B,
A versus C, and B versus C). (1) These two choices have profound
implications for determining the order of finish in cross-country meets,
and thus have similarly profound implications regarding the three
different general purposes of scoring methods used for cross-country
meets. According to Hammond:
"First, we usually want to find an overall winner of the meet:
of all the teams running, which is the 'best'? Second, we may
also want a ranking of how the teams finished: we are often interested
in the top-3 finishers, for example, not just the first; it is most
desirable, of course, to finish first, but it is often considered
noteworthy to have finished second or third (think of the awarding of
the silver and bronze medals in the Olympics, in addition to the gold).
Third, we sometimes also want to be able to compare teams by pairs, as
when a multi-team ([greater than or equal to] 3) meet is scored as
several dual meets, so that we may know whether team A is better than,
as good as, or worse than team B, no matter how they fared against other
teams. (p. 360)"
As Hammond indicates, the current scoring method for cross-country
is plagued by two problems related to inconsistency and ambiguity in the
results--problems that can be characterized as violations of the
principles of independence from irrelevant teams (IIT) and transitivity.
(2) The principle of IIT means that whether team A is scored as
defeating, tying or losing to team B should not be affected by whether
team C's results are included in the scoring. (3) The principle of
transitivity means if team A beats team B, and team B beats team C, then
team A should be expected to beat team C. (4) Interestingly, these
social choice principles can be violated in an order-of-finish scored
meet (as described above) when, for any combination of participating
teams (m) and runners' scores counted (k), there are at least three
participating teams (m [greater than or equal to]3) and at least three
runners' scores (k [greater than or equal to]3) counted toward each
team's overall score (Hammond, 2007). (5) Using data from a
girls' high school cross-country meet in Michigan, Hammond
demonstrates that such violations are not simply academic concerns--they
do occur.
How might cross-country officials clean up or avoid such messes?
There are at least two possible solutions. First, we could retain the
current scoring method, but for multi-team meets (m [greater than or
equal to]3) the winner of the overall meet would be that team which
defeated the most other teams in the pairwise comparisons, using the
standard order-of-finish dual-meet scoring method. This approach is a
direct analogue of what is called a "Condorcet winner" in
social choice theory: the actor or option that defeats the most other
actors or options in pairwise, head-to-head comparisons is the winner.
Second, Hammond (2007) points out that a "sum of the
times" method of scoring, whereby the top k runners' times are
summed for each team, would prevent the types of outcome cycles
described above. However, the high school coaches interviewed by Hammond
listed several concerns with using such a scoring method instead of the
traditional approach, suggesting that (to them) the costs of a "sum
of the times" scoring method (e.g., possible injury/burnout from
added incentive to run harder in pre-championships meets) may be greater
than the benefits associated with avoiding violations in these social
choice principles. Finally, some of the coaches also told Hammond that,
though such violations as found at their cross-country meet were
regrettable, they had never seen nor heard of such violations of IIT and
transitivity in prior meets. Thus, their expectations are that these are
rare occurrences in the high school cross-country universe.
The present note begins where Hammond's study ended, by
examining the results from both the 2008 and 2009 NCAA Division I
men's cross-country championships. To the extent that the high
school coaches interviewed by Hammond are correct, one would expect that
finding violations in the two main social choice principles from these
two cross-country meets would be difficult. At the same time, one would
also expect that college cross-country coaches would be much more
concerned about such violations, given their relatively high level of
compensation, including performance bonuses, and the added pressure they
face to win on a national, not local, level. As such, any findings using
NCAA results that support Hammond, and thus refute the expectations of
the high school coaches who were canvassed therein, should be of
interest to college cross-country coaches and athletics administrators
and officials, as well as to public choice scholars and students, if not
high school cross-country coaches.
II. Violations of IIT and Transitivity from the NCAA Championships
A look at the results from the 2008 and 2009 NCAA Men's
Division I Cross-Country Championships reveals some of the violations of
social choice principles discussed and observed by Hammond. As Table 1
indicates, the 2008 NCAA Division I men's cross-country
championship meet was won by Oregon with an overall score of 93, placing
it above the other 30 participating institutions. Oregon was followed by
Iona, Stanford, Wisconsin, and Auburn using traditional m-way meet
scoring for m=31 and k=5. However, Wisconsin's ranking (4th) above
Auburn (5th) was due to the presence of other (irrelevant) teams, as
Auburn defeats Wisconsin by a score of 28 to 29 according to dual meet
scoring. Similarly, Brigham Young, which finished 9th overall, defeats
Oklahoma State, which finished 8th overall, by a score of 27 to 28 using
dual meet scoring. (6) Both of these involve IIT problems among top ten
finishers, while the former involves an IIT violation among two top five
institutions.
Another issue arises with regard to transitivity. For example, a
dual meets series between Northern Arizona (6th overall), Portland (7th
overall) and Georgetown (tied for 10th overall) produces a cycle.
Specifically, Portland defeats Northern Arizona (27 to 28), Northern
Arizona defeats Georgetown (27 to 28), and Georgetown defeats Portland
(27 to 28). A second cycle involves Oklahoma State (8th overall),
Alabama (tied for 10th overall), and Iowa State, which finished outside
of the top 10. Here, Iowa State defeats Alabama (27 to 28), Alabama
defeats Oklahoma State (27 to 28), and Oklahoma State defeats Iowa State
(24 to 30) in a dual meets series. This cycle is repeated when Brigham
Young (9th overall) replaces Oklahoma State.
The dual meets analysis described above was carried further in
order to re-rank the 31 participants in 2008. To do so, the teams'
wins and losses, based on standard two-team meet scoring rules (see
Appendix), from the 465 dual (pairwise) meets are tabulated in order to
produce an overall record consisting of 30 contests for each team. Those
(Condorcet) records and overall (Condorcet) rankings are provided on the
right-hand side of Table 1. The various "highlights" from dual
meets competition that are described above are also included in this
portion of Table 1. Because each of the teams meet in head-to-head
competition in the dual meets construct, ties can generally be broken,
unlike the case of traditional m-way scoring. (7) As pointed out in
Table 1, with its 30-0-0 (wins-losses-ties) record, Oregon would have
been declared national champion on a dual meets basis. Rather than its
26-4-0 record using traditional m-way scoring, Auburn earns a record of
27-3-0 on a dual meets basis. Similarly, Portland improves its m-way
scoring record from 23-7-0 to 23-6-1 using a dual meets approach, while
Georgetown moves from 20-9-1 to 23-7-0, an improvement of 8.3 percentage
points. As stated above, Georgetown improves its ranking from 10th (tie)
using traditional m-way scoring to 8th based on dual meet scoring.
The results from the 2009 championship meet are contained in Table
2. Some of the violations of social choice principles observed in the
2009 results are possibly more egregious than those found for 2008. For
instance, although Oklahoma State defeated 30 other institutions to win
the 2009 championships using traditional, m-way meet scoring, it would
have fallen to Northern Arizona (4th overall) in a dual meet setting.
Put differently, a dual meets series would have resulted in a tie for
first between Oklahoma State and Alabama (3rd overall); our Table 2
ranking places Oklahoma State above Alabama as a result of Oklahoma
State's victory over Alabama in a dual meet setting. However,
Alabama still retains a better position--2nd place instead of 3rd
place--as a result of its victory over Oregon (2nd overall) in a dual
meets series. Thus, the violations of IIT found here impact the way the
top three teams finish in the overall championships. (8)
The 2009 results also produce an interesting cycle between Colorado
(6th overall), Iona (tied for 8th overall), and Stanford (tied for 10th
overall). In a dual meets series, Stanford ties Iona (28 to 28), Iona
ties Colorado (28 to 28), yet Colorado is defeated by Stanford (30 to
26). Two other cycles--one between Oklahoma State (1st overall), Oregon
(2nd overall), and Northern Arizona (4th overall), and the other between
Oklahoma State, Alabama (3rd overall), and Northern Arizona--are also
found among the top 10 teams in Table 2. In the first cycle, Northern
Arizona defeats Oklahoma State (27 to 28), Oklahoma State defeats Oregon
(22 to 33), yet Oregon defeats Northern Arizona (26 to 29). In the
second cycle, Northern Arizona defeats Oklahoma State (27 to 28),
Oklahoma State defeats Alabama (23 to 32), yet Alabama defeats Northern
Arizona (27 to 28). Interestingly, both of these cycles involve top four
finishers from the 2009 championships.
As was done for 2008, the dual meets analysis described above was
again carried further in order to re-rank the 31 participants in 2009.
To do so, each team's wins and losses from a dual meets series are
tabulated in order to produce an overall record. Those (Condorcet)
records and overall (Condorcet) rankings are provided on the right-hand
side of Table 2. The various "highlights" from dual meets
competition that are described above are also included in this portion
of Table 2. Note that on a dual meets basis, Oklahoma State wins the
national title, but not with the 30-0-0 record it achieved with
traditional m-way scoring. Instead, Oklahoma State finishes with a
record of 29-1-0, owing to a dual meet loss to Northern Arizona. By
virtue of its dual meet victory over Oregon, Alabama finishes 29-1-0
instead of 28-2-0, while Oregon's record moves from 29-1-0 to
28-2-0 when a dual meets series is used instead of traditional m-way
scoring. Again, these changes in records result in changes in the
respective rankings, as pointed out in Table 2.
A solution to the violations of IIT principles and transitivity
proposed by Hammond (2007) is to simply sum the times of each
team's qualifying runners (top 5) and use that sum to rank the
teams participating in a given year's championships. A look at how
that proposal may have impacted the 2008 and 2009 NCAA Championships is
presented in Table 3.9 The sum of times (hereafter SoT) scoring method
would have generated national titles for Oregon and Oklahoma State in
2008 and 2009, respectively, thus leaving the actual outcome unaffected.
However, Northern Arizona would have been able to claim a second place
finish in 2009, up from fifth, while Stanford would have finished
seventh instead of tenth that same year. Using SoT in 2008 would perhaps
have resulted in minor upward changes only among those teams finishing
in the top 10. As Table 4 indicates, Portland, Oklahoma State, and
Georgetown may have secured an improvement of one spot each using SoT
scoring.
The high school cross-country coaches referenced in Hammond
indicate opposition to SoT scoring, pointing out that such a system
favors teams with one or two world-class runners. However, collegiate
golf generally operates on a sum of scores method that is equivalent to
sum of times in cross-country to determine its national champion each
year. Clearly, a sum of scores method in golf, as opposed to a sum of
positions method such as that used in cross-country, favors collegiate
golf teams with one or two PGA-caliber golfers. An interesting example
comes from the 2011 NCAA East Regional, where Duke defeated Georgia Tech
by a three-day total of 865 to 869 to take first place. However, Duke
would have scored a 51 based on the placement of its top four golfers
(5th, 8th, 19th, and 19th), while Georgia Tech would have scored a 49 on
that basis (2nd, 2nd, 17th, and 28th).
The three ranking procedures presented here traditional m-way
scoring, dual meets scoring, and sum of times scoring--provide three
unique ranking outcomes. Given the relative importance of changes among
the top 10, Spearman rank-correlation coefficients for the top 10 in
both 2008 and 2009 are provided in Table 4. As indicated there, the
rank-correlations between traditional m-way scoring and dual meets
scoring for 2008 and 2009, respectively, are +0.920 and +0.954,
reflecting the differences discussed above. When the 2008 and 2009
rankings for traditional m-way scoring and sum of times scoring are
compared, the rank-correlation coefficients are +0.957 and +0.888.
Finally, 2008 and 2009 comparisons of dual meets scoring and sum of
times scoring produces rank-correlation coefficients of +0.882 and
+0.867, respectively. These coefficients, ranging from + 0.867 to +
0.957, respectively, reflect the noticeable differences in outcomes when
various scoring methods are used in collegiate cross-country
championships.
It is not surprising, even given the results in Hammond and here,
that high school cross-country coaches fail to appreciate fully the
significance of violations of IIT and transitivity principles in
cross-country meets using traditional m-way scoring. Even with such an
appreciation, interest in making changes to the sport at that level
might be as low as the salary stipends awarded to its coaches. High
school cross-country salaries are but a small fraction of a high school
teacher's base salary plus benefits. However, according to a 2010
NCAA report on revenues and expenses included in Sander (2010), the
median salary (with benefits) of collegiate head cross-country/track
coaches for 2009 is $79,000. (10) The median allotment by universities
to cross-country/ track coaches' salaries is $184,000. At the
individual level, a 2007 report by espn.com stated that the University
of Oklahoma's head cross-country/track coach, Martin Smith, was
awarded a raise in base pay from $117,000 to $130,000 per year after
winning the Big 12 outdoor track title earlier that year. A
contemporaneous report by Shinn (2007) indicates that Smith's
assistant coaches also received raises of $17,000 and $8,000, pushing
their respective base salaries to $80,000 and $60,000. (11) Even with
these relatively large figures, however, Oklahoma is not a perennial top
10 finisher (see Tables 1 and 2) at the collegiate level.
These aggregate NCAA figures in Sander apparently do not include
bonuses for winning conference/ national championships, finishing among
the top 10 (five; three) in the NCAA championships (or regionals), or
finishing runner-up at the NCAA meet. Contractual provisions, such as
performance bonuses as small as 10 percent, would increase the aggregate
NCAA figures above by about $8,000 and $18,000, respectively. These
represent one-time payments that are separate from base pay increases,
as in the Smith case above. The figures also do not include potential
earnings from summer camps and other types of coaching clinics and/or
personal training. These can add significantly to a college coach's
institution-based earnings. Thus, collegiate-level cross-country
coaching is much more lucrative than its high school-level counterpart,
and, as such, one would think that coaches at this level would be more
interested than their high school counterparts in scoring or outcomes
cycles of the types discussed in Hammond and in this study.
III. Concluding Comments
Hammond explains that the current scoring method for high school
cross-country is potentially plagued by two problems related to
inconsistency and ambiguity in the results--problems that can be
characterized as violations of the principles of independence from
irrelevant teams (IIT) and transitivity. The principle of IIT means that
whether team A is scored as defeating, tying or losing to team B should
not be affected by whether team C's results are included in the
scoring, and the principle of transitivity means if team A beats team B,
and team B beats team C, then team A should be expected to beat team C.
Hammond shows, using results from a girls' high school
cross-country meet in Michigan, that violations of both of these
principles are present in cross-country scoring.
Our study supports and extends Hammond by examining the results
from the 2008 and 2009 NCAA Division I cross-country championships.
Again, both types of scoring problems found in Hammond are present.
However, unlike high school-level cross-country, we show that salaries,
bonuses, and budgets at the collegiate level can be substantial, so that
any inconsistencies and ambiguities in the scoring mechanism can be
quite costly for individuals and institutions. In this case, violations
of social choice axioms can lead to distortions in salaries, bonuses and
other types of remuneration and rewards. As for a solution, Condorcet
rankings could be tabulated; the highest-ranking teams would be those
that defeated the most other teams in head-to-head comparisons of team
performance. This approach would involve relatively modest changes in
the standard scoring procedures. Alternatively, Hammond's
suggestion of a "sum of the times" scoring method could be
considered by both high school- and collegiate-level cross-country
coaches, at least for championship meets. There, runner burnout and
other considerations related to some subset of a cross-country team not
putting forth maximum effort are minimal or near nonexistent compared to
meets associated with regular season competition. It is also at these
types of meets where, at the collegiate level, bonuses and other forms
of compensation are perhaps most significantly impacted.
APPENDIX
Cross-Country Scoring from the 2009 NCAA Men's DI
Championships Oklahoma State, the winner of 2009 Men's Division I
championships, placed its seven runners in 7th, 8th, 11th, 24th, 77th,
80th, and 123rd overall. William & Mary, which finished 5th overall,
placed its seven runners in 15th, 30th, 35th, 45th, 101st, 167th, and
176th overall. Stanford, which finished 10th overall, placed its seven
runners in 2nd, 33rd, 46th, 93rd, 180th, 196th, and 209th overall. Using
the traditional scoring method (k=5) for an m-way meet, these teams
scored 127 (i.e., 7+8+11+24+77), 226 (i.e., 15+30+35+45+ 101), and 354
(i.e., 2+33+46+93+ 180), respectively.
Had the meet been scored as individual dual meets for each
participating school, Oklahoma State would have defeated William &
Mary 20 to 36. This result is obtained because Oklahoma State's top
three runners finished in the top three spots, followed by William &
Mary's top runner in 4th, followed by Oklahoma State's
fourth-fastest runner in 5th, followed by William & Mary's
second- through fourth-fastest competitors in 6th, 7th, and 8th.
Oklahoma State's fifth-fastest racer finishes in 9th, followed by
its sixth- fastest runner in 10th. Note that this last runner's
score is not counted as part of Oklahoma State's total. However, he
does push William & Mary's fifth-fastest competitor into 11th
overall, (1) Thus, William & Mary's score of 36 comes from
(4+6+7+8+11), while Oklahoma State's total of 20 is obtained from
(1+2+3+5+9). Similarly, Oklahoma State defeats Stanford in a dual meet
by a score of 22 (i.e., 2+3+4+5+8) to 36 (i.e., 1+6+7+ 10+12), while
William & Mary defeats Stanford in a dual meet by a score of 25
(i.e., 2+3+5+6+9) to 32 (i.e., 1+4+7+8+12).
(1) Oklahoma State's sixth-fastest runner placed 80th overall
at the 2009 NCAA championships. Though his "80" was not added
to the team's total, this particular runner's presence in the
race did mean that William & Mary's fifth-best finisher placed
101st instead of within the top 100 finishers, thus raising William
& Mary's points total. Similarly, Alabama's sixth-best
finisher, who placed 94th overall, also contributed to William &
Mary's point total being one point higher, than it would have been
had Alabama, which finished 3rd overall in 2009, not included its
runners who finished sixth and seventh among the team's
participants in this particular meet. Thus, a given team's sixth
and seventh finishers do potentially impact the overall scores of the
other teams at the NCAA cross-country championships.
Acknowledgements
The authors thank an anonymous referee and Bill Bosshardt for
helpful comments. Any remaining errors are our own.
References
Arrow, K.J. (1963). Social Choice and Individual Values. New Haven:
Yale University Press.
Brams, S.J. and P.C. Fishburn (2002). "Voting
Procedures." Pp. 173-236 in Handbook of Social Choice and Welfare,
edited by K.J. Arrow, A.K. Sen and K. Suzumura. Amsterdam:
North-Holland.
Hammond, T.H. (2007). "Rank Injustice? How the Scoring Method
for Cross-Country Running Competitions Violates Major Social Choice
Principles." Public: Choice, 133: 359-375.
MacKay, A.F. (1980). Arrow's Theorem: The Paradox of Social
Choice. New Haven: Yale University Press.
Plott, C.R. (1976). "Axiomatic Social Choice Theory: An
Overview and Interpretation." American Journal of Political
Science, 20:511-596.
Saari, D.G. (2001). Decisions and Elections: Explaining the
Unexpected. New York: Cambridge University Press.
Sander, L. (2010). "Balancing the Books." The Chronicle
of Higher Education, 18 August 2010, Retrieved [6 October 2011]
(http://chronicle.com/blogs/players/balancing-the-books/26319).
Sen, A.K. (1970). Collective Choice and Social Welfare. San
Francisco: Holden-Day.
Schwartz, T. (1986). The Logic of Collective Choice. New York:
Columbia University Press.
Shinn, J. (2007). "Throwing Some Money Around." The
Norman Transcript, 27 June 2007, Retrieved [6 October 2011]
(http://normantranscript.com/
ousports/x518988697/Throwing-some-moneyaround).
Notes
(1.) See the Appendix for an example from the 2009 NCAA Men's
Division I cross-country championships.
(2.) Hammond points out that a violation of the former principle
involves a violation of the Weak Axiom of Revealed Preference (WARP), as
in Plott (1976).
(3.) This is the athletic contests' counterpart of
Arrow's independence from irrelevant alternatives (IIA).
(4.) Hammond is correct to point out that "... intransitivity
is often observed across athletic contests: in league competition, for
example, we often observe that team A will beat team B, team B will beat
team C in a subsequent contest, but team C will beat team A in yet
another contest ... Hence, we should not be disturbed by intransitivity
in a series of athletic competitions ... But for a particular athletic
event, such as a multi-team cross-country meet, the case for respecting
transitivity seems much stronger: after all, one purpose of the meet is
to rank the teams, from best to worst, at least at that particular site
on that particular day, and when transitivity is violated, there are
ambiguous indications about what the best team is and how the remaining
teams should be ranked overall. (p. 364)"
(5.) In the example in the Appendix, there is no violation of
either IIT or transitivity.
(6.) How the teams would have fared relative to one another using
different scoring procedures cannot be known. For the purposes of the
present analysis, it is assumed that the runners' times would have
been unchanged by a movement from traditional, m-way scoring to dual
meet (Condorcet) scoring.
(7.) In cases where head-to-head competition results in a tie, two
teams may remain tied in Condorcet rankings. However, a tie-breaker used
in dual meets, wherein the finish of each team's sixth-fastest
runner determines the dual-meet winner, could be employed. For example,
the three-way tied for 12th overall in 2008 could be broken using the
154th place, 171st place and 183rd place overall finishes of the
sixth-best runners for Virginia, Colorado and Tulsa, respectively. Using
this secondary tie-breaker would result in these three teams finishing
12th, 13th and 14th overall in the 2008 Condorcet ranking.
(8.) Secondarily, this marks two consecutive years--2008 and
2009--in which Oklahoma State was involved in an IIT violation, both of
which occurred to its benefit. Oklahoma State was also involved in two
violations of transitivity among the top 10 teams from 2008.
(9.) Again, how the teams would have fared relative to one another
using different scoring procedures cannot be known. For the purposes of
the present analysis, it is assumed that the runners' times would
have been unchanged by a movement from traditional, m-way scoring to sum
of times.
(10.) The NCAA survey includes the approximately 120 universities
that compete at the highest level of college football.
(11.) Shinn (2007) reports that Martin's salary rose by
$13,000 to $140,000, not to $130,000 as reported by espn.com.
by Franklin G. Mixon, Jr., Corresponding author: D. Abbott Turner
College of Business, Columbus State University, 4225 University Avenue,
Columbus, GA 31907, USA, 706-568-5368, mixon_franklin@columbusstate.edu
and
Ernest W. King, Department of Legal Studies, University of Southern
Mississippi, Hattiesburg, MS 39407
TABLE 1.
2008 NCAA Men's Division I Cross-Country (10,000 Meter)
Championships
m-WM m-WM ni-WM
Rank Team Points Record
1 University of Oregon 93 30-0-0
2 Iona University 147 29-1-0
3 Stanford University 227 28-2-0
4 University of Wisconsin 229 27-3-0
5 Auburn University 264 26-4-0
6 Northern Arizona U 281 25-5-0
7 University of Portland 293 24-6-0
8 Oklahoma State 305 23-7-0
University
9 Brigham Young 310 22-8-0
University
10 Georgetown University 319 20-9-1
University of Alabama 319 20-9-1
12 University of Colorado 372 19-11-0
13 University of Tulsa 377 18-12-0
14 University of Virginia 383 17-13-0
15 University of Minnesota 385 16-14-0
16 College of William 412 15-15-0
& Mary
17 Iowa State University 435 14-16-0
18 University of Washington 438 13-17-0
19 University of Notre Dame 446 12-18-0
20 Providence College 465 11-19-0
21 North Carolina State U 473 10-20-0
22 University of California 477 9-21-0
23 Cal Poly 513 8-22-0
24 University of Michigan 522 7-23-0
25 Pennsylvania State U 547 6-24-0
26 Florida State University 576 4-25-1
UCLA 576 4-25-1
28 University of Arkansas 579 3-27-0
29 Butler University 602 2-28-0
30 Texas A&M University 609 1-29-0
31 Villanova University 643 0-30-0
Condorcet Condorcet
m-WM Competition
Rank Team Highlights Record Rank
1 University of Oregon 30-0-0 1
2 Iona University 29-1-0 2
3 Stanford University 28-2-0 3
4 University of Wisconsin Lost to Auburn (29 26-4-0 5
to 28)
5 Auburn University Beat Wisconsin (28 27-3-0 4
to 29)
6 Northern Arizona U Lost to Portland 24-6-0 6
(28 to 27)
7 University of Portland Beat Northern 23-6-1 7
Arizona (27 to 28)
Tied Brigham Young
(28 to 28)
Lost to Georgetown
(28 to 27)
8 Oklahoma State Lost to Brigham 20-10-0 11
University Young (28 to 27)
Lost to Georgetown
(28 to 27)
Lost to Alabama
(28 to 27)
9 Brigham Young Tied Portland (28 22-7-1 9
University to 28)
Beat Oklahoma
State (27 to 28)
Lost to Alabama
(28 to 27)
10 Georgetown University Beat Portland (27 23-7-0 8
to 28)
Beat Oklahoma
State (27 to 28)
Beat Alabama (27
to 28)
University of Alabama Beat Oklahoma 21-9-0 10
State (27 to 28)
Beat Brigham Young
(27 to 28)
Lost to Georgetown
(28 to 27)
Lost to Iowa State
(28 to 27)
12 University of Colorado Lost to Tulsa (29 18-12-0 12
to 26)
13 University of Tulsa Beat Colorado (26 18-12-0 12
to 29)
Lost to Virginia
(28 to 27)
14 University of Virginia Beat Tulsa (27 to 18-12-0 12
28)
15 University of Minnesota Lost to William & 15-15-0 15
Mary (28 to 27)
16 College of William Beat Minnesota (27 15-15-0 15
& Mary to 28)
Lost to Iowa State
(30 to 26)
17 Iowa State University Beat Alabama (27 15-15-0 15
to 28)
Beat William &
Mary (26 to 30)
Lost to California
(28 to 27)
18 University of Washington Lost to North 12-18-0 18
Carolina St. (28
to 27)
19 University of Notre Dame 12-18-0 19
20 Providence College 11-19-0 20
21 North Carolina State U Beat Washington 10-20-0 22
(27 to 28)
Lost to California
(28 to 27)
22 University of California Beat Iowa State 11-19-0 21
(25 to 30)
Beat North
23 Cal Poly Carolina St. (27 8-22-0 23
to 28)
24 University of Michigan 7-23-0 24
25 Pennsylvania State U 6-24-0 25
26 Florida State University Beat UCLA (26 to 5-25-0 26
29)
UCLA Lost to Florida 4-26-0 27
State (29 to 26)
28 University of Arkansas 3-27-0 28
29 Butler University 2-28-0 29
30 Texas A&M University 1-29-0 30
31 Villanova University 0-30-0 31
Note: m-WM = m-Way Meet
TABLE 2.
2009 NCAA Men's Division I Cross-Country (10,000 Meter) Championships
m-WM m-WM m-WM
Rank Team Points Record
1 Oklahoma State 127 30-0-0
University
2 University of Oregon 143 29-1-0
3 University of Alabama 173 28-2-0
4 Northern Arizona U 190 27-3-0
5 William & Mary 226 26-4-0
6 University of Colorado 315 25-5-0
7 University of Wisconsin 321 24-6-0
8 University of New Mexico 350 22-7-1
Iona University 350 22-7-1
10 Stanford University 354 21-9-0
11 Villanova University 359 20-10-0
12 University of Oklahoma 386 19-11-0
13 University of Portland 394 18-12-0
14 Syracuse University 405 17-13-0
15 University of Virginia 408 16-14-0
16 Iowa State University 430 15-15-0
17 Brigham Young University 468 14-16-0
18 University of Washington 470 13-17-0
19 Arizona State University 472 12-18-0
20 Providence College 482 11-19-0
21 Ohio State University 483 10-20-0
22 Georgetown University 485 9-21-0
23 University of Louisville 490 8-22-0
24 University of Minnesota 493 7-23-0
25 Auburn University 504 6-24-0
26 University of Arkansas 535 5-25-0
27 North Carolina State U 539 4-26-0
28 University of Texas 605 2-27-1
Duke University 605 2-27-1
30 Florida State University 612 1-29-0
31 Michigan State 654 0-30-0
University
Condorcet Condorcet
m-WM Competition
Rank Team Highlights Record Rank
1 Oklahoma State Lost to Northern 29-1-0 1
University Arizona (28 to 27)
2 University of Oregon Lost to Alabama 28-2-0 3
(28 to 27)
3 University of Alabama Beat Oregon (27 to 29-1-0 2
28)
4 Northern Arizona U Beat Oklahoma 28-2-0 4
State (27 to 28)
5 William & Mary 26-4-0 5
6 University of Colorado Tied Iona (28 to 23-6-1 7
28)
Lost to Stanford
(30 to 26) 24-6-0 6
7 University of Wisconsin
8 University of New Mexico Beat Iona (27 to 23-7-0 8
30)
Iona University Tied Colorado (28 21-7-2 10
to 28)
Lost to New Mexico
(30 to 27)
Tied Stanford (28
to 28)
10 Stanford University Beat Colorado (26 22-7-1 9
to 30)
Tied Iona (28 to
28)
11 Villanova University Lost to Portland 19-11-0 12
(30 to 25)
12 University of Oklahoma Tied Portland (28 18-10-1 13
to 28)
13 University of Portland Beat Villanova (25 19-10-1 11
to 30)
Tied Oklahoma (28
to 28)
14 Syracuse University 17-13-0 14
15 University of Virginia 16-14-0 15
16 Iowa State University 15-15-0 16
17 Brigham Young University Lost to Ohio State 13-17-0 17
(29 to 26)
18 University of Washington Lost to Providence 12-18-0 18
(28 to 27)
19 Arizona State University Lost to Ohio State 10-19-1 20
(28 to 27)
Tied Minnesota (28
to 28)
20 Providence College Beat Washington 8-21-1 21
(27 to 28)
Lost to Ohio State
(28 to 27)
Lost to Georgetown
(28 to 27)
Tied Auburn (28 to
28)
Lost to Arkansas
(28 to 27)
21 Ohio State University Beat Brigham Young 12-18-0 19
(26 to 29)
Beat Arizona State
(27 to 28)
Beat Providence
(27 to 28)
Lost to Minnesota
(29 to 27)
22 Georgetown University Beat Providence 7-23-0 25
(27 to 28)
Lost to Louisville
(28 to 27)
Lost to Minnesota
(28 to 27)
Lost to Arkansas
(29 to 26)
23 University of Louisville Beat Georgetown 8-22-0 23
(27 to 28)
Lost to Auburn (29
to 27)
24 University of Minnesota Tied Arizona State 8-21-1 22
(28 to 28)
Beat Ohio State
(27 to 29)
Beat Georgetown
(27 to 28)
Lost to Arkansas
(29 to 28)
25 Auburn University Tied Providence 7-22-1 24
(28 to 28)
Beat Louisville
(27 to 29)
26 University of Arkansas Beat Georgetown 4-26-0 27
(26 to 29)
Beat Minnesota (28
to 29)
Lost to North
Carolina State (28
to 27)
Lost to Duke (33
to 25)
Lost to Michigan
State (30 to 25)
27 North Carolina State U Beat Arkansas (27 5-25-0 26
to 28)
28 University of Texas 2-27-1 29
Duke University Beat Arkansas (25 3-26-1 28
to 33)
30 Florida State University Lost to Michigan 0-30-0 31
State (30 to 27)
31 Michigan State Beat Arkansas (25 2-28-0 30
University to 30)
Beat Florida State
(27 to 30)
Note: m-WM = m-Way Meet
TABLE 3.
2008-09 NCAA Men's Division I Cross-Country (10,000 Meter)
Championships
2008 Results
SoT
Rank Team SoT
1 University of Oregon 2:29:09 [1]
2 Iona University 2:30:24 [2]
3 Stanford University 2:31:52 [3]
4 University of Wisconsin 2:32:05 [4]
5 Auburn University 2:32:14 [5]
6 University of Portland 2:32:21 [7]
7 Oklahoma State University 2:32:34 [8]
8 Northern Arizona U 2:32:49 [6]
9 Georgetown University 2:33:07 [10]
10 Brigham Young University 2:33:11 [9]
11 University of Alabama 2:33:34 [10]
12 University of Colorado 2:33:49 [12]
University of Minnesota 2:33:49 [15]
13 University of Tulsa 2:34:03 [13]
University of Virginia 2:34:03 [14]
15 College of William & Mary 2:34:36 [16]
University of Notre Dame 2:34:36 [19]
18 Iowa State University 2:34:44 [17]
19 Providence College 2:34:49 [20]
20 University of Washington 2:34:50 [18]
21 University of California 2:35:03 [22]
22 North Carolina State U 2:35:14 [21]
23 California Polytechnic 2:35:38 [23]
24 University of Michigan 2:35:41 [24]
25 University of Arkansas 2:35:59 [28]
26 Pennsylvania State U 2:36:00 [25]
27 Texas A&M University 2:36:21 [30]
28 Butler University 2:36:23 [29]
UCLA 2:36:23 [26]
30 Florida State University 2:36:25 [26]
31 Villanova University 2:37:07 [31]
2009 Results
SoT
Rank Team SoT
1 Oklahoma State University 2:30:21 [1]
2 Northern Arizona U 2:30:47 [4]
3 University of Oregon 2:31:17 [2]
4 University of Alabama 2:31:36 [3]
5 College of William & Mary 2:32:15 [5]
6 University of Colorado 2:33:32 [6]
7 Stanford University 2:33:36 [10]
8 University of Wisconsin 2:33:38 [7]
9 Iona University 2:33:42 [81
10 University of New Mexico 2:33:50 [8]
11 Villanova University 2:34:11 [11]
12 University of Portland 2:34:33 [13]
13 University of Oklahoma 2:34:34 [12]
14 Syracuse University 2:34:37 [14]
15 University of Virginia 2:34:41 [15]
16 Iowa State University 2:35:01 [16]
17 Arizona State University 2:35:05 [19]
18 Georgetown University 2:35:23 [22]
19 Brigham Young University 2:35:24 [17]
University of Washington 2:35:24 [18]
21 Ohio State University 2:35:29 [211
22 Providence College 2:35:39 [20]
23 University of Louisville 2:35:45 [23]
24 University of Minnesota 2:35:54 [24]
25 University of Arkansas 2:35:55 [26]
26 North Carolina State U 2:36:22 [27]
27 Auburn University 2:36:50 [25]
28 Duke University 2:37:03 [28]
29 University of Texas 2:37:07 [28]
30 Florida State University 2:37:29 [30]
31 Michigan State University 2:37:31 [31]
Notes: SoT = Sum of Times; numbers in brackets above represent
actual rankings from the respective cross-country meets using
traditional m-Way meet scoring.
TABLE 4.
2008-09 NCAA Men's Division I Cross-Country
(10,000 Meter) Championships
Spearman Rank-Correlations across Top 10, 2008
Condorcet Sum of
Scoring Times
m-Way Meet (Actual) +0.920 +0.957
Condorcet Scoring * +0.882
Spearman Rank-Correlations across Top 10, 2009
Condorcet Sum of
Scoring Times
m-Way Meet (Actual) +0.954 +0.888
Condorcet Scoring * +0.867
