Social choice theory in 10,000 meters: examining independence and transitivity in the NCAA cross-country championships.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.
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.
The authors thank an anonymous referee and Bill Bosshardt for helpful comments. Any remaining errors are our own.
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).
(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, email@example.com
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  2 Iona University 2:30:24  3 Stanford University 2:31:52  4 University of Wisconsin 2:32:05  5 Auburn University 2:32:14  6 University of Portland 2:32:21  7 Oklahoma State University 2:32:34  8 Northern Arizona U 2:32:49  9 Georgetown University 2:33:07  10 Brigham Young University 2:33:11  11 University of Alabama 2:33:34  12 University of Colorado 2:33:49  University of Minnesota 2:33:49  13 University of Tulsa 2:34:03  University of Virginia 2:34:03  15 College of William & Mary 2:34:36  University of Notre Dame 2:34:36  18 Iowa State University 2:34:44  19 Providence College 2:34:49  20 University of Washington 2:34:50  21 University of California 2:35:03  22 North Carolina State U 2:35:14  23 California Polytechnic 2:35:38  24 University of Michigan 2:35:41  25 University of Arkansas 2:35:59  26 Pennsylvania State U 2:36:00  27 Texas A&M University 2:36:21  28 Butler University 2:36:23  UCLA 2:36:23  30 Florida State University 2:36:25  31 Villanova University 2:37:07  2009 Results SoT Rank Team SoT 1 Oklahoma State University 2:30:21  2 Northern Arizona U 2:30:47  3 University of Oregon 2:31:17  4 University of Alabama 2:31:36  5 College of William & Mary 2:32:15  6 University of Colorado 2:33:32  7 Stanford University 2:33:36  8 University of Wisconsin 2:33:38  9 Iona University 2:33:42 [81 10 University of New Mexico 2:33:50  11 Villanova University 2:34:11  12 University of Portland 2:34:33  13 University of Oklahoma 2:34:34  14 Syracuse University 2:34:37  15 University of Virginia 2:34:41  16 Iowa State University 2:35:01  17 Arizona State University 2:35:05  18 Georgetown University 2:35:23  19 Brigham Young University 2:35:24  University of Washington 2:35:24  21 Ohio State University 2:35:29 [211 22 Providence College 2:35:39  23 University of Louisville 2:35:45  24 University of Minnesota 2:35:54  25 University of Arkansas 2:35:55  26 North Carolina State U 2:36:22  27 Auburn University 2:36:50  28 Duke University 2:37:03  29 University of Texas 2:37:07  30 Florida State University 2:37:29  31 Michigan State University 2:37:31  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