454:. But across all conditions, "simply playing at home increases the chances of winning." A win away from home is therefore seen more favorably than a win at home, because it was more challenging. Home advantage (which, for sports played on a pitch, is almost always called "home field advantage") is also based on the qualities of the individual stadium and crowd; the advantage in the NFL can be more than a 4-point difference from the stadium with the least advantage to the stadium with the most.
222:
437:
63:
3112:
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126:
22:
3100:
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difficult to model. "Throw-away games" are games where teams have already earned playoff slots and have secured their playoff seeding before the end of the regular season, and want to rest/protect their starting players by benching them for remaining regular season games. This usually results in unpredictable outcomes and may skew the outcome of rating systems.
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percentage of 57.5%, based on 208 points scored and 183 points allowed. Multiplied by 9 games played, the
Cardinals' Pythagorean expectation was 5.2 wins and 3.8 losses. The team had "overachieved" at that time by 2.8 wins, derived from their actual 8 wins less the expected 5.2 wins, an increase of 0.8 overachieved wins from just a week prior.
755:
1309:
This is a look at 20 of the teams (in alphabetical order) residing on this year's big ol' bubble. We've included three statistical rankings. The RPI (ratings percentage index, taken from collegeRPI.com) is considered the standard and is provided to committee members during the selection process. The
668:
Pythagorean expectation, or
Pythagorean projection, calculates a percentage based on the number of points a team has scored and allowed. Typically the formula involves the number of points scored, raised to some exponent, placed in the numerator. Then the number of points the team allowed, raised to
640:
I went through the first few weeks of games and redid everyone’s records, tagging each game as either a legitimate win or loss, an ass-kicking win or loss, or an either/or game. And if anything else happened in that game with gambling repercussions – a comeback win, a blown lead, major dysfunction,
468:
Strength of schedule refers to the quality of a team's opponents. A win against an inferior opponent is usually seen less favorably than a win against a superior opponent. Often teams in the same league, who are compared against each other for championship or playoff consideration, have not played
533:
Beyond points or wins, some system designers choose to include more granular information about the game. Examples include time of possession of the ball, individual statistics, and lead changes. Data about weather, injuries, or "throw-away" games near season's end may affect game outcomes but are
358:
If sufficient "inter-divisional" league play is not accomplished, teams in an isolated division may be artificially propped up or down in the overall ratings due to a lack of correlation to other teams in the overall league. This phenomenon is evident in systems that analyze historical college
268:
writes that an advantage of computer rating systems is that they can "objectively track all" 351 college basketball teams, while human polls "have limited value". Computer ratings are verifiable and repeatable, and are comprehensive, requiring assessment of all selected criteria. By comparison,
772:
cites
Barnwell's work before week 10 of that season and adds that "any numbers nerd is waving a “REGRESSION!!!!!” flag right now." In this example, the Arizona Cardinals' regular season record was 8-1 going into the 10th week of the 2014 season. The Pythagorean win formula implied a winning
303:
Sports ratings systems use a variety of methods for rating teams, but the most prevalent method is called a power rating. The power rating of a team is a calculation of the team's strength relative to other teams in the same league or division. The basic idea is to maximize the amount of
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Goals of some rating systems differ from one another. For example, systems may be crafted to provide a perfect retrodictive analysis of the games played to-date, while others are predictive and give more weight to future trends rather than past results. This results in the potential for
1071:
and was a classmate of Jeff
Sagarin at MIT. He published several editions of a text on the Microsoft Excel spreadsheet software that includes material on ranking sports teams, as well as a book focused directly on this topic. He and Sagarin created rating systems together.
631:
Several methods offer some permutation of traditional standings. This search for the "real" win–loss record often involves using other data, such as point differential or identity of opponents, to alter a team's record in a way that is easily understandable. Sportswriter
578:
At the beginning of a season, there have been no games from which to judge teams' relative quality. Solutions to the cold start problem often include some measure of the previous season, perhaps weighted by what percent of the team is returning for the new season.
1310:
two other ranking indexes include margin of victory in their formulas—the
Pomeroy ratings (at kenpom.com) and Sagarin ratings (via USA Today)—aren't new but have played an increased role in discussions about potential seeds during this college basketball season.
679:
315:
relation is established (A > B > C > A) and a ranking violation will occur if this is the only data available. Scenarios such as this happen fairly regularly in sports—for example, in the
257:. They are often mentioned in discussions about the teams that could or should receive invitations to participate in certain contests, despite not earning the most direct entrance path (such as a league championship).
277:
Sports ratings systems have been around for almost 80 years, when ratings were calculated on paper rather than by computer, as most are today. Some older computer systems still in use today include:
332:, and Michigan beat Penn State. To address these logical breakdowns, rating systems usually consider other criteria such as the game's score and where the match was held (for example, to assess a
760:
The resulting percentage is often compared to a team's true winning percentage, and a team is said to have "overachieved" or "underachieved" compared to the
Pythagorean expectation. For example,
379:. This conflicts with the subjective opinion that claims that while good in their own right, they were not nearly as good as those top programs. However, this may be considered a "pro" by non-
517:
of additional points as the margin of victory increases. Sagarin chose to clamp the margin of victory to a predetermined amount. Other approaches include the use of a decay function, such as a
387:
team that went undefeated in the regular season and earned a BCS bowl bid due to the bump in their overall BCS ratings via the computer ratings component. They went on to play and defeat the
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created a measure of
Authentic Games, which only considers games played against opponents deemed to be of sufficiently high quality. The consensus is that all wins are not created equal.
542:
Teams often shift their composition between and within games, and players routinely get injured. Rating a team is often about rating a specific collection of players. Some systems assume
1127:
Barrow, Daniel; Drayer, Ian; Elliott, Peter; Gaut, Garren; Osting, Braxton (May 2013). "Ranking rankings: an empirical comparison of the predictive power of sports ranking methods".
383:
teams in
Division I-A college football who point out that ratings systems have proven that their top teams belong in the same strata as the BCS teams. This is evidenced by the 2004
1426:
450:
When two teams of equal quality play, the team at home tends to win more often. The size of the effect changes based on the era of play, game type, season length, sport, even
2408:
791:
as a method for ranking chess players, several people have adapted the Elo rating system for team sports such as basketball, soccer and
American football. For instance,
490:
The college football playoff committee uses a limited strength-of-schedule algorithm that only considers opponents' records and opponents' opponents' records (much like
799:
publish NFL football rankings using Elo methods. Elo ratings initially assign strength values to each team, and teams trade points based on the outcome of each game.
750:{\displaystyle {\text{Pythagorean wins}}={\frac {{\text{Points For}}^{2.37}}{{\text{Points For}}^{2.37}+{\text{Points Against}}^{2.37}}}\times {\text{Games Played}}.}
1545:
1165:
Sports
Rankings REU Final Report 2012: An Analysis of Pairwise-Comparison Based Sports Ranking Methods and a Novel Agent-Based Markovian Basketball Simulation
507:
336:). In most cases though, each team plays a sufficient amount of other games during a given season, which lessens the overall effect of such violations.
1327:"@kenpomeroy human polls have limited value. Computer systems can objectively track all the teams. http://www.masseyratings.com/cb/compare.htm #all351"
510:. Rating teams based on margin of victory is often criticized as creating an incentive for coaches to run up the score, an "unsportsmanlike" outcome.
3186:
2323:
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rating systems relying on human polls include inherent human subjectivity; this may or may not be an attractive property depending on system needs.
202:, are numerical representations of competitive strength, often directly comparable so that the game outcome between any two teams can be predicted.
412:
400:
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136:
73:
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misinterpretation of rating system results by people unfamiliar with these goals; for example, a rating system designed to give accurate
1179:
Gray, Kathy L.; Schwertman, Neil C. (March 2012). "Comparing Team Selection and Seeding for the 2011 NCAA men's basketball tournament".
2249:
1292:
1041:
2284:
1483:
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In collegiate American football, the following people's systems were used to choose teams to play in the national championship game.
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predictions for gamblers might be ill-suited for use in selecting teams most deserving to play in a championship game or tournament.
210:, can be directly provided (e.g., by asking people to rank teams), or can be derived by sorting each team's ratings and assigning an
2780:
2471:
2069:
874:
230:
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in a given data set due to game outcomes. For example, if A defeats B and B defeats C, then one can safely say that A>B>C.
214:
rank to each team, so that the highest rated team earns the #1 rank. Rating systems provide an alternative to traditional sports
3146:
2466:
2299:
317:
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are popular among many of the systems' authors to determine their ratings. Some academic work is published in forums like the
2451:
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1614:
1108:
1087:
352:
35:
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A key dichotomy among sports rating systems lies in the representation of game outcomes. Some systems store final scores as
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1164:
603:
2924:
1889:
1017:
893:
388:
2304:
2166:
1985:
1229:
861:
570:. This is certainly not the case in collegiate leagues such as Division I-A football or men's and women's basketball.
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discrete events: wins, draws, and losses. Other systems record the exact final game score, then judge teams based on
372:
173:
107:
49:
522:
1851:
1244:"A Penalized Maximum Likelihood Approach for the Ranking of College Football Teams Independent of Victory Margins"
3022:
2543:
2279:
2269:
2256:
2244:
963:
563:
367:, were calculated by some rating systems to be comparable with accomplished powerhouse teams of that era such as
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There are obvious problems with basing a system solely on wins and losses. For example, if C defeats A, then an
1079:
Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football
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1882:
1665:
1634:
2803:
2436:
2431:
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2234:
2159:
2140:
993:
482:
321:
1960:
3171:
2381:
1825:
979:
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is an example of a system that uses multiple previous years plus a percentage weight of returning players.
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1950:
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906:
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among all members of the league, such as each team being built from an equitable pool of players via a
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championship game participants were determined by a combination of expert polls and computer systems.
1453:"Committee doesn't use an SOS ranking. It looks at opponents' record and opponents' opponents record"
148:
85:
41:
1830:
Indiana University Bloomington - Kelley School of Business - Operations & Decisions Technologies
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555:
491:
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89:
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1995:
1990:
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Football Outsiders Almanac 2011: The Essential Guide to the 2011 NFL and College Football Seasons
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to model college football games, with team strength scores as outcomes. Algorithms like Google's
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404:
1800:
485:, press conference, week 12 of the 2014 season, after ranking 9–1 Oregon above 9–0 Florida State
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We looked beyond the record. The committee placed significant value on Oregon's quality of wins.
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2413:
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368:
329:
607:
144:
81:
2748:
2079:
2024:
1077:
968:
559:
376:
325:
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355:, others in traditional statistics, mathematics, psychology, and computer science journals.
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8:
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the same exponent, is placed in the denominator and added to the value in the numerator.
451:
305:
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1975:
1970:
1955:
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1204:
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1068:
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877:
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833:
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670:
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503:
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the same opponents. Therefore, judging their relative win–loss records is complicated.
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242:
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2715:
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2010:
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633:
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were awarded an at-large tournament bid due to their regular season record and their
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1220:
3078:
2989:
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2909:
2818:
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2790:
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2681:
2566:
1965:
1856:
1452:
1372:
1270:
1258:
1233:
1188:
1168:
1136:
897:
885:
881:
856:
852:
291:, which dates back to 1929. Before the advent of the college football playoff, the
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2758:
2656:
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1934:
1695:
1604:
1514:
1098:
796:
543:
234:
241:. Sports ratings systems are also used to help determine the field for the NCAA
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1919:
1603:
Schatz, Aaron; Alamar, Ben; Barnwell, Bill; Bill Connelly; Doug Farrar (2011).
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889:
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283:
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958:
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808:
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221:
211:
195:
436:
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2488:
2401:
2125:
2084:
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2019:
1924:
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1572:
1510:
1192:
1140:
984:
838:
792:
769:
646:
420:
288:
278:
229:
In the United States, the biggest use of sports ratings systems is to rate
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2743:
2130:
2120:
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396:
2151:
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for each team or player. Common systems include polls of expert voters,
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is a system that analyzes the results of sports competitions to provide
3004:
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2571:
2135:
2110:
1488:
1322:
901:
551:
360:
348:
265:
191:
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non-expert voters, betting markets, and computer systems. Ratings, or
2000:
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1581:
1519:
1403:
916:
788:
650:
518:
215:
1719:"Using Continuous-Time Markov Chains to Rank College Football Teams"
2936:
2763:
2619:
1748:
1042:"How to understand college football analytics – the ultimate guide"
926:
812:
340:
2999:
2059:
1602:
1468:
1342:
203:
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had a Pythagorean record two wins lower than their real record.
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by a score of 35-7. A related example occurred during the 2006
2951:
1776:
910:
842:
254:
250:
1055:"College Football Rankers by the Dozen Ask the No. 1 Question"
2552:
72:
deal primarily with the United States and do not represent a
2984:
1980:
1550:
246:
764:
calculated that before week 9 of the 2014 NFL season, the
554:
system as is done in many major league sports such as the
264:, without specific player, team, regional, or style bias.
1772:"Modifying Google's Page Ranking Algorithm to rank teams"
513:
Still other systems choose a middle ground, reducing the
2521:
1358:"The Home Field Advantage in Athletics: A Meta-Analysis"
1230:
Statistical Models Applied to the Rating of Sports Teams
1126:
1067:
Wayne Winston is a professor of decision sciences at
682:
1801:"A Bayesian Approximation Method for Online Ranking"
1100:
Microsoft® Excel Data Analysis and Business Modeling
776:
1013:"Bibliography on College Football Ranking Systems"
749:
1826:"Wayne Winston: Analytics in the World of Sports"
3138:
1427:"Oregon up to 2 in playoff rankings; TCU to 4th"
927:Bowl Championship Series computer rating systems
818:
815:have also been adapted to rank football teams.
1447:
1178:
2537:
2167:
1890:
411:and rode that opportunity all the way to the
225:College football players in the United States
133:The examples and perspective in this article
70:The examples and perspective in this article
1635:"NFL at the Half: Breaking Down the Numbers"
919:, a Bayesian ranking system inspired by the
1666:"Revisiting the Y2K-Compliant Quarterbacks"
1540:
626:
50:Learn how and when to remove these messages
2544:
2530:
2174:
2160:
1897:
1883:
1321:
1181:Journal of Quantitative Analysis in Sports
1129:Journal of Quantitative Analysis in Sports
2181:
2009:
1904:
1744:"Ranking NFL teams using Network Science"
1293:"Sorting through teams on one big bubble"
1163:Much of this information is available at
174:Learn how and when to remove this message
108:Learn how and when to remove this message
3187:American football records and statistics
2070:Harris Interactive College Football Poll
1629:
1481:
1396:
1355:
435:
426:
260:Computer rating systems can tend toward
220:
218:which are based on win–loss–tie ratios.
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1660:
1571:
1509:
1484:"BCS removes margin-of-victory element"
1096:
1075:
457:
359:football seasons, such as when the top
3139:
1685:
1215:
1052:
528:
318:2005 NCAA Division I-A football season
2525:
2155:
2065:FWAA-NFF Grantland Rice Super 16 Poll
1878:
1799:Weng, Ruby C.; Lin, Chih-Jen (2011).
1716:
1424:
1290:
1241:
497:
353:MIT Sloan Sports Analytics Conference
1808:Journal of Machine Learning Research
1425:Russo, Ralph D. (11 November 2014).
1397:Barnwell, Bill (December 20, 2013).
1365:Journal of Applied Social Psychology
1039:
802:
590:
440:France national basketball team fans
119:
56:
15:
1577:"Week 8 Picks: A Gambling Epiphany"
1546:"More flags on D spins scoreboards"
1053:Mather, Victor (October 23, 2012).
537:
13:
1986:Pomeroy College Basketball Ratings
1010:
999:
862:Pomeroy College Basketball Ratings
14:
3198:
1004:
586:
431:
31:This article has multiple issues.
3120:
3111:
3110:
3098:
1971:English Chess Federation grading
1717:Mills, Matt (21 December 2014).
1377:10.1111/j.1559-1816.2010.00641.x
1120:
1033:
807:Researchers like Matt Mills use
594:
523:cumulative distribution function
401:NCAA men's basketball tournament
245:tournaments, men's professional
237:, choosing teams to play in the
124:
61:
20:
3121:
1844:
1818:
1792:
1764:
1736:
1710:
1679:
1654:
1623:
1596:
1565:
1221:"Honors Project in Mathematics"
1018:University of Wisconsin–Madison
39:or discuss these issues on the
1609:. CreateSpace. p. xviii.
1534:
1503:
1475:
1441:
1418:
1390:
1349:
1315:
1284:
1082:. Princeton University Press.
871:Ratings Percentage Index (RPI)
657:
641:whatever — I tagged that, too.
1:
3147:Sports records and statistics
2085:USA Today/Amway Coaches' Poll
1996:Rating Percentage Index (RPI)
1691:"Introducing NFL Elo Ratings"
1278:
1040:Feng, Ed (24 November 2014).
819:List of sports rating systems
573:
147:and discuss the issue on the
1515:"NCAAF Jeff Sagarin Ratings"
1356:Jamieson, Jeremy P. (2010).
954:Atlanta Journal-Constitution
602:This sports-related list is
452:number of time zones crossed
243:men's and women's basketball
7:
1951:Advanced Football Analytics
1944:Methods and computer models
909:, United States of America
873:, United States of America
864:, United States of America
855:, United States of America
827:, United States of America
84:, discuss the issue on the
10:
3205:
1291:Fagan, Ryan (2011-03-09).
1097:Winston, Wayne L. (2009).
1076:Winston, Wayne L. (2012).
907:Smithman Qualitative Index
780:
661:
461:
443:
272:
249:tournaments, professional
233:college football teams in
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3046:
3013:
2970:
2882:
2837:
2789:
2736:
2610:
2559:
2551:
2187:
2093:
2052:
1943:
1912:
1482:Richards, Darryl (2001).
1251:The American Statistician
363:teams of the 1970s, like
298:
2694:Bodybuilding supplements
1961:Bowl Championship Series
829:National Football League
627:Permutation of standings
479:College football playoff
343:perspective, the use of
293:Bowl Championship Series
239:College Football Playoff
2222:Baseball & softball
1991:Pythagorean expectation
787:Originally designed by
664:Pythagorean expectation
1193:10.1515/1559-0410.1369
1141:10.1515/jqas-2013-0013
777:Trading "skill points"
751:
655:
488:
441:
226:
3177:Basketball statistics
2182:Sports world rankings
1906:Sports rating systems
1263:10.1198/0003130032396
1242:Mease, David (2003).
936:Anderson & Hester
752:
638:
471:
439:
427:Rating considerations
224:
1930:Strength of schedule
1689:(4 September 2014).
1633:(November 5, 2014).
1544:(18 November 2014).
921:Glicko rating system
680:
608:adding missing items
464:Strength of schedule
458:Strength of schedule
334:home field advantage
306:transitive relations
188:sports rating system
145:improve this article
135:may not represent a
90:create a new article
82:improve this article
3172:Baseball statistics
2398:Mixed martial arts
1664:(7 November 2014).
1575:(24 October 2014).
1103:. Microsoft Press.
945:Richard Billingsley
529:In-game information
481:committee chairman
389:Big East Conference
3152:Sports terminology
2711:Physical education
2080:NAIA Coaches' Poll
1976:Litkenhous Ratings
1956:ARGH Power Ratings
1780:. 21 December 2014
1542:Easterbrook, Gregg
1429:. Associated Press
1069:Indiana University
866:college basketball
834:ARGH Power Ratings
825:Advanced NFL Stats
747:
671:Football Outsiders
606:; you can help by
581:ARGH Power Ratings
521:or placement on a
498:Points versus wins
442:
328:, Ohio State beat
227:
3134:
3133:
3105:Sports portal
2716:Physical activity
2662:Athletic training
2645:Strength training
2597:Semi-professional
2519:
2518:
2149:
2148:
2053:Polls and opinion
2048:
2047:
1616:978-1-4662-4613-3
1110:978-0-7356-3714-6
1089:978-1-4008-4207-0
803:Solving equations
783:Elo rating system
766:Arizona Cardinals
742:
734:
725:
710:
697:
686:
634:Gregg Easterbrook
624:
623:
508:margin of victory
253:tournaments, and
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183:
176:
166:
165:
118:
117:
110:
92:, as appropriate.
54:
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2847:General managers
2749:Governing bodies
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2523:
2522:
2285:WODI & WT20I
2217:Beach volleyball
2176:
2169:
2162:
2153:
2152:
2007:
2006:
1966:Dickinson System
1899:
1892:
1885:
1876:
1875:
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1865:
1860:. April 13, 2004
1857:Washington Times
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1729:
1714:
1708:
1707:
1705:
1703:
1683:
1677:
1676:
1674:
1672:
1658:
1652:
1651:
1649:
1647:
1627:
1621:
1620:
1600:
1594:
1593:
1591:
1589:
1569:
1563:
1562:
1560:
1558:
1538:
1532:
1531:
1529:
1527:
1507:
1501:
1500:
1498:
1496:
1479:
1473:
1472:
1466:
1464:
1445:
1439:
1438:
1436:
1434:
1422:
1416:
1415:
1413:
1411:
1394:
1388:
1387:
1385:
1383:
1371:(7): 1819–1848.
1362:
1353:
1347:
1346:
1340:
1338:
1319:
1313:
1312:
1306:
1305:
1288:
1274:
1248:
1238:
1234:Internet Archive
1227:
1225:
1212:
1173:
1169:Internet Archive
1160:
1114:
1093:
1064:
1049:
1029:
1027:
1025:
971:/ Scripps Howard
857:college football
853:Dickinson System
841:, international
756:
754:
753:
748:
743:
740:
735:
733:
732:
731:
726:
723:
717:
716:
711:
708:
704:
703:
698:
695:
692:
687:
685:Pythagorean wins
684:
653:
649:, sportswriter,
619:
616:
598:
597:
591:
538:Team composition
486:
287:system, and the
179:
172:
161:
158:
152:
128:
127:
120:
113:
106:
102:
99:
93:
65:
64:
57:
46:
24:
23:
16:
3204:
3203:
3197:
3196:
3195:
3193:
3192:
3191:
3167:Sports business
3157:Sports rankings
3137:
3136:
3135:
3130:
3099:
3097:
3088:
3047:Sport by region
3042:
3009:
2980:Artificial turf
2966:
2937:Olympic culture
2878:
2833:
2785:
2732:
2606:
2577:Military sports
2555:
2550:
2520:
2515:
2296:Cycling (road)
2183:
2180:
2150:
2145:
2089:
2044:
2005:
1939:
1935:Win probability
1908:
1903:
1873:
1863:
1861:
1850:
1849:
1845:
1835:
1833:
1824:
1823:
1819:
1803:
1797:
1793:
1783:
1781:
1770:
1769:
1765:
1755:
1753:
1752:. 17 March 2016
1742:
1741:
1737:
1727:
1725:
1715:
1711:
1701:
1699:
1696:FiveThirtyEight
1684:
1680:
1670:
1668:
1659:
1655:
1645:
1643:
1628:
1624:
1617:
1601:
1597:
1587:
1585:
1570:
1566:
1556:
1554:
1539:
1535:
1525:
1523:
1508:
1504:
1494:
1492:
1480:
1476:
1462:
1460:
1451:(12 Nov 2014).
1449:Stewart Mandel
1446:
1442:
1432:
1430:
1423:
1419:
1409:
1407:
1395:
1391:
1381:
1379:
1360:
1354:
1350:
1336:
1334:
1320:
1316:
1303:
1301:
1289:
1285:
1281:
1246:
1236:
1223:
1219:(Spring 1997).
1171:
1123:
1111:
1090:
1036:
1023:
1021:
1011:Wilson, David.
1007:
1002:
1000:Further reading
969:Herman Matthews
929:
821:
805:
797:FiveThirtyEight
785:
779:
739:
727:
722:
721:
712:
707:
706:
705:
699:
694:
693:
691:
683:
681:
678:
677:
666:
660:
654:
645:
629:
620:
614:
611:
595:
589:
576:
540:
531:
500:
487:
477:
466:
460:
448:
434:
429:
301:
275:
180:
169:
168:
167:
162:
156:
153:
142:
129:
125:
114:
103:
97:
94:
79:
66:
62:
25:
21:
12:
11:
5:
3202:
3201:
3190:
3189:
3184:
3179:
3174:
3169:
3164:
3162:Sports science
3159:
3154:
3149:
3132:
3131:
3129:
3128:
3118:
3108:
3093:
3090:
3089:
3087:
3086:
3081:
3076:
3071:
3066:
3061:
3056:
3050:
3048:
3044:
3043:
3041:
3040:
3035:
3033:National sport
3030:
3025:
3019:
3017:
3011:
3010:
3008:
3007:
3002:
2997:
2992:
2987:
2982:
2976:
2974:
2968:
2967:
2965:
2964:
2959:
2954:
2952:Sports mascots
2949:
2944:
2939:
2934:
2929:
2928:
2927:
2917:
2912:
2907:
2902:
2897:
2892:
2886:
2884:
2880:
2879:
2877:
2876:
2871:
2870:
2869:
2864:
2859:
2849:
2843:
2841:
2835:
2834:
2832:
2831:
2826:
2821:
2816:
2811:
2806:
2801:
2795:
2793:
2787:
2786:
2784:
2783:
2778:
2773:
2768:
2767:
2766:
2761:
2751:
2746:
2740:
2738:
2734:
2733:
2731:
2730:
2725:
2720:
2719:
2718:
2713:
2703:
2702:
2701:
2696:
2686:
2685:
2684:
2679:
2674:
2669:
2664:
2654:
2649:
2648:
2647:
2642:
2637:
2632:
2627:
2616:
2614:
2608:
2607:
2605:
2604:
2599:
2594:
2589:
2584:
2579:
2574:
2569:
2563:
2561:
2557:
2556:
2549:
2548:
2541:
2534:
2526:
2517:
2516:
2514:
2513:
2508:
2503:
2502:
2501:
2496:
2491:
2481:
2476:
2475:
2474:
2469:
2461:
2456:
2455:
2454:
2449:
2441:
2440:
2439:
2434:
2429:
2421:
2416:
2411:
2406:
2405:
2404:
2396:
2391:
2386:
2385:
2384:
2379:
2371:
2370:
2369:
2364:
2359:
2351:
2350:
2349:
2344:
2342:unofficial elo
2339:
2331:
2326:
2324:Figure skating
2321:
2320:
2319:
2309:
2308:
2307:
2302:
2294:
2289:
2288:
2287:
2282:
2277:
2272:
2264:
2259:
2254:
2253:
2252:
2247:
2239:
2238:
2237:
2232:
2224:
2219:
2214:
2209:
2199:
2194:
2188:
2185:
2184:
2179:
2178:
2171:
2164:
2156:
2147:
2146:
2144:
2143:
2138:
2133:
2128:
2123:
2118:
2116:Kenneth Massey
2113:
2108:
2106:John Hollinger
2103:
2097:
2095:
2091:
2090:
2088:
2087:
2082:
2077:
2072:
2067:
2062:
2056:
2054:
2050:
2049:
2046:
2045:
2043:
2042:
2037:
2032:
2027:
2022:
2016:
2014:
2004:
2003:
1998:
1993:
1988:
1983:
1978:
1973:
1968:
1963:
1958:
1953:
1947:
1945:
1941:
1940:
1938:
1937:
1932:
1927:
1922:
1920:Home advantage
1916:
1914:
1910:
1909:
1902:
1901:
1894:
1887:
1879:
1872:
1871:
1852:"Numbers game"
1843:
1832:. Nov 25, 2013
1817:
1791:
1763:
1735:
1709:
1678:
1653:
1631:Barnwell, Bill
1622:
1615:
1595:
1564:
1533:
1502:
1474:
1440:
1417:
1399:"Safe at Home"
1389:
1348:
1325:(3 Nov 2014).
1314:
1282:
1280:
1277:
1276:
1275:
1257:(4): 241–248.
1239:
1213:
1176:
1175:
1174:
1122:
1119:
1118:
1117:
1116:
1115:
1109:
1094:
1088:
1065:
1060:New York Times
1050:
1046:The Power Rank
1035:
1032:
1031:
1030:
1006:
1005:Bibliographies
1003:
1001:
998:
997:
996:
991:
982:
977:
975:New York Times
972:
966:
964:Kenneth Massey
961:
959:Richard Dunkel
956:
947:
942:
928:
925:
924:
923:
914:
904:
868:
859:
850:
845:
836:
831:
820:
817:
804:
801:
781:Main article:
778:
775:
758:
757:
746:
738:
730:
724:Points Against
720:
715:
702:
690:
662:Main article:
659:
656:
643:
628:
625:
622:
621:
601:
599:
588:
587:Rating methods
585:
575:
572:
539:
536:
530:
527:
515:marginal value
499:
496:
475:
462:Main article:
459:
456:
446:Home advantage
444:Main article:
433:
432:Home advantage
430:
428:
425:
345:linear algebra
300:
297:
284:New York Times
279:Jeff Sagarin's
274:
271:
235:Division I FBS
208:power rankings
182:
181:
164:
163:
157:September 2016
139:of the subject
132:
130:
123:
116:
115:
98:September 2016
76:of the subject
74:worldwide view
69:
67:
60:
55:
29:
28:
26:
19:
9:
6:
4:
3:
2:
3200:
3199:
3188:
3185:
3183:
3180:
3178:
3175:
3173:
3170:
3168:
3165:
3163:
3160:
3158:
3155:
3153:
3150:
3148:
3145:
3144:
3142:
3127:
3119:
3117:
3109:
3107:
3106:
3095:
3094:
3091:
3085:
3084:South America
3082:
3080:
3077:
3075:
3074:North America
3072:
3070:
3067:
3065:
3062:
3060:
3057:
3055:
3052:
3051:
3049:
3045:
3039:
3036:
3034:
3031:
3029:
3026:
3024:
3021:
3020:
3018:
3016:
3012:
3006:
3003:
3001:
2998:
2996:
2993:
2991:
2988:
2986:
2983:
2981:
2978:
2977:
2975:
2973:
2969:
2963:
2960:
2958:
2957:Sportsmanship
2955:
2953:
2950:
2948:
2945:
2943:
2940:
2938:
2935:
2933:
2930:
2926:
2923:
2922:
2921:
2918:
2916:
2913:
2911:
2908:
2906:
2903:
2901:
2900:Entertainment
2898:
2896:
2893:
2891:
2888:
2887:
2885:
2881:
2875:
2872:
2868:
2865:
2863:
2860:
2858:
2855:
2854:
2853:
2850:
2848:
2845:
2844:
2842:
2840:
2839:Communication
2836:
2830:
2827:
2825:
2822:
2820:
2817:
2815:
2812:
2810:
2807:
2805:
2802:
2800:
2797:
2796:
2794:
2792:
2788:
2782:
2781:International
2779:
2777:
2774:
2772:
2769:
2765:
2762:
2760:
2757:
2756:
2755:
2752:
2750:
2747:
2745:
2742:
2741:
2739:
2737:Organizations
2735:
2729:
2726:
2724:
2723:Rating system
2721:
2717:
2714:
2712:
2709:
2708:
2707:
2704:
2700:
2697:
2695:
2692:
2691:
2690:
2687:
2683:
2680:
2678:
2675:
2673:
2670:
2668:
2665:
2663:
2660:
2659:
2658:
2655:
2653:
2650:
2646:
2643:
2641:
2638:
2636:
2635:Periodization
2633:
2631:
2628:
2626:
2623:
2622:
2621:
2618:
2617:
2615:
2613:
2609:
2603:
2600:
2598:
2595:
2593:
2590:
2588:
2585:
2583:
2580:
2578:
2575:
2573:
2570:
2568:
2565:
2564:
2562:
2558:
2554:
2547:
2542:
2540:
2535:
2533:
2528:
2527:
2524:
2512:
2509:
2507:
2504:
2500:
2497:
2495:
2492:
2490:
2487:
2486:
2485:
2482:
2480:
2477:
2473:
2470:
2468:
2465:
2464:
2462:
2460:
2457:
2453:
2450:
2448:
2445:
2444:
2442:
2438:
2435:
2433:
2430:
2428:
2425:
2424:
2423:Rugby league
2422:
2420:
2419:Roller hockey
2417:
2415:
2412:
2410:
2407:
2403:
2400:
2399:
2397:
2395:
2392:
2390:
2387:
2383:
2380:
2378:
2375:
2374:
2373:Field hockey
2372:
2368:
2365:
2363:
2360:
2358:
2355:
2354:
2352:
2348:
2345:
2343:
2340:
2338:
2335:
2334:
2332:
2330:
2327:
2325:
2322:
2318:
2315:
2314:
2313:
2310:
2306:
2303:
2301:
2298:
2297:
2295:
2293:
2290:
2286:
2283:
2281:
2278:
2276:
2273:
2271:
2268:
2267:
2265:
2263:
2260:
2258:
2255:
2251:
2248:
2246:
2243:
2242:
2240:
2236:
2233:
2231:
2228:
2227:
2225:
2223:
2220:
2218:
2215:
2213:
2210:
2207:
2203:
2200:
2198:
2195:
2193:
2190:
2189:
2186:
2177:
2172:
2170:
2165:
2163:
2158:
2157:
2154:
2142:
2139:
2137:
2134:
2132:
2129:
2127:
2124:
2122:
2119:
2117:
2114:
2112:
2109:
2107:
2104:
2102:
2101:Mark Glickman
2099:
2098:
2096:
2092:
2086:
2083:
2081:
2078:
2076:
2073:
2071:
2068:
2066:
2063:
2061:
2058:
2057:
2055:
2051:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2021:
2018:
2017:
2015:
2012:
2008:
2002:
1999:
1997:
1994:
1992:
1989:
1987:
1984:
1982:
1979:
1977:
1974:
1972:
1969:
1967:
1964:
1962:
1959:
1957:
1954:
1952:
1949:
1948:
1946:
1942:
1936:
1933:
1931:
1928:
1926:
1923:
1921:
1918:
1917:
1915:
1911:
1907:
1900:
1895:
1893:
1888:
1886:
1881:
1880:
1877:
1859:
1858:
1853:
1847:
1831:
1827:
1821:
1813:
1809:
1802:
1795:
1779:
1778:
1773:
1767:
1751:
1750:
1745:
1739:
1724:
1720:
1713:
1698:
1697:
1692:
1688:
1682:
1667:
1663:
1662:Simmons, Bill
1657:
1642:
1641:
1636:
1632:
1626:
1618:
1612:
1608:
1607:
1599:
1584:
1583:
1578:
1574:
1573:Simmons, Bill
1568:
1553:
1552:
1547:
1543:
1537:
1522:
1521:
1516:
1513:(Fall 2014).
1512:
1511:Sagarin, Jeff
1506:
1491:
1490:
1485:
1478:
1470:
1458:
1454:
1450:
1444:
1428:
1421:
1406:
1405:
1400:
1393:
1378:
1374:
1370:
1366:
1359:
1352:
1344:
1332:
1328:
1324:
1318:
1311:
1300:
1299:
1298:Sporting News
1294:
1287:
1283:
1272:
1268:
1264:
1260:
1256:
1252:
1245:
1240:
1235:
1231:
1228:available at
1222:
1218:
1214:
1210:
1206:
1202:
1198:
1194:
1190:
1186:
1182:
1177:
1170:
1166:
1162:
1161:
1158:
1154:
1150:
1146:
1142:
1138:
1134:
1130:
1125:
1124:
1121:Academic work
1112:
1106:
1102:
1101:
1095:
1091:
1085:
1081:
1080:
1074:
1073:
1070:
1066:
1062:
1061:
1056:
1051:
1047:
1043:
1038:
1037:
1034:Popular press
1020:
1019:
1014:
1009:
1008:
995:
992:
990:
986:
983:
981:
980:David Rothman
978:
976:
973:
970:
967:
965:
962:
960:
957:
955:
951:
948:
946:
943:
941:
940:Seattle Times
937:
934:
933:
932:
922:
918:
915:
912:
908:
905:
903:
899:
895:
891:
887:
883:
879:
876:
872:
869:
867:
863:
860:
858:
854:
851:
849:
848:Colley Matrix
846:
844:
840:
837:
835:
832:
830:
826:
823:
822:
816:
814:
810:
809:Markov chains
800:
798:
794:
790:
784:
774:
771:
767:
763:
762:Bill Barnwell
744:
736:
728:
718:
713:
700:
688:
676:
675:
674:
672:
665:
652:
648:
642:
637:
635:
618:
609:
605:
600:
593:
592:
584:
582:
571:
569:
565:
561:
557:
553:
549:
545:
535:
526:
524:
520:
516:
511:
509:
505:
495:
493:
484:
480:
474:
470:
465:
455:
453:
447:
438:
424:
422:
416:
414:
410:
406:
402:
398:
394:
390:
386:
382:
378:
374:
370:
366:
362:
356:
354:
350:
346:
342:
337:
335:
331:
327:
323:
319:
314:
309:
307:
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2020:Chessmetrics
1925:Sabermetrics
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2131:Nate Silver
2121:Ken Pomeroy
1784:22 December
1728:21 December
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1671:10 November
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1217:Massey, Ken
1024:18 November
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397:Fiesta Bowl
262:objectivity
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3028:Ministries
3023:Sports law
3005:Sportswear
2942:Philosophy
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2111:Bill James
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1723:The Spread
1646:January 7,
1489:Fox Sports
1304:2011-03-24
1279:References
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913:- obsolete
902:volleyball
878:basketball
709:Points For
696:Points For
604:incomplete
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377:Ohio State
361:Ivy League
349:statistics
326:Ohio State
322:Penn State
266:Ken Massey
36:improve it
3182:Analytics
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2947:Rivalries
2932:Numbering
2925:Nicknames
2874:Promoters
2857:Magazines
2819:Marketing
2809:Economics
2728:Sociology
2689:Nutrition
2409:Muay Thai
2333:Football
2329:Floorball
2202:Badminton
2197:Athletics
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2001:TrueSkill
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1582:Grantland
1520:USA Today
1404:Grantland
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1201:1559-0410
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1149:1559-0410
989:USA Today
917:TrueSkill
789:Arpad Elo
737:×
673:has used
651:Grantland
519:logarithm
483:Jeff Long
391:champion
365:Dartmouth
216:standings
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137:full view
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3116:Category
3015:Politics
2995:Exercise
2962:Violence
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882:baseball
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2890:Betting
2883:Culture
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2602:Amateur
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3054:Africa
2990:Caving
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