465:. 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.
233:
448:
74:
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137:
33:
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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.
784:
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.
766:
1320:
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
679:
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
651:
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,
479:
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
544:
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
369:
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
279:
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,
783:
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
314:
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
429:
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
1082:
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.
642:
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
589:
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.
1321:
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.
690:
326:
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
268:. 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).
288:
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:
343:, 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
771:
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,
390:. 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-
528:
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
398:
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.
553:
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
1138:
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".
394:
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
1437:
461:
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
2419:
802:
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,
501:
The college football playoff committee uses a limited strength-of-schedule algorithm that only considers opponents' records and opponents' opponents' records (much like
810:
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.
761:{\displaystyle {\text{Pythagorean wins}}={\frac {{\text{Points For}}^{2.37}}{{\text{Points For}}^{2.37}+{\text{Points Against}}^{2.37}}}\times {\text{Games Played}}.}
1556:
1176:
Sports
Rankings REU Final Report 2012: An Analysis of Pairwise-Comparison Based Sports Ranking Methods and a Novel Agent-Based Markovian Basketball Simulation
518:
347:). 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.
1338:"@kenpomeroy human polls have limited value. Computer systems can objectively track all the teams. http://www.masseyratings.com/cb/compare.htm #all351"
521:. Rating teams based on margin of victory is often criticized as creating an incentive for coaches to run up the score, an "unsportsmanlike" outcome.
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2334:
280:
rating systems relying on human polls include inherent human subjectivity; this may or may not be an attractive property depending on system needs.
213:, are numerical representations of competitive strength, often directly comparable so that the game outcome between any two teams can be predicted.
423:
411:
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1907:
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147:
84:
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misinterpretation of rating system results by people unfamiliar with these goals; for example, a rating system designed to give accurate
1190:
Gray, Kathy L.; Schwertman, Neil C. (March 2012). "Comparing Team Selection and Seeding for the 2011 NCAA men's basketball tournament".
2260:
1303:
1052:
2295:
1494:
942:
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.
221:, 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
2791:
2482:
2080:
885:
241:
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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.
225:
rank to each team, so that the highest rated team earns the #1 rank. Rating systems provide an alternative to traditional sports
3157:
2477:
2310:
328:
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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
2462:
2075:
1625:
1119:
1098:
363:
46:
513:
A key dichotomy among sports rating systems lies in the representation of game outcomes. Some systems store final scores as
2227:
1175:
614:
2935:
1900:
1028:
904:
399:
2315:
2177:
1996:
1240:
872:
581:. 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
383:
184:
118:
60:
533:
1862:
1255:"A Penalized Maximum Likelihood Approach for the Ranking of College Football Teams Independent of Victory Margins"
3033:
2554:
2290:
2280:
2267:
2255:
974:
574:
378:, 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
1090:
Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football
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2372:
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1893:
1676:
1645:
2814:
2447:
2442:
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2245:
2170:
2151:
1004:
493:
332:
17:
1971:
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2392:
1836:
990:
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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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1961:
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917:
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among all members of the league, such as each team being built from an equitable pool of players via a
1587:
306:
championship game participants were determined by a combination of expert polls and computer systems.
1464:"Committee doesn't use an SOS ranking. It looks at opponents' record and opponents' opponents record"
159:
96:
52:
1841:
Indiana University Bloomington - Kelley School of Business - Operations & Decisions Technologies
3177:
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881:
839:
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502:
489:
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303:
249:
100:
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2006:
2001:
1617:
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
674:
415:
1811:
496:, 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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2429:
2424:
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578:
379:
340:
618:
155:
92:
2759:
2090:
2035:
1088:
979:
570:
387:
336:
272:
366:, others in traditional statistics, mathematics, psychology, and computer science journals.
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1940:
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8:
3048:
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2635:
2602:
2547:
2232:
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the same exponent, is placed in the denominator and added to the value in the numerator.
462:
316:
1337:
3192:
3069:
3038:
3005:
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2302:
2222:
1986:
1981:
1966:
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1215:
1163:
1079:
955:
888:
876:
844:
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681:
591:
514:
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the same opponents. Therefore, judging their relative win–loss records is complicated.
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253:
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1219:
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793:
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were awarded an at-large tournament bid due to their regular season record and their
375:
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3089:
3000:
2982:
2920:
2829:
2819:
2801:
2699:
2692:
2577:
1976:
1867:
1463:
1383:
1281:
1269:
1244:
1199:
1179:
1147:
908:
896:
892:
867:
863:
302:, which dates back to 1929. Before the advent of the college football playoff, the
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3079:
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2990:
2942:
2867:
2857:
2769:
2667:
2662:
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1945:
1706:
1615:
1525:
1109:
807:
554:
245:
252:. Sports ratings systems are also used to help determine the field for the NCAA
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2622:
2612:
2540:
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1930:
1614:
Schatz, Aaron; Alamar, Ben; Barnwell, Bill; Bill Connelly; Doug Farrar (2011).
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1368:
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1227:
1070:
900:
558:
525:
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355:
323:
294:
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2764:
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2111:
1641:
1308:
1211:
1159:
969:
960:
858:
819:
772:
232:
222:
206:
447:
2915:
2877:
2809:
2709:
2509:
2504:
2499:
2412:
2136:
2095:
2085:
2030:
1935:
1672:
1583:
1521:
1203:
1151:
995:
849:
803:
780:
657:
431:
299:
289:
240:
In the United States, the biggest use of sports ratings systems is to rate
1273:
2786:
2754:
2141:
2131:
1697:
407:
2162:
1885:
205:
for each team or player. Common systems include polls of expert voters,
201:
is a system that analyzes the results of sports competitions to provide
3015:
2592:
2582:
2146:
2121:
1499:
1333:
912:
562:
371:
359:
276:
202:
209:
non-expert voters, betting markets, and computer systems. Ratings, or
2011:
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1592:
1530:
1414:
927:
799:
661:
529:
226:
1730:"Using Continuous-Time Markov Chains to Rank College Football Teams"
2947:
2774:
2630:
1759:
1053:"How to understand college football analytics – the ultimate guide"
937:
823:
351:
3010:
2070:
1613:
1479:
1353:
214:
779:
had a Pythagorean record two wins lower than their real record.
410:
by a score of 35-7. A related example occurred during the 2006
2962:
1787:
921:
853:
265:
261:
1066:"College Football Rankers by the Dozen Ask the No. 1 Question"
2563:
83:
deal primarily with the United States and do not represent a
2995:
1991:
1561:
257:
775:
calculated that before week 9 of the 2014 NFL season, the
565:
system as is done in many major league sports such as the
275:, without specific player, team, regional, or style bias.
1783:"Modifying Google's Page Ranking Algorithm to rank teams"
524:
Still other systems choose a middle ground, reducing the
2532:
1369:"The Home Field Advantage in Athletics: A Meta-Analysis"
1241:
Statistical Models Applied to the Rating of Sports Teams
1137:
1078:
Wayne Winston is a professor of decision sciences at
693:
1812:"A Bayesian Approximation Method for Online Ranking"
1111:
Microsoft® Excel Data Analysis and Business Modeling
787:
1024:"Bibliography on College Football Ranking Systems"
760:
1837:"Wayne Winston: Analytics in the World of Sports"
3149:
1438:"Oregon up to 2 in playoff rankings; TCU to 4th"
938:Bowl Championship Series computer rating systems
829:
826:have also been adapted to rank football teams.
1458:
1189:
2548:
2178:
1901:
422:and rode that opportunity all the way to the
236:College football players in the United States
144:The examples and perspective in this article
81:The examples and perspective in this article
1646:"NFL at the Half: Breaking Down the Numbers"
930:, a Bayesian ranking system inspired by the
1677:"Revisiting the Y2K-Compliant Quarterbacks"
1551:
637:
61:Learn how and when to remove these messages
2555:
2541:
2185:
2171:
1908:
1894:
1332:
1192:Journal of Quantitative Analysis in Sports
1140:Journal of Quantitative Analysis in Sports
2192:
2020:
1915:
1755:"Ranking NFL teams using Network Science"
1304:"Sorting through teams on one big bubble"
1174:Much of this information is available at
185:Learn how and when to remove this message
119:Learn how and when to remove this message
3198:American football records and statistics
2081:Harris Interactive College Football Poll
1640:
1492:
1407:
1366:
446:
437:
271:Computer rating systems can tend toward
231:
229:which are based on win–loss–tie ratios.
1809:
1671:
1582:
1520:
1495:"BCS removes margin-of-victory element"
1107:
1086:
468:
370:football seasons, such as when the top
14:
3150:
1696:
1226:
1063:
539:
329:2005 NCAA Division I-A football season
2536:
2166:
2076:FWAA-NFF Grantland Rice Super 16 Poll
1889:
1810:Weng, Ruby C.; Lin, Chih-Jen (2011).
1727:
1435:
1301:
1252:
508:
364:MIT Sloan Sports Analytics Conference
1819:Journal of Machine Learning Research
1436:Russo, Ralph D. (11 November 2014).
1408:Barnwell, Bill (December 20, 2013).
1376:Journal of Applied Social Psychology
1050:
813:
601:
451:France national basketball team fans
130:
67:
26:
1588:"Week 8 Picks: A Gambling Epiphany"
1557:"More flags on D spins scoreboards"
1064:Mather, Victor (October 23, 2012).
548:
24:
1997:Pomeroy College Basketball Ratings
1021:
1010:
873:Pomeroy College Basketball Ratings
25:
3209:
1015:
597:
442:
42:This article has multiple issues.
3131:
3122:
3121:
3109:
1982:English Chess Federation grading
1728:Mills, Matt (21 December 2014).
1388:10.1111/j.1559-1816.2010.00641.x
1131:
1044:
818:Researchers like Matt Mills use
605:
534:cumulative distribution function
412:NCAA men's basketball tournament
256:tournaments, men's professional
248:, choosing teams to play in the
135:
72:
31:
3132:
1855:
1829:
1803:
1775:
1747:
1721:
1690:
1665:
1634:
1607:
1576:
1232:"Honors Project in Mathematics"
1029:University of Wisconsin–Madison
50:or discuss these issues on the
1620:. CreateSpace. p. xviii.
1545:
1514:
1486:
1452:
1429:
1401:
1360:
1326:
1295:
1093:. Princeton University Press.
882:Ratings Percentage Index (RPI)
668:
652:whatever — I tagged that, too.
13:
1:
3158:Sports records and statistics
2096:USA Today/Amway Coaches' Poll
2007:Rating Percentage Index (RPI)
1702:"Introducing NFL Elo Ratings"
1289:
1051:Feng, Ed (24 November 2014).
830:List of sports rating systems
584:
158:and discuss the issue on the
1526:"NCAAF Jeff Sagarin Ratings"
1367:Jamieson, Jeremy P. (2010).
965:Atlanta Journal-Constitution
613:This sports-related list is
463:number of time zones crossed
254:men's and women's basketball
7:
1962:Advanced Football Analytics
1955:Methods and computer models
920:, United States of America
884:, United States of America
875:, United States of America
866:, United States of America
838:, United States of America
95:, discuss the issue on the
10:
3214:
1302:Fagan, Ryan (2011-03-09).
1108:Winston, Wayne L. (2009).
1087:Winston, Wayne L. (2012).
918:Smithman Qualitative Index
791:
672:
472:
454:
283:
260:tournaments, professional
244:college football teams in
3103:
3057:
3024:
2981:
2893:
2848:
2800:
2747:
2621:
2570:
2562:
2198:
2104:
2063:
1954:
1923:
1493:Richards, Darryl (2001).
1262:The American Statistician
374:teams of the 1970s, like
309:
2705:Bodybuilding supplements
1972:Bowl Championship Series
840:National Football League
638:Permutation of standings
490:College football playoff
354:perspective, the use of
304:Bowl Championship Series
250:College Football Playoff
2233:Baseball & softball
2002:Pythagorean expectation
798:Originally designed by
675:Pythagorean expectation
1204:10.1515/1559-0410.1369
1152:10.1515/jqas-2013-0013
788:Trading "skill points"
762:
666:
499:
452:
237:
3188:Basketball statistics
2193:Sports world rankings
1917:Sports rating systems
1274:10.1198/0003130032396
1253:Mease, David (2003).
947:Anderson & Hester
763:
649:
482:
450:
438:Rating considerations
235:
1941:Strength of schedule
1700:(4 September 2014).
1644:(November 5, 2014).
1555:(18 November 2014).
932:Glicko rating system
691:
619:adding missing items
475:Strength of schedule
469:Strength of schedule
345:home field advantage
317:transitive relations
199:sports rating system
156:improve this article
146:may not represent a
101:create a new article
93:improve this article
3183:Baseball statistics
2409:Mixed martial arts
1675:(7 November 2014).
1586:(24 October 2014).
1114:. Microsoft Press.
956:Richard Billingsley
540:In-game information
492:committee chairman
400:Big East Conference
3163:Sports terminology
2722:Physical education
2091:NAIA Coaches' Poll
1987:Litkenhous Ratings
1967:ARGH Power Ratings
1791:. 21 December 2014
1553:Easterbrook, Gregg
1440:. Associated Press
1080:Indiana University
877:college basketball
845:ARGH Power Ratings
836:Advanced NFL Stats
758:
682:Football Outsiders
617:; you can help by
592:ARGH Power Ratings
532:or placement on a
509:Points versus wins
453:
339:, Ohio State beat
238:
3145:
3144:
3116:Sports portal
2727:Physical activity
2673:Athletic training
2656:Strength training
2608:Semi-professional
2530:
2529:
2160:
2159:
2064:Polls and opinion
2059:
2058:
1627:978-1-4662-4613-3
1121:978-0-7356-3714-6
1100:978-1-4008-4207-0
814:Solving equations
794:Elo rating system
777:Arizona Cardinals
753:
745:
736:
721:
708:
697:
645:Gregg Easterbrook
635:
634:
519:margin of victory
264:tournaments, and
195:
194:
187:
177:
176:
129:
128:
121:
103:, as appropriate.
65:
16:(Redirected from
3205:
3135:
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3114:
3113:
3112:
2858:General managers
2760:Governing bodies
2557:
2550:
2543:
2534:
2533:
2296:WODI & WT20I
2228:Beach volleyball
2187:
2180:
2173:
2164:
2163:
2018:
2017:
1977:Dickinson System
1910:
1903:
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1887:
1886:
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1871:. April 13, 2004
1868:Washington Times
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1745:
1744:
1742:
1740:
1725:
1719:
1718:
1716:
1714:
1694:
1688:
1687:
1685:
1683:
1669:
1663:
1662:
1660:
1658:
1638:
1632:
1631:
1611:
1605:
1604:
1602:
1600:
1580:
1574:
1573:
1571:
1569:
1549:
1543:
1542:
1540:
1538:
1518:
1512:
1511:
1509:
1507:
1490:
1484:
1483:
1477:
1475:
1456:
1450:
1449:
1447:
1445:
1433:
1427:
1426:
1424:
1422:
1405:
1399:
1398:
1396:
1394:
1382:(7): 1819–1848.
1373:
1364:
1358:
1357:
1351:
1349:
1330:
1324:
1323:
1317:
1316:
1299:
1285:
1259:
1249:
1245:Internet Archive
1238:
1236:
1223:
1184:
1180:Internet Archive
1171:
1125:
1104:
1075:
1060:
1040:
1038:
1036:
982:/ Scripps Howard
868:college football
864:Dickinson System
852:, international
767:
765:
764:
759:
754:
751:
746:
744:
743:
742:
737:
734:
728:
727:
722:
719:
715:
714:
709:
706:
703:
698:
696:Pythagorean wins
695:
664:
660:, sportswriter,
630:
627:
609:
608:
602:
549:Team composition
497:
298:system, and the
190:
183:
172:
169:
163:
139:
138:
131:
124:
117:
113:
110:
104:
76:
75:
68:
57:
35:
34:
27:
21:
3213:
3212:
3208:
3207:
3206:
3204:
3203:
3202:
3178:Sports business
3168:Sports rankings
3148:
3147:
3146:
3141:
3110:
3108:
3099:
3058:Sport by region
3053:
3020:
2991:Artificial turf
2977:
2948:Olympic culture
2889:
2844:
2796:
2743:
2617:
2588:Military sports
2566:
2561:
2531:
2526:
2307:Cycling (road)
2194:
2191:
2161:
2156:
2100:
2055:
2016:
1950:
1946:Win probability
1919:
1914:
1884:
1874:
1872:
1861:
1860:
1856:
1846:
1844:
1835:
1834:
1830:
1814:
1808:
1804:
1794:
1792:
1781:
1780:
1776:
1766:
1764:
1763:. 17 March 2016
1753:
1752:
1748:
1738:
1736:
1726:
1722:
1712:
1710:
1707:FiveThirtyEight
1695:
1691:
1681:
1679:
1670:
1666:
1656:
1654:
1639:
1635:
1628:
1612:
1608:
1598:
1596:
1581:
1577:
1567:
1565:
1550:
1546:
1536:
1534:
1519:
1515:
1505:
1503:
1491:
1487:
1473:
1471:
1462:(12 Nov 2014).
1460:Stewart Mandel
1457:
1453:
1443:
1441:
1434:
1430:
1420:
1418:
1406:
1402:
1392:
1390:
1371:
1365:
1361:
1347:
1345:
1331:
1327:
1314:
1312:
1300:
1296:
1292:
1257:
1247:
1234:
1230:(Spring 1997).
1182:
1134:
1122:
1101:
1047:
1034:
1032:
1022:Wilson, David.
1018:
1013:
1011:Further reading
980:Herman Matthews
940:
832:
816:
808:FiveThirtyEight
796:
790:
750:
738:
733:
732:
723:
718:
717:
716:
710:
705:
704:
702:
694:
692:
689:
688:
677:
671:
665:
656:
640:
631:
625:
622:
606:
600:
587:
551:
542:
511:
498:
488:
477:
471:
459:
445:
440:
312:
286:
191:
180:
179:
178:
173:
167:
164:
153:
140:
136:
125:
114:
108:
105:
90:
77:
73:
36:
32:
23:
22:
15:
12:
11:
5:
3211:
3201:
3200:
3195:
3190:
3185:
3180:
3175:
3173:Sports science
3170:
3165:
3160:
3143:
3142:
3140:
3139:
3129:
3119:
3104:
3101:
3100:
3098:
3097:
3092:
3087:
3082:
3077:
3072:
3067:
3061:
3059:
3055:
3054:
3052:
3051:
3046:
3044:National sport
3041:
3036:
3030:
3028:
3022:
3021:
3019:
3018:
3013:
3008:
3003:
2998:
2993:
2987:
2985:
2979:
2978:
2976:
2975:
2970:
2965:
2963:Sports mascots
2960:
2955:
2950:
2945:
2940:
2939:
2938:
2928:
2923:
2918:
2913:
2908:
2903:
2897:
2895:
2891:
2890:
2888:
2887:
2882:
2881:
2880:
2875:
2870:
2860:
2854:
2852:
2846:
2845:
2843:
2842:
2837:
2832:
2827:
2822:
2817:
2812:
2806:
2804:
2798:
2797:
2795:
2794:
2789:
2784:
2779:
2778:
2777:
2772:
2762:
2757:
2751:
2749:
2745:
2744:
2742:
2741:
2736:
2731:
2730:
2729:
2724:
2714:
2713:
2712:
2707:
2697:
2696:
2695:
2690:
2685:
2680:
2675:
2665:
2660:
2659:
2658:
2653:
2648:
2643:
2638:
2627:
2625:
2619:
2618:
2616:
2615:
2610:
2605:
2600:
2595:
2590:
2585:
2580:
2574:
2572:
2568:
2567:
2560:
2559:
2552:
2545:
2537:
2528:
2527:
2525:
2524:
2519:
2514:
2513:
2512:
2507:
2502:
2492:
2487:
2486:
2485:
2480:
2472:
2467:
2466:
2465:
2460:
2452:
2451:
2450:
2445:
2440:
2432:
2427:
2422:
2417:
2416:
2415:
2407:
2402:
2397:
2396:
2395:
2390:
2382:
2381:
2380:
2375:
2370:
2362:
2361:
2360:
2355:
2353:unofficial elo
2350:
2342:
2337:
2335:Figure skating
2332:
2331:
2330:
2320:
2319:
2318:
2313:
2305:
2300:
2299:
2298:
2293:
2288:
2283:
2275:
2270:
2265:
2264:
2263:
2258:
2250:
2249:
2248:
2243:
2235:
2230:
2225:
2220:
2210:
2205:
2199:
2196:
2195:
2190:
2189:
2182:
2175:
2167:
2158:
2157:
2155:
2154:
2149:
2144:
2139:
2134:
2129:
2127:Kenneth Massey
2124:
2119:
2117:John Hollinger
2114:
2108:
2106:
2102:
2101:
2099:
2098:
2093:
2088:
2083:
2078:
2073:
2067:
2065:
2061:
2060:
2057:
2056:
2054:
2053:
2048:
2043:
2038:
2033:
2027:
2025:
2015:
2014:
2009:
2004:
1999:
1994:
1989:
1984:
1979:
1974:
1969:
1964:
1958:
1956:
1952:
1951:
1949:
1948:
1943:
1938:
1933:
1931:Home advantage
1927:
1925:
1921:
1920:
1913:
1912:
1905:
1898:
1890:
1883:
1882:
1863:"Numbers game"
1854:
1843:. Nov 25, 2013
1828:
1802:
1774:
1746:
1720:
1689:
1664:
1642:Barnwell, Bill
1633:
1626:
1606:
1575:
1544:
1513:
1485:
1451:
1428:
1410:"Safe at Home"
1400:
1359:
1336:(3 Nov 2014).
1325:
1293:
1291:
1288:
1287:
1286:
1268:(4): 241–248.
1250:
1224:
1187:
1186:
1185:
1133:
1130:
1129:
1128:
1127:
1126:
1120:
1105:
1099:
1076:
1071:New York Times
1061:
1057:The Power Rank
1046:
1043:
1042:
1041:
1017:
1016:Bibliographies
1014:
1012:
1009:
1008:
1007:
1002:
993:
988:
986:New York Times
983:
977:
975:Kenneth Massey
972:
970:Richard Dunkel
967:
958:
953:
939:
936:
935:
934:
925:
915:
879:
870:
861:
856:
847:
842:
831:
828:
815:
812:
792:Main article:
789:
786:
769:
768:
757:
749:
741:
735:Points Against
731:
726:
713:
701:
673:Main article:
670:
667:
654:
639:
636:
633:
632:
612:
610:
599:
598:Rating methods
596:
586:
583:
550:
547:
541:
538:
526:marginal value
510:
507:
486:
473:Main article:
470:
467:
457:Home advantage
455:Main article:
444:
443:Home advantage
441:
439:
436:
356:linear algebra
311:
308:
295:New York Times
290:Jeff Sagarin's
285:
282:
246:Division I FBS
219:power rankings
193:
192:
175:
174:
168:September 2016
150:of the subject
143:
141:
134:
127:
126:
109:September 2016
87:of the subject
85:worldwide view
80:
78:
71:
66:
40:
39:
37:
30:
9:
6:
4:
3:
2:
3210:
3199:
3196:
3194:
3191:
3189:
3186:
3184:
3181:
3179:
3176:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3155:
3153:
3138:
3130:
3128:
3120:
3118:
3117:
3106:
3105:
3102:
3096:
3095:South America
3093:
3091:
3088:
3086:
3085:North America
3083:
3081:
3078:
3076:
3073:
3071:
3068:
3066:
3063:
3062:
3060:
3056:
3050:
3047:
3045:
3042:
3040:
3037:
3035:
3032:
3031:
3029:
3027:
3023:
3017:
3014:
3012:
3009:
3007:
3004:
3002:
2999:
2997:
2994:
2992:
2989:
2988:
2986:
2984:
2980:
2974:
2971:
2969:
2968:Sportsmanship
2966:
2964:
2961:
2959:
2956:
2954:
2951:
2949:
2946:
2944:
2941:
2937:
2934:
2933:
2932:
2929:
2927:
2924:
2922:
2919:
2917:
2914:
2912:
2911:Entertainment
2909:
2907:
2904:
2902:
2899:
2898:
2896:
2892:
2886:
2883:
2879:
2876:
2874:
2871:
2869:
2866:
2865:
2864:
2861:
2859:
2856:
2855:
2853:
2851:
2850:Communication
2847:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2823:
2821:
2818:
2816:
2813:
2811:
2808:
2807:
2805:
2803:
2799:
2793:
2792:International
2790:
2788:
2785:
2783:
2780:
2776:
2773:
2771:
2768:
2767:
2766:
2763:
2761:
2758:
2756:
2753:
2752:
2750:
2748:Organizations
2746:
2740:
2737:
2735:
2734:Rating system
2732:
2728:
2725:
2723:
2720:
2719:
2718:
2715:
2711:
2708:
2706:
2703:
2702:
2701:
2698:
2694:
2691:
2689:
2686:
2684:
2681:
2679:
2676:
2674:
2671:
2670:
2669:
2666:
2664:
2661:
2657:
2654:
2652:
2649:
2647:
2646:Periodization
2644:
2642:
2639:
2637:
2634:
2633:
2632:
2629:
2628:
2626:
2624:
2620:
2614:
2611:
2609:
2606:
2604:
2601:
2599:
2596:
2594:
2591:
2589:
2586:
2584:
2581:
2579:
2576:
2575:
2573:
2569:
2565:
2558:
2553:
2551:
2546:
2544:
2539:
2538:
2535:
2523:
2520:
2518:
2515:
2511:
2508:
2506:
2503:
2501:
2498:
2497:
2496:
2493:
2491:
2488:
2484:
2481:
2479:
2476:
2475:
2473:
2471:
2468:
2464:
2461:
2459:
2456:
2455:
2453:
2449:
2446:
2444:
2441:
2439:
2436:
2435:
2434:Rugby league
2433:
2431:
2430:Roller hockey
2428:
2426:
2423:
2421:
2418:
2414:
2411:
2410:
2408:
2406:
2403:
2401:
2398:
2394:
2391:
2389:
2386:
2385:
2384:Field hockey
2383:
2379:
2376:
2374:
2371:
2369:
2366:
2365:
2363:
2359:
2356:
2354:
2351:
2349:
2346:
2345:
2343:
2341:
2338:
2336:
2333:
2329:
2326:
2325:
2324:
2321:
2317:
2314:
2312:
2309:
2308:
2306:
2304:
2301:
2297:
2294:
2292:
2289:
2287:
2284:
2282:
2279:
2278:
2276:
2274:
2271:
2269:
2266:
2262:
2259:
2257:
2254:
2253:
2251:
2247:
2244:
2242:
2239:
2238:
2236:
2234:
2231:
2229:
2226:
2224:
2221:
2218:
2214:
2211:
2209:
2206:
2204:
2201:
2200:
2197:
2188:
2183:
2181:
2176:
2174:
2169:
2168:
2165:
2153:
2150:
2148:
2145:
2143:
2140:
2138:
2135:
2133:
2130:
2128:
2125:
2123:
2120:
2118:
2115:
2113:
2112:Mark Glickman
2110:
2109:
2107:
2103:
2097:
2094:
2092:
2089:
2087:
2084:
2082:
2079:
2077:
2074:
2072:
2069:
2068:
2066:
2062:
2052:
2049:
2047:
2044:
2042:
2039:
2037:
2034:
2032:
2029:
2028:
2026:
2023:
2019:
2013:
2010:
2008:
2005:
2003:
2000:
1998:
1995:
1993:
1990:
1988:
1985:
1983:
1980:
1978:
1975:
1973:
1970:
1968:
1965:
1963:
1960:
1959:
1957:
1953:
1947:
1944:
1942:
1939:
1937:
1934:
1932:
1929:
1928:
1926:
1922:
1918:
1911:
1906:
1904:
1899:
1897:
1892:
1891:
1888:
1870:
1869:
1864:
1858:
1842:
1838:
1832:
1824:
1820:
1813:
1806:
1790:
1789:
1784:
1778:
1762:
1761:
1756:
1750:
1735:
1731:
1724:
1709:
1708:
1703:
1699:
1693:
1678:
1674:
1673:Simmons, Bill
1668:
1653:
1652:
1647:
1643:
1637:
1629:
1623:
1619:
1618:
1610:
1595:
1594:
1589:
1585:
1584:Simmons, Bill
1579:
1564:
1563:
1558:
1554:
1548:
1533:
1532:
1527:
1524:(Fall 2014).
1523:
1522:Sagarin, Jeff
1517:
1502:
1501:
1496:
1489:
1481:
1469:
1465:
1461:
1455:
1439:
1432:
1417:
1416:
1411:
1404:
1389:
1385:
1381:
1377:
1370:
1363:
1355:
1343:
1339:
1335:
1329:
1322:
1311:
1310:
1309:Sporting News
1305:
1298:
1294:
1283:
1279:
1275:
1271:
1267:
1263:
1256:
1251:
1246:
1242:
1239:available at
1233:
1229:
1225:
1221:
1217:
1213:
1209:
1205:
1201:
1197:
1193:
1188:
1181:
1177:
1173:
1172:
1169:
1165:
1161:
1157:
1153:
1149:
1145:
1141:
1136:
1135:
1132:Academic work
1123:
1117:
1113:
1112:
1106:
1102:
1096:
1092:
1091:
1085:
1084:
1081:
1077:
1073:
1072:
1067:
1062:
1058:
1054:
1049:
1048:
1045:Popular press
1031:
1030:
1025:
1020:
1019:
1006:
1003:
1001:
997:
994:
992:
991:David Rothman
989:
987:
984:
981:
978:
976:
973:
971:
968:
966:
962:
959:
957:
954:
952:
951:Seattle Times
948:
945:
944:
943:
933:
929:
926:
923:
919:
916:
914:
910:
906:
902:
898:
894:
890:
887:
883:
880:
878:
874:
871:
869:
865:
862:
860:
859:Colley Matrix
857:
855:
851:
848:
846:
843:
841:
837:
834:
833:
827:
825:
821:
820:Markov chains
811:
809:
805:
801:
795:
785:
782:
778:
774:
773:Bill Barnwell
755:
747:
739:
729:
724:
711:
699:
687:
686:
685:
683:
676:
663:
659:
653:
648:
646:
629:
620:
616:
611:
604:
603:
595:
593:
582:
580:
576:
572:
568:
564:
560:
556:
546:
537:
535:
531:
527:
522:
520:
516:
506:
504:
495:
491:
485:
481:
476:
466:
464:
458:
449:
435:
433:
427:
425:
421:
417:
413:
409:
405:
401:
397:
393:
389:
385:
381:
377:
373:
367:
365:
361:
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2137:Jeff Sagarin
2086:Legends Poll
2031:Chessmetrics
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1739:21 December
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1228:Massey, Ken
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2122:Bill James
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1734:The Spread
1657:January 7,
1500:Fox Sports
1315:2011-03-24
1290:References
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924:- obsolete
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360:statistics
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277:Ken Massey
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2820:Economics
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2700:Nutrition
2420:Muay Thai
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2340:Floorball
2213:Badminton
2208:Athletics
2051:Universal
2012:TrueSkill
1651:Grantland
1593:Grantland
1531:USA Today
1415:Grantland
1248: PDF
1220:121322446
1212:1559-0410
1183: PDF
1168:199665454
1160:1559-0410
1000:USA Today
928:TrueSkill
800:Arpad Elo
748:×
684:has used
662:Grantland
530:logarithm
494:Jeff Long
402:champion
376:Dartmouth
227:standings
160:talk page
148:full view
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3006:Exercise
2973:Violence
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1924:Concepts
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893:baseball
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215:Rankings
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2921:History
2901:Betting
2894:Culture
2765:Leagues
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2613:Amateur
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2470:Snooker
2425:Netball
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223:ordinal
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154:Please
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3065:Africa
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2931:Naming
2810:Agents
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