This paper discusses the project topic in depth and the procedures and logic used during the project to achieve our results.

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Producing Valid College Football Rankings in Reasonable Time
Mark Edwards
Department of Mechanical Engineering
Jonathan Shumaker
Department of Chemical Engineering
Faculty Mentor: C. Richard Cassady Ph.D.
Department of Industrial Engineering
Abstract
College footballis anannualsource ofcontroversywhenit comes time to produce the NCAA Bowl
ChampionshipSubdivisionrankings at the end ofthe regular season. From the secrecyof how the computer
systems rank teams, to the bizarre ballots submittedfor the coach’s poll, everyyear people askthe
question:is there a better wayto do this? Ina couple years, there willbe a four-team playoff to determine
the two teams that playinthe national championship, andthe CMS+ rankingsystemaims to guide the
counselthat will select the teams that playinthe playoff. The CMS+ system uses the quadratic assignment
problem, a wayto mathematicallypush winningteams to the top ofthe rankings andlosingteams to the
bottom produce results. Currentlyit takes a long time for the CMS+ to produce results, andthis is where we
are doing our research. We improvedthe CMS+ systemintwo ways. We have foundand set parameters for
degree of victoryto be based off of withinthe CMS+ system. We also have found the ideal amount of
mutations andrepeatedtests for the CMS+ systemto produce rankings of high quality.
1. The PresentState ofCollege Football
There are currently124 teamsinthe NCAA Football Bowl Subdivision. Eachteam will play around12
gameseach season. Thismeansthatonlyaboutnine percentof the matchupsthat couldhappen
actuallyhappen. Obviouslythere are manymatchupsthatdo not occur, thusit isveryhard to decide
whoshouldplayinthe National Championshipgame. Currentlythere are onlytwoteamschosentoplay
inthe national championshipgame,butthiswillchange in2014 withthe additionof a four-teamplayoff.
There are manyfinancial implicationstoplayinginthe National ChampionshipandotherBCSbowl
games. There couldbe evenmore moneyonthe line whentheymove toa playoff system. Itisvery
hard to choose the twoteamsthat playfor the national championshipformultiple reasons. The firstis
that there are many possible rankings;124! to be exact. Because there are so many possible rankingsit
ishard to findthe rankingthat ismost accurate. Itis alsoveryhard to thinkaboutwhatshouldbe
consideredinthe rankings. There are manyfactorsthat can be considered,forexample:strengthof
schedule,strengthof conference,marginof victory,orlocation. Itisveryhard to apply all of these
factors across teamsequally. There are alsoconflictswhenyourankteams because there willalwaysbe
teamsthat are disappointedandfeel like they shouldbe placedhigherinthe rankings. It ishard to
determine which teamsshouldplayinthe National Championshipif there are more thantwo
undefeatedteamsinthe same season. All of these ideasprovethatitisverydifficult torankthe teams.
This,alongwiththe financial aspect,isdescribedbyMartinich(2002) “Giventhe substantial financial
implications,aswell asthe desire toselectthe bestteamsforthe championshipandotherBCSbowls,it
isimperative thatthe rankingsystemsincludedinthe selectionformulabe the mostaccurate at ranking

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teams.” Giventhese difficultiesandproblemsinthe approachtorankingCollege football teams,itis
evidentthatafair and quality systemisneededtoinsure the bestrankings.
1.1. How the Teams are CurrentlyRanked
The Bowl ChampionshipSeries(BCS) systemispresentlyusedtorankthe teams in college football. The
BCS systemcombinescomputerrankings andhumanpollstoformulate itsfinal rankings. The two
opinionpollsare the HarrisPoll andthe USA Today/CoachesPoll. The humanpollsaccountfortwo
thirdsof the total BCS rankings;one thirdeach. Opinionpollshave afew flaws. Theyare afterall
opinion,sothere will be biasinthe rankingsthattheyproduce. A discrepancyassociatedwiththe
coach’s poll isthat,insome cases the personvotingisa coach assistantor someone associatedwiththe
school. There are also timeswhenthe ballotsare filledoutinaway thata teamis leftoff. Thishappens
simplybecause people are liable to messupwhenfillingouttheirballots. The otherone thirdconsists
of six computerrankings. These rankingshave manyproblems. The firstisthat theyare mostlysecret,
withonlyone of the six beingpublic. The factthat theyare not all publishedandpeerreviewedproves
that there couldbe majorproblemswiththem. Because we don’tknow how theyare formed,we don’t
knowif theyare qualityandcan evencome upwiththe correct rankings. There are alsodata errors.
The one rankingthatis nota secretwasfoundto have errorsin itsdata. Whenthere are data errors
theyneedtobe found,andtheywill notbe foundif there are secretrankings. There will alsobe design
biasin the computerrankings. The waya program is made will introduce bias. Whenthere isbiasitwill
affectthe resultsthatare generatedbythe computer. These flawsinthe BCSsystemcombinedwiththe
manydifficultiesthatarise inrankingteams prove thatthere couldbe a systemthatbetterranksthe
teamsthat shouldplayinthe National Championshipgame andeventuallydecide the teamsthatshould
playinthe fourteamplayoff.
2. A NewSystem for Ranking College Football Teams
We believe thatdue tothe numerous flawswiththe BCSsystemforrankingteamsthere shouldbe a
newsystemforrankingcollege football teams.
2.1. Our Platform
Firstwe believe thatafourteamplayoff increasesthe needforabetterrankingsystem. The selection
committee willneedhelpdecidingthe teamsthatshouldplayinthe fourteamplayoff. Itwill actuallybe
a more rigorous process todistinguish betweenthe fourthandfifthteamsthantodistinguish between
the secondand thirdteams. Second,we believe thatthere isnosuchthingas an unbiasedsystem, so
the systemshouldbe public. The committee shouldalsostate whatisimportantinthe rankingssothe
teamsknow whatto do in creatingtheirschedulesandhow theyplaytheirgames. Finally,we believe
that a computer-basedsystemshouldbe usedtocreate rankings. Thisisthe case because humans
cannot simultaneously thinkaboutall the gamesthathappened throughoutthe season. Humansdonot
remembereverygame. Theycannotthinkaboutwhere theywere played,orthe score,or all the other
information pertainingtoeachand everygame. Computerscan simultaneously process eachof these
aspectsand compare them. Alsocomputerscanapplythe biasthat the committee wantconsistently

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across all the teams. If the methodusedtorank teamsisappliedequallytoeachschool,theneachteam
wouldbe placedinthe bestand mostaccurate position.
2.2. Our System
We propose usingthe CMS+ systemforrankingcollege football teamsprovidedbySullivanandCassady
(2009). The CMS+ definesthe problemmathematically usingaquadraticassignmentproblem(QAP).
The onlyissue withthe QAP isthat it ison such a massive scale. The largestproblemsthathave been
solvedare foraround n=40. Inour case n=124, so we cannot use the solution.Nevertheless thereare
methodsforacquiringvalidresults forsuchlarge QAPs. Inour QAPthere are twoinputs:degree of
victoryand relative distance. The degree of victoryis asystemforcomparingteams the rankings. The
degree of victoryis adjustedbythingssuchas headto headvictories,marginof victory,andlocationof
the game. The otherinputisrelative distance. Thisis definedasthe distance betweenthe teamsinthe
ranking. We will use the bell curve togeta general rankingsetupwhere the distance betweenteamsat
the endsof the bell curve are furtherapart thanthe teamsinthe middle. The waythat we attemptto
solve the QAP isthrougha two stage heuristicapproach. Firstwe will use a geneticalgorithmthatuses
a survival of the fittestapproach. We do thisprocess100,000 timestomake sure that the rankingsare
as close to perfectaspossible. Afterthe geneticalgorithm hasbeencompleted, we use alocal search.
The search switchesone teamata time andif the switchmakesthe rankingbetterthanit makesthat
adjustmentandredoesthe local searchforswitching. Thisentire heuristicapproachisredone twenty
timesbecause the startof the geneticalgorithmisdone randomly.
2.3 Problemswith the CMS+ System
There are two mainfeatures thatcan be studiedtofurtherimprove the CMS+systemforrankingteams.
The firstproblemisdecidingwhat parameters shouldbe includedin degree of victory. We know that
there are thingsthat shouldbe included,butthe difficultyis whichfactorstoinclude and how to include
them. The secondproblemwiththe CMS+ system isthat itis a longprocess.
3. Our Research Plan: Improvingthe CMS+ System
As statedbefore there are problemswiththe CMS+System. Our goal isto improve the systemandwe
will dothisintwo ways,improvingthe degreeof victoryandshorteningthe runtime.
3.1. Degree of Victory Research
We workedtoimprove the Degree of Victoryby findingpossible factorstoinclude andwaystoquantify
these factorsdetermined. Thiswasdone bycollectingdatafrompastseasons. The data collectedwas
fromthe informationprovidedbyJamesHowell onhisdatabase,ESPN.com, and
collegepollarchive.com. Once we hadthe data we were able touse it to findrankingsandanalyze the
effectsourfactorshad on the rankingscreated fromthe years. Thispart of the projectwas done with
the othergroup workingonthe project: (T. DodsonandA. McElhenney).
3.2. Run Time Research

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Our secondresearchgoal was to shortenthe run time. We had to findwaysto getvalidrankings, while
alsoshorteningruntime. Thiswasdone by experimentationandadjustmentstothe CMS+ system
throughthe use of variouscombinationsof GA generationsandheuristicreplications.
4. ImprovingDegree of Victory
The firstway that we workedtoimprove the CMS+ Systemof rankingwasby establishingwhatshould
be includedindegree of victoryand uponcompletionof thistaskwe createdadegree of victorymatrix.
Findingfactorstoinclude wasdone inpartnershipwith T.DodsonandA. McElhenny.
4.1. Factors to Include in Degree ofVictory
Ultimatelyfivefactorswere chosentobe adjustedin ourDegree of Victorythat ledto our rankings. Of
the five factorsthat were chosenfourcan be variedintheirweight. The total amountof degree of
victorypointsthatcan be giventoone team in the degree of victorymatrix is100 points. The factor
that cannot be removedisthe game result,whichisjustwhowonthe game. Thisfactor can be lowered
inweightbasedonhowmuch influenceisgiventothe otherfouraspects that gointo the ranking. The
fourotherfactors that are included,andwhichcanalsobe varied are:if the game wasplayedat home
or on the road, if the teamhas more winsagainstcommonopponents,if theyare theirconference
champion,andif theyhave a higherrank inthe AP poll. These factorscanall carry a total weightof 60
pointsinthe degree of victorymatrix. Thismeans the winnerof the game must receive 40 points. The
waythat more than40 pointscan be giventothe winnerisif some of the four variedfactorsare turned
off. In that case the unallocatedpointsare all giventothe winnerof the game.
4.2. The Degree of Victory Matrix
The bestway to compare teamsisthrough a matrix. The creationof thismatrix isdone throughvisual
basicprogrammingandit is adjustable basedonthe variationsthateachpersoncanchoose fordegree
of victorypoints. Pointsare awardedtoeachteam basedonthe factors that were establishedabove.
For everygame played,the systemtakesintoaccountwhowonandwholostthe game and if itwas a
home or awaygame. The pointsallocatedare giventoan awayteam thatwinsbasedon the ideathat
gamesplayedonthe road are harderto winthan gamesat home. For everysingle pairof teamsthe
othercategoriesare compared. The teamthat has more winsovercommonopponentswill getthe
allocatedpoints. Thisisa wayto establishadifference betweenteamsthatmayhave the same record
but mayhave competedbetteragainstteamsthatthe teamshave incommon. The pointsassignedto
APpointsare giventothe teamthat is rankedhigherinthe APpoll. Thisisa wayto include ahuman
aspect,or the “eye test,”whichissomething thatishard to do withincomputerrankings. The final
aspectis that if the teamsare inthe same conference thenthe championof thatconference willbe
giventhe pointsallocatedforconference championsoverevery otherteaminthe conference. Using
visual basicthe matrix fordegree of victorycan be createdwhere eachteamis bothalongthe vertical
and horizontal sidesandthe pointsthatare allocatedforeachteamare withinthe matrix. Thismatrix is
usedinthe CMS+ systemforrankingteamsand will be able toproduce rankingswiththisdegree of
victorymatrix.

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4.3. Results
Once we determinedthe factorsthatshouldbe includedindegree of victorywe testedthe effectthat
the factors have on rankings. Thiswasdone bydefiningsixteendifferentcasestoworkonfor past
years. These caseswill allowustorun the program andevaluate how changingall of the factors affects
the ranking. The testcasescome from the fourfactors that we vary andtheyare all turnedon andoff in
varyingarrangementssuchthatall variouscombinationsof the fourfactorsare tested. Whenwe turned
a factor on we gave it fifteenpointsandnone whenitwasturneditoff. The resultsforthe rankingsare
seeninour Appendix. The resultsforfitnessthat we foundproducedanaverage standarddeviation
above the meanof close to10,000 basedon the informationfrom Dodson andMcElhenny. Thatis such
a large value that calculatinghowmanybetterrankingswouldbe producedcomesupwithsuchasmall
numberthatit readsit as zero. This meansthatusingour degree of victorywe are able to calculate the
ideal rankingsthatcorrespondtothe factors we included.
5. ReducingRun Time
Improvingthe problemof alengthyruntime isdone throughtestingandexperimentation. The best
wayto do thisis through testson pastyears. We neededtofindthe pointatwhichthe run time is
minimizedbutstill avalidrankingisproduced.
5.1. CreatingTests
Reducingthe runtime isdone by decreasingthe amountof GA generationsandheuristic replications.
We neededto testthe effectthatdecreasingthe generationsandreplicationshason solutionquality.
We decreasedthe generationsfromthe 100,000 initiallyusedinthe CMS+ system. Intervalsusedto
decrease the generationwere of 25,000. Replicationswere alsoreduced,butonlyonce by10. After
completingtestsdownto25,000 total generations,we noticedthatwhetherwe were at10 replications
or 20 replications, we gotvirtuallythe same runtime. ThisisseeninTable 1. Because the numberof
replicationsdoesnotaffectthe runtime we decidedtoleaveitat20 replications. Whenthese
generationsare decreasedthe runtime goesdowntoa certainpoint,butif loweredtoofarthe time will
start to increase again. We foundoutthat no matterhow low we go withthe numberof generations
and replicationssolutionqualityisnotaffectedatall. We took a range of values,goingfrom100,000 to
100 to see howtime variesforeachamount.We wentinstepsof 25,000 from100,000 downto 25,000,
and thenvariedstepsfrom10,000 to 100 just to findtimesincertainrangesthat correspondtothe ideal
time.
5.2 Run Time Results
Thistable expressesperfectlythe factthatrun time isnot affectbyreplicationsbecausethe same times
are producedforboththe setsof 20 and 10 replications. Alsothe fitnessneverchangedwhichmeans
that no matterhowwe adjustthe generationsandreplicationsthe same fitnesswill be calculated.

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Table 1: RunTime and SolutionQualityforCombinationsof GA GenerationsandHeuristicReplications
GA Generations HeuristicReplications Run Time (seconds) Fitness
100,000 20 139 196313
75,000 20 107.68 196313
50,000 20 71.72 196313
25,000 20 40.12 196313
10,000 20 28.62 196313
100,000 10 139 196313
75,000 10 105 196313
50,000 10 71 196313
25,000 10 40.67 196313
10,000 10 27.92 196313
Figure 1: The Effectof GenerationsonRunTime at 20 Replications
We noticedthatwhenwe loweredthe generationspastacertainpointthe time startedto increase
again. This isseeninthe 4,000 to 1,000 range where the time changesandwill increase oneitherside
of thisrange. Goingfrom 3,500 to 1,000, there wasa 19.74 secondjumpintime.Goingfrom1,000 to
100 generations,there wasa230.26 secondjumpintime. The same increase isseengoingthe other
way,justnot inas significantof jumps. Thisgraphalongwiththisanalysisleadsustobelievethatthe
0
50
100
150
200
250
300
0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000
Time(sec)
Total Genera ons at 20 Replica ons
Time per Total Amount of Genera ons at 20
Replica ons

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area where the shortestruntime wouldcorrespondtoisinthe range of 3,500 to 4,000 generations.
Thisis a large decrease fromthe initial 100,000 usedinthe CMS+ system. The 100,000 generations
produceda run time of 139 seconds,throughour experimentationwe were able tofindinthisrange we
will geta run time of about25 secondswhichisone fifthof the initial time.
7. Conclusions
Throughoutthisresearch,we were able to achieve all of ourgoals.We definedparametersforand
computeddegree of victory throughthe use of data collectedfrompastyears.Usingourdegree of
victory,we producedrankingsforeachsetof parametercombinations,whichwe comparedtothe BCS
rankingsforthe year of 2010. Basedon calculationsfromourfitnessvalue,the ranksthatare better
than the one producedisso small thatit roundsdownto zero,meaningourrankingsare highquality.
We were alsoable toreduce run time byeffectivelyandefficientlyreducingthe generationamount.We
alsovariedthe replicationamountinourtests,butfoundthatchangingthe replicationamounthadno
affectonthe rankingor run time. However,there’splentyof researchthatcanbe done in the future on
thisproject. The main areathat can be expandedisthroughfurtherworkondegree of victory. Our
factors were notall that couldbe included. There are multiple more factorsandmore waysto include
the factors that we expressed. Itwouldbe possible toadjustfactorsindifferentwaysandprovide an
evenmore personal approach. Runtime issomethingthatcanbe decreasedinmanywaysas well.
There are otheraspectswithinthe CMS+ systemthatcan be adjustedtomake the time neededtorun
the program shorter,andthere are waysto adjustthe program as a whole torun inlesstime. Our
researchbringsto the forefrontthe ideathatthere can be a personalizedaspecttothe ranking,andthat
there can be many factorsthat can be turnedonand off. We alsoimprovedthe CMS+systemby
shorteningthe time ittakestorun the program while stillgettingvalidresults. Overall bothgoalswere
metand the CMS+ systemwasimprovedinthe areasof degree of victoryandrun time.
8. References
Cassady,C. Richard,Maillart,LisaM., and Salman,Sinan,2005, “RankingSportsTeams:A Customizable
QuadraticApproach,”Interfaces,35(6),497-510.
Martinich,Joseph.2002. “College football rankings:Dothe computersknow best?”Interfaces32(5) 85–
94.
Sullivan,Kelly,Cassady,C.Richard,2009. “The CMS+ SystemforRankingCollege Football Teams.”
Proceedingsof the 2009 Industrial EngineeringResearchConference.

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9. Appendix:
DOV 01 DOV 02 DOV 03 DOV 04 DOV 05 DOV 06 DOV 07 DOV 08 REAL BCS
Fitness 244343 224675 226317 219045 246025 237197 221582 238751
1 TexasChristian Oregon Oregon Oregon Oregon Oregon Oregon Oregon Auburn
2 Oregon TexasChristian TexasChristian TexasChristian TexasChristian TexasChristian TexasChristian TexasChristian Oregon
3 Stanford Stanford BoiseState Auburn BoiseState Auburn Auburn Auburn TCU
4 Wisconsin BoiseState Auburn BoiseState Auburn Stanford MichiganState OhioState Stanford
5 MichiganState Auburn Nevada Stanford OhioState MichiganState BoiseState Nevada Wisconsin
6 Nevada Wisconsin Wisconsin Nevada Nevada OhioState Wisconsin MichiganState Ohio State
7 OhioState Nevada Stanford OhioState Wisconsin Nevada Nevada BoiseState Oklahoma
8 BoiseState OhioState OhioState Wisconsin Stanford BoiseState VirginiaTech Stanford Arkansas
9 Auburn MichiganState MichiganState MichiganState MichiganState Wisconsin OhioState Wisconsin Michigan State
10 VirginiaTech Utah Utah VirginiaTech Utah VirginiaTech Stanford VirginiaTech Boise State
11 Utah VirginiaTech VirginiaTech Utah VirginiaTech Utah Oklahoma Utah LSU
12 Oklahoma Missouri Oklahoma Oklahoma Oklahoma OklahomaState Utah Oklahoma Missouri
13 Nebraska Nebraska Missouri OklahomaState OklahomaState Oklahoma Nebraska OklahomaState Virginia Tech
14 OklahomaState Oklahoma OklahomaState Missouri Missouri Missouri Missouri Missouri Oklahoma State
15 Missouri OklahomaState Arkansas Arkansas Arkansas Nebraska OklahomaState Arkansas Nevada
16 Arkansas Arkansas CentralFlorida CentralFlorida Nebraska Arkansas CentralFlorida CentralFlorida Alabama
17 SouthCarolina CentralFlorida Nebraska Hawaii CentralFlorida CentralFlorida Arkansas Hawaii Texas A&M
18 WestVirginia Hawaii Tulsa Tulsa FloridaState Hawaii Hawaii Nebraska Nebraska
19 Alabama Tulsa Hawaii FloridaState Tulsa FloridaState WestVirginia FloridaState Utah
20 LouisianaState FloridaState WestVirginia Nebraska WestVirginia Tulsa Tulsa Tulsa South Carolina
21 Hawaii Alabama FloridaState WestVirginia Hawaii WestVirginia FloridaState WestVirginia Mississippi State
22 FloridaState WestVirginia LouisianaState LouisianaState LouisianaState LouisianaState LouisianaState LouisianaState West Virginia
23 Tulsa LouisianaState SouthCarolina Alabama SouthCarolina Alabama Alabama Alabama Florida State
24 CentralFlorida SouthCarolina Alabama SouthCarolina Alabama SouthCarolina Miami(Ohio) SouthCarolina Hawaii
25 TexasA&M Temple TexasA&M Miami(Ohio) TexasA&M Toledo TexasA&M TexasA&M UCF
DOV 09 DOV 10 DOV 11 DOV 12 DOV 13 DOV 14 DOV 15 DOV 16 REAL BCS
Fitness 201622 214227 203404 216012 216012 217337 223232 196313
1 Oregon Oregon Oregon Oregon Oregon Oregon Oregon Oregon Auburn
2 TexasChristian TexasChristian TexasChristian Auburn Auburn TexasChristian TexasChristian Auburn Oregon
3 Auburn Auburn Auburn TexasChristian TexasChristian Stanford Auburn TexasChristian TCU
4 BoiseState MichiganState BoiseState MichiganState MichiganState Auburn BoiseState BoiseState Stanford
5 MichiganState BoiseState Wisconsin BoiseState BoiseState Nevada MichiganState MichiganState Wisconsin
6 Wisconsin Wisconsin MichiganState Wisconsin Wisconsin BoiseState Wisconsin Wisconsin Ohio State
7 Nevada VirginiaTech Nevada VirginiaTech VirginiaTech OhioState Nevada VirginiaTech Oklahoma
8 Stanford Nevada VirginiaTech Nevada Nevada MichiganState VirginiaTech Nevada Arkansas
9 VirginiaTech OhioState Stanford OhioState OhioState Wisconsin OhioState Stanford Michigan State
10 OhioState Stanford OhioState Stanford Stanford VirginiaTech Stanford OhioState Boise State
11 Oklahoma Oklahoma Oklahoma Oklahoma Oklahoma Utah Oklahoma Oklahoma LSU
12 Utah Utah Utah Utah Utah Oklahoma Utah Utah Missouri
13 Missouri OklahomaState Missouri OklahomaState OklahomaState OklahomaState Missouri CentralFlorida Virginia Tech
14 Nebraska Missouri CentralFlorida CentralFlorida CentralFlorida Missouri OklahomaState OklahomaState Oklahoma State
15 OklahomaState Nebraska OklahomaState Missouri Missouri Nebraska CentralFlorida Missouri Nevada
16 CentralFlorida CentralFlorida Hawaii Hawaii Hawaii Arkansas Arkansas Hawaii Alabama
17 Hawaii Hawaii Arkansas Arkansas Arkansas CentralFlorida Hawaii Arkansas Texas A&M
18 Arkansas Arkansas WestVirginia WestVirginia WestVirginia Hawaii WestVirginia WestVirginia Nebraska
19 WestVirginia WestVirginia Tulsa FloridaState FloridaState FloridaState Nebraska Miami(Ohio) Utah
20 Tulsa FloridaState Nebraska Tulsa Tulsa Tulsa Tulsa Tulsa South Carolina
21 FloridaState Tulsa FloridaState Nebraska Nebraska WestVirginia FloridaState FloridaState Mississippi State
22 Alabama LouisianaState Miami(Ohio) LouisianaState LouisianaState LouisianaState LouisianaState LouisianaState West Virginia
23 LouisianaState Alabama LouisianaState Miami(Ohio) Miami(Ohio) Alabama Alabama Nebraska Florida State
24 Miami(Ohio) Miami(Ohio) Alabama Alabama Alabama SouthCarolina Miami(Ohio) Alabama Hawaii
25 NorthCarolinaStateTexasA&M Connecticut TexasA&M TexasA&M TexasA&M Connecticut TexasA&M UCF