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<body lang=3DEN-US style=3D'tab-interval:.5in'>

<div class=3DSection1>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:18.0pt'>Marshall University Math Colloquiu=
m<o:p></o:p></span></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:8.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span=
></p>

<p class=3DMsoSubtitle><u><span style=3D'font-size:22.0pt'>Friday, Septembe=
r 24 <o:p></o:p></span></u></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><st1:time H=
our=3D"15"
Minute=3D"0" w:st=3D"on"><u><span style=3D'font-size:18.0pt'>3:00 P.M.</spa=
n></u></st1:time><u><span
style=3D'font-size:18.0pt'><o:p></o:p></span></u></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:18.0pt'>Smith Hall 509<o:p></o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></span></p>

<h1><b style=3D'mso-bidi-font-weight:normal'><i style=3D'mso-bidi-font-styl=
e:normal'><span
style=3D'font-size:16.0pt;mso-bidi-font-size:12.0pt'>Alfred Akinsete</span>=
</i></b><b
style=3D'mso-bidi-font-weight:normal'><i style=3D'mso-bidi-font-style:norma=
l'><span
style=3D'mso-bidi-font-size:24.0pt;font-family:Arial'><o:p></o:p></span></i=
></b></h1>

<h1><st1:place w:st=3D"on"><st1:PlaceName w:st=3D"on"><span style=3D'font-s=
ize:16.0pt;
  mso-bidi-font-style:italic'>Marshall</span></st1:PlaceName><span
 style=3D'font-size:16.0pt;mso-bidi-font-style:italic'> <st1:PlaceName w:st=
=3D"on">University</st1:PlaceName></span></st1:place><span
style=3D'font-size:16.0pt'><o:p></o:p></span></h1>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:22.0pt'>&#8220;The winning probability and
ranking models for teams in<o:p></o:p></span></b></p>

<p class=3DMsoTitle><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:22.0pt'><span style=3D'mso-spacerun:yes'>&nbsp;</span><s=
pan
class=3DGramE>soccer</span> tournaments&#8221;<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'margin-left:1.5in;text-indent:.5in'><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></p>

<p class=3DMsoNormal style=3D'margin-left:1.5in;text-indent:.5in'><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>&nbsp;<o:p></o:p></spa=
n></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><u><span
style=3D'font-size:14.0pt'>Abstract</span>:</u></b> We discuss the statisti=
cal
analysis of the 1993 &#8211; 2003 soccer results from the 20 teams in the <i
style=3D'mso-bidi-font-style:normal'>FA</i> Premier League (<i style=3D'mso=
-bidi-font-style:
normal'>FAPLE</i>). Using the Clarke-Norman (<i style=3D'mso-bidi-font-styl=
e:
normal'>CLAMAN</i>) model, we obtain the home advantage and strength of each
team. The work focuses on ranking methodologies and develops new ranking mo=
dels
for teams in soccer tournaments. We show that the ranking, and the distance
between any pair of teams prior to their encounter is equivalent to <span
class=3DSpellE><i style=3D'mso-bidi-font-style:normal'>CLAMAN</i>'s</span> =
model.
The winning probabilities of a team defeating other teams in the league are
obtained. These probabilities form a ranking procedure, and provide a source
for the performance evaluation of each team in the tournament. The results =
show
that our ranking models are adequate, evidently from the 2003/2004 end-of-y=
ear
ladder. The work leads to further investigation of stochastic modeling of
soccer data.</p>

<p class=3DMsoNormal style=3D'text-indent:.5in;mso-layout-grid-align:none;
text-autospace:none'><span style=3D'font-size:14.0pt;mso-bidi-font-size:10.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal>&nbsp;</p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><i style=3D=
'mso-bidi-font-style:
normal'><span style=3D'font-size:14.0pt'>Students! Remember, only the speak=
er
will understand everything!<o:p></o:p></span></i></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><span style=3D'font-size:14.0pt'>Snacks will be served=
.</span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><span style=3D'font-size:14.0pt'>Next Colloquium: Octo=
ber 8.</span></p>

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