The Pi-Rate Ratings

October 18, 2021

PiRate Ratings–NFL for Week 7, October 21-25, 2021

This Week’s PiRate Ratings Spreads

HomeVisitorPiRateMeanBias
ClevelandDenver6.36.65.9
Green BayWashington13.012.713.8
TennesseeKansas City-0.7-0.6-0.3
MiamiAtlanta1.31.90.9
New EnglandN.Y. Jets11.49.89.9
N.Y. GiantsCarolina-0.8-0.8-1.9
BaltimoreCincinnati12.211.112.4
Las VegasPhiladelphia4.54.73.7
LA RamsDetroit20.120.720.5
ArizonaHouston21.724.022.3
Tampa BayChicago14.513.913.9
San FranciscoIndianapolis2.22.72.4
SeattleNew Orleans-1.40.4-2.1

This Week’s PiRate Ratings Totals

HomeVisitorTotal
ClevelandDenver43.5
Green BayWashington48
TennesseeKansas City60.5
MiamiAtlanta50
New EnglandN.Y. Jets38.5
N.Y. GiantsCarolina43.5
BaltimoreCincinnati48.5
Las VegasPhiladelphia47
LA RamsDetroit54
ArizonaHouston51.5
Tampa BayChicago44
San FranciscoIndianapolis47
SeattleNew Orleans48.5

Teams With Byes This Week

Buffalo
Pittsburgh
Jacksonville
LA Chargers
Dallas
Minnesota

This Week’s PiRate Ratings

A F C
EastPiRateMeanBiasAvgTotalsW-L
Buffalo109.8109.6110.2109.8254-2
New England99.698.798.999.1182-4
Miami95.495.896.095.7211-5
N. Y. Jets91.291.991.991.720.51-4


NorthPiRateMeanBiasAvgTotalsW-L
Baltimore108.0107.6108.1107.924.55-1
Cleveland101.7101.8100.9101.5263-3
Pittsburgh101.3100.6101.0101.0183-3
Cincinnati98.899.698.799.0244-2


SouthPiRateMeanBiasAvgTotalsW-L
Indianapolis102.6102.0102.2102.3242-4
Tennessee101.3101.4101.6101.428.54-2
Jacksonville89.791.289.690.2231-5
Houston89.488.189.689.124.51-5


WestPiRateMeanBiasAvgTotalsW-L
Kansas City104.5104.5104.4104.5323-3
LA Chargers100.6100.9100.9100.8244-2
Denver98.498.298.098.217.53-3
Las Vegas97.697.897.897.726.54-2


N F C
EastPiRateMeanBiasAvgTotalsW-L
Dallas102.5103.6102.1102.730.55-1
Philadelphia96.196.197.196.420.52-4
Washington93.693.893.193.5212-4
N.Y. Giants93.793.592.893.320.51-5


NorthPiRateMeanBiasAvgTotalsW-L
Green Bay103.7103.4103.9103.7275-1
Minnesota100.3100.599.7100.222.53-3
Chicago97.097.396.997.115.53-3
Detroit91.591.591.491.526.50-6


SouthPiRateMeanBiasAvgTotalsW-L
Tampa Bay108.5108.2107.8108.228.55-1
New Orleans107.7105.9108.1107.222.53-2
Carolina97.497.397.797.5233-3
Atlanta96.195.997.196.4292-3


WestPiRateMeanBiasAvgTotalsW-L
LA Rams108.6109.2108.9108.927.55-1
Arizona108.1109.1109.0108.7276-0
Seattle103.3103.3103.0103.2262-4
San Francisco101.8101.7101.6101.7232-3

Playoff Projections

Current Playoff Seedings

AFC
1Baltimore
2LA Chargers
3Tennessee
4Buffalo
5Cincinnati
6Las Vegas
7Pittsburgh
NFC
1Arizona
2Tampa Bay
3Green Bay
4Dallas
5LA Rams
6New Orleans
7Minnesota

PiRate Projections

AFC Seeding
1Baltimore
2Buffalo
3Kansas City
4Tennessee
5Pittsburgh
6Cincinnati
7Las Vegas
NFC Seeding
1Tampa Bay
2Arizona
3Green Bay
4Dallas
5LA Rams
6Minnesota
7New Orleans

Projected Playoff Rounds

Wildcard Round
Buffalo over Las Vegas
Kansas City over Cincinnati
Pittsburgh over Tennessee
Arizona over New Orleans
Green Bay over Minnesota
LA Rams over Dallas


Divisional Round
Baltimore over Pittsburgh
Kansas City over Buffalo
Tampa Bay over LA Rams
Arizona over Green Bay


Conference Championship
Kansas City over Baltimore
Tampa Bay over Arizona


Super Bowl 56 (LA)
Kansas City over Tampa Bay

October 11, 2021

PiRate Ratings–NFL for Week 6, October 14-18, 2021

This Week’s PiRate Ratings Spreads

HomeVisitorPiRateMeanBias
PhiladelphiaTampa Bay-9.6-9.5-8.1
Jacksonville (N)Miami-7.3-6.2-8.6
IndianapolisHouston13.013.512.2
ChicagoGreen Bay-3.8-3.0-4.0
WashingtonKansas City-5.8-5.4-5.8
CarolinaMinnesota0.1-0.21.5
BaltimoreLA Chargers5.64.55.0
DetroitCincinnati-1.2-1.8-0.7
N.Y. GiantsLA Rams-8.2-8.8-9.0
ClevelandArizona0.90.2-0.6
DenverLas Vegas6.56.56.4
New EnglandDallas0.1-1.9-0.2
PittsburghSeattle1.00.31.0
TennesseeBuffalo-7.1-6.9-7.8

This Week’s PiRate Ratings Totals

HomeVisitorTotal
PhiladelphiaTampa Bay49
Jacksonville (N)Miami44
IndianapolisHouston50
ChicagoGreen Bay43
WashingtonKansas City54
CarolinaMinnesota43.5
BaltimoreLA Chargers49.5
DetroitCincinnati50.5
N.Y. GiantsLA Rams48
ClevelandArizona53
DenverLas Vegas42
New EnglandDallas47.5
PittsburghSeattle44.5
TennesseeBuffalo52.5

This Week’s PiRate Ratings

A F C
EastPiRateMeanBiasAvgTotalsW-L
Buffalo110.6110.5111.3110.824.54-1
New England99.698.798.999.117.52-3
Miami96.496.897.396.8211-4
N. Y. Jets90.991.691.691.420.51-4

NorthPiRateMeanBiasAvgTotalsW-L
Baltimore105.7105.1105.6105.5254-1
Cleveland103.7103.9103.0103.5263-2
Pittsburgh101.3100.6101.0101.0182-3
Cincinnati97.197.996.897.3243-2

SouthPiRateMeanBiasAvgTotalsW-L
Indianapolis101.5100.8101.0101.124.51-4
Tennessee100.5100.5100.5100.5283-2
Houston91.089.891.390.725.51-4
Jacksonville89.190.688.789.5230-5

WestPiRateMeanBiasAvgTotalsW-L
Kansas City103.6103.5103.3103.532.52-3
LA Chargers102.6103.1103.1102.924.54-1
Denver99.899.799.699.716.53-2
Las Vegas96.296.396.296.225.53-2

N F C
EastPiRateMeanBiasAvgTotalsW-L
Dallas102.5103.6102.1102.7304-1
Philadelphia96.095.996.996.320.52-3
N.Y. Giants95.795.695.095.420.51-4
Washington94.895.194.594.821.52-3

NorthPiRateMeanBiasAvgTotalsW-L
Green Bay103.5103.1103.6103.4274-1
Minnesota100.3100.599.5100.121.52-3
Chicago97.297.697.297.3163-2
Detroit93.593.593.693.526.50-5

SouthPiRateMeanBiasAvgTotalsW-L
Tampa Bay108.6108.4108.0108.328.54-1
New Orleans107.4105.6107.8106.922.53-2
Carolina97.497.397.997.6223-2
Atlanta95.895.696.896.1292-3

WestPiRateMeanBiasAvgTotalsW-L
LA Rams106.9107.4107.0107.127.54-1
Arizona105.8106.7106.6106.4275-0
Seattle103.3103.3103.0103.226.52-3
San Francisco101.5101.4101.3101.4232-3

This Week’s Playoff Projections

If the Playoffs Began Today

AFC
1LA Chargers
2Baltimore
3Buffalo
4Tennessee
5Cincinnati
6Las Vegas
7Denver

NFC
1Arizona
2Dallas
3Tampa Bay
4Green Bay
5LA Rams
6Chicago
7Carolina

Projected Playoff Positions

AFC Seeding
1Buffalo
2LA Chargers
3Cleveland
4Tennessee
5Baltimore
6Cincinnati
7Denver

NFC Seeding
1Tampa Bay
2Arizona
3Green Bay
4Dallas
5LA Rams
6Chicago
7Carolina

Projected Playoff Rounds

Wildcard Round
LA Chargers over Denver
Cleveland over Cincinnsti
Baltimore over Tennessee
Arizona over Carolina
Green Bay over Chicago
LA Rams over Dallas

Divisional Round
Buffalo over Baltimore
LA Chargers over Cleveland
Tampa Bay over LA Rams
Arizona over Green Bay

Conference Championship
Buffalo over LA Chargers
Tampa Bay over Arizona

Super Bowl 56 (LA)
Tampa Bay over Buffalo

December 14, 2020

PiRate Ratings for NFL Week 15: December 17-21, 2020

This Week’s PiRate Ratings Spreads

HomeVisitorPiRateMeanBias
Las VegasLA Chargers4.64.74.4
DenverBuffalo-5.7-6.3-6.0
Green BayCarolina8.59.19.0
TennesseeDetroit8.38.79.1
IndianapolisHouston8.79.39.3
LA RamsN.Y. Jets21.721.423.0
AtlantaTampa Bay-2.3-3.2-3.2
MiamiNew England1.93.22.9
MinnesotaChicago-0.8-0.6-0.8
N.Y. GiantsCleveland-3.1-2.3-2.9
WashingtonSeattle-3.2-3.2-3.1
BaltimoreJacksonville18.418.418.4
ArizonaPhiladelphia7.17.17.5
New OrleansKansas City-3.7-4.4-4.1
DallasSan Francisco-5.4-4.9-5.5
CincinnatiPittsburgh-15.0-15.1-15.2

This Week’s PiRate Ratings Totals

HomeVisitorTotal
Las VegasLA Chargers52
DenverBuffalo40
Green BayCarolina52.5
TennesseeDetroit55
IndianapolisHouston51
LA RamsN.Y. Jets42
AtlantaTampa Bay57
MiamiNew England46.5
MinnesotaChicago42.5
N.Y. GiantsCleveland47
WashingtonSeattle50.5
BaltimoreJacksonville45
ArizonaPhiladelphia51.5
New OrleansKansas City52.5
DallasSan Francisco50.5
CincinnatiPittsburgh37.5

This Week’s PiRate Ratings

A F C
EastPiRateMeanBiasAvgTotalsW-L
Buffalo105.4106.1106.0105.92110-3
Miami100.7101.7101.1101.226.58-5
New England100.499.999.7100.0206-7
N. Y. Jets86.186.685.486.0180-13

NorthPiRateMeanBiasAvgTotalsW-L
Baltimore107.3107.1107.2107.224.58-5
Pittsburgh104.0104.4104.3104.218.511-2
Cleveland99.699.7100.199.826.59-4
Cincinnati88.088.388.188.1192-10-1

SouthPiRateMeanBiasAvgTotalsW-L
Indianapolis105.1105.2105.3105.2259-4
Tennessee102.5102.6102.9102.7289-4
Houston97.997.497.497.6264-9
Jacksonville90.490.290.390.320.51-12

WestPiRateMeanBiasAvgTotalsW-L
Kansas City109.9110.2110.1110.12712-1
Las Vegas99.599.599.299.429.57-6
Denver98.398.398.598.4195-8
LA Chargers95.895.995.895.822.54-9

N F C
EastPiRateMeanBiasAvgTotalsW-L
Washington98.398.598.598.421.56-7
Philadelphia97.897.797.397.623.04-8-1
N.Y. Giants95.095.995.795.620.55-8
Dallas93.593.593.093.325.54-9

NorthPiRateMeanBiasAvgTotalsW-L
Green Bay105.7105.8106.3105.92510-3
Chicago100.599.9100.2100.2186-7
Minnesota98.798.398.498.424.56-7
Detroit95.294.994.894.9275-8

SouthPiRateMeanBiasAvgTotalsW-L
Tampa Bay105.7105.6106.1105.8318-5
New Orleans104.7104.3104.5104.525.510-3
Atlanta102.4101.5101.9101.9264-9
Carolina98.798.298.798.627.54-9

WestPiRateMeanBiasAvgTotalsW-L
LA Rams105.8106.0106.4106.1249-4
Seattle103.4103.7103.5103.6299-4
Arizona103.0102.7102.8102.828.57-6
San Francisco100.8100.4100.5100.6255-8

Playoff Projections

AFC Seeding
1Kansas City
2Buffalo
3Pittsburgh
4Tennessee
5Cleveland
6Baltimore
7Indianapolis

NFC Seeding
1Green Bay
2New Orleans
3Los Angeles
4Washington
5Seattle
6Tampa Bay
7Arizona

Wildcard Round
Buffalo over Indianapolis
Pittsburgh over Baltimore
Cleveland over Tennessee
Arizona over New Orleans
Los Angeles over Tampa Bay
Seattle over Washington

Divisional Round
Kansas City over Cleveland
Buffalo over Pittsburgh
Green Bay over Arizona
Los Angeles over Seattle

Conference Championship
Kansas City over Buffalo
Green Bay over Los Angeles

Super Bowl
Kansas City over Green Bay

December 8, 2020

PiRate Ratings–NFL For Week 14: December 10-14, 2020

This Week’s PiRate Ratings Spreads

HomeVisitorPiRateMeanBias
LA RamsNew England5.15.66.2
ChicagoHouston-0.5-0.8-0.8
CincinnatiDallas1.01.31.6
DetroitGreen Bay-9.3-9.6-10.4
MiamiKansas City-7.2-6.5-7.0
N.Y. GiantsArizona-2.7-1.6-1.7
Tampa BayMinnesota8.48.68.8
CarolinaDenver3.53.23.8
JacksonvilleTennessee-7.8-7.9-7.9
Las VegasIndianapolis-0.3-0.2-0.4
SeattleN.Y. Jets16.215.516.5
PhiladelphiaNew Orleans-7.8-7.7-8.7
LA ChargersAtlanta-6.0-5.3-6.0
San FranciscoWashington5.04.34.7
BuffaloPittsburgh-0.4-0.3-0.5
ClevelandBaltimore-5.9-5.6-5.3

This Week’s PiRate Ratings Totals

HomeVisitorTotal
LA RamsNew England45
ChicagoHouston44
CincinnatiDallas46.5
DetroitGreen Bay52
MiamiKansas City52.5
N.Y. GiantsArizona51
Tampa BayMinnesota57
CarolinaDenver44.5
JacksonvilleTennessee49.5
Las VegasIndianapolis52
SeattleN.Y. Jets48
PhiladelphiaNew Orleans48.5
LA ChargersAtlanta50.5
San FranciscoWashington47
BuffaloPittsburgh39.5
ClevelandBaltimore48

This Week’s PiRate Ratings

A F C
EastPiRateMeanBiasAvgTotalsW-L
Buffalo103.6104.2104.0104.0219-3
Miami100.7101.7101.1101.2268-4
New England101.5101.1100.9101.220.56-6
N. Y. Jets87.988.687.488.019.50-12

NorthPiRateMeanBiasAvgTotalsW-L
Baltimore107.0106.8106.9106.9237-5
Cincinnati91.591.891.691.620.52-9-1
Cleveland99.699.7100.199.8259-3
Pittsburgh105.5106.0106.0105.818.511-1

SouthPiRateMeanBiasAvgTotalsW-L
Houston100.299.899.9100.0264-8
Indianapolis103.4103.4103.4103.4248-4
Jacksonville91.591.491.691.5211-11
Tennessee101.3101.3101.5101.428.58-4

WestPiRateMeanBiasAvgTotalsW-L
Denver97.797.697.797.7184-8
Kansas City109.9110.2110.1110.126.511-1
Las Vegas101.1101.2101.0101.1287-5
LA Chargers94.994.994.794.823.53-9

N F C
EastPiRateMeanBiasAvgTotalsW-L
Dallas92.092.091.591.8263-9
N.Y. Giants96.397.297.196.921.55-7
Philadelphia96.696.495.896.2233-8-1
Washington97.297.497.397.321.55-7

NorthPiRateMeanBiasAvgTotalsW-L
Chicago98.297.597.797.8185-7
Detroit95.194.894.694.8275-7
Green Bay105.8105.9106.5106.1259-3
Minnesota98.998.698.898.725.56-6

SouthPiRateMeanBiasAvgTotalsW-L
Atlanta103.0102.2102.7102.6274-8
Carolina99.298.899.499.226.54-8
New Orleans105.9105.6106.0105.825.510-2
Tampa Bay105.3105.1105.5105.331.57-5

WestPiRateMeanBiasAvgTotalsW-L
Arizona101.6101.3101.3101.429.56-6
LA Rams104.6104.7105.1104.824.58-4
San Francisco101.6101.2101.4101.425.55-7
Seattle101.5101.6101.4101.528.58-4

Playoff Projections

AFC Seedings

1Kansas City
2Pittsburgh
3Buffalo
4Indianapolis
5Cleveland
6Tennessee
7Baltimore

NFC Seedings

1New Orleans
2Green Bay
3Los Angeles
4Washington
5Tampa Bay
6Seattle
7Minnesota

Wildcard Round
Pittsburgh over Baltimore
Buffalo over Tennessee
Cleveland over Indianapolis
Green Bay over Minnesota
Los Angeles over Seattle
Tampa Bay over Washington

Divisional Round
Cleveland over Kansas City
Buffalo over Pittsburgh
Tampa Bay over New Orleans
Green Bay over Los Angeles

Conference Championship
Buffalo over Cleveland
Green Bay over Tampa Bay

Super Bowl
Green Bay over Buffalo

December 2, 2019

PiRate Ratings NFL Forecast for Week 14: December 5-9, 2019

This Week’s PiRate Ratings Spreads

 

Margins

Home

Visitor

PiRate

Mean

Bias

Chicago

Dallas

2.6

-0.6

-0.2

Atlanta

Carolina

3.3

3.5

2.8

Buffalo

Baltimore

-6.3

-5.3

-6.2

Cleveland

Cincinnati

8.0

8.4

8.1

Green Bay

Washington

13.6

13.0

13.7

Houston

Denver

8.1

8.0

8.1

Minnesota

Detroit

11.5

11.5

11.6

New Orleans

San Francisco

1.4

-1.4

-1.7

N. Y. Jets

Miami

8.5

8.8

8.1

Tampa Bay

Indianapolis

2.6

3.6

4.4

Jacksonville

LA Chargers

-4.3

-3.9

-3.5

Arizona

Pittsburgh

-3.6

-3.7

-3.6

New England

Kansas City

9.0

9.1

8.9

Oakland

Tennessee

-4.5

-5.2

-4.7

LA Rams

Seattle

4.2

3.0

3.1

Philadelphia

N. Y. Giants

12.1

10.4

9.7

 

Totals

 

Home

Visitor

Total

Chicago

Dallas

38

Atlanta

Carolina

51

Buffalo

Baltimore

42

Cleveland

Cincinnati

45.5

Green Bay

Washington

42.5

Houston

Denver

41

Minnesota

Detroit

47.5

New Orleans

San Francisco

49

N. Y. Jets

Miami

48.5

Tampa Bay

Indianapolis

51.5

Jacksonville

LA Chargers

39.5

Arizona

Pittsburgh

44

New England

Kansas City

51.5

Oakland

Tennessee

44

LA Rams

Seattle

50.5

Philadelphia

N. Y. Giants

49.5

 

This Week’s PiRate Ratings

 

Current NFL PiRate Ratings

A F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

New England

108.9

109.6

109.1

109.2

20.5

10-2

Buffalo

101.8

102.9

102.8

102.5

17.5

9-3

N. Y. Jets

94.9

95.6

94.7

95.1

21

4-8

Miami

89.5

89.7

89.5

89.6

27.5

3-9

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Baltimore

111.1

111.1

112.0

111.4

24.5

10-2

Pittsburgh

99.5

100.0

100.4

99.9

20

7-5

Cleveland

99.2

99.5

99.5

99.4

23

5-7

Cincinnati

93.2

93.1

93.4

93.2

22.5

1-11

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

Houston

103.1

103.4

103.2

103.3

23

8-4

Tennessee

100.9

101.4

101.3

101.2

19.5

7-5

Indianapolis

99.3

100.1

99.6

99.7

22.5

6-6

Jacksonville

93.6

93.8

93.6

93.7

18.5

4-8

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

Kansas City

102.9

103.5

103.2

103.2

31

8-4

LA Chargers

101.0

100.7

100.1

100.6

21

4-8

Denver

98.1

98.4

98.1

98.2

18

4-8

Oakland

93.4

93.3

93.6

93.4

24.5

6-6

 

 

N F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

Dallas

103.3

103.9

103.5

103.6

21

6-6

Philadelphia

102.0

100.4

100.0

100.8

24.5

5-7

N.Y. Giants

91.9

92.0

92.2

92.0

25

2-10

Washington

91.4

92.2

91.8

91.8

18

3-9

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Minnesota

106.4

105.0

105.2

105.6

23

8-4

Green Bay

102.0

102.2

102.5

102.2

24.5

9-3

Chicago

103.0

100.3

100.3

101.2

17

6-6

Detroit

97.4

96.0

96.1

96.5

24.5

3-8-1

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

New Orleans

107.4

105.5

105.8

106.2

25

10-2

Tampa Bay

98.9

100.6

101.0

100.2

29

5-7

Atlanta

97.5

97.5

97.1

97.3

25.5

3-9

Carolina

96.6

96.5

96.8

96.6

25.5

5-7

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

San Francisco

109.0

109.9

110.5

109.8

24

10-2

LA Rams

105.5

104.3

104.7

104.8

25.5

7-5

Seattle

104.3

104.3

104.6

104.4

25

10-2

Arizona

93.0

93.2

93.8

93.3

24

3-8-1

 

This Week’s Playoff Projections

 

AFC Seeding

1

Baltimore

2

New England

3

Houston

4

Kansas City

5

Buffalo

6

Pittsburgh

 

 

NFC Seeding

1

Seattle

2

New Orleans

3

Green Bay

4

Dallas

5

San Francisco

6

Minnesota

Wildcard Round

Houston over Pittsburgh

Buffalo over Kansas City

Green Bay over Minnesota

San Francisco over Dallas

 

 

Divisional Round

Buffalo over Baltimore

Houston over New England

Seattle over San Francisco

New Orleans over Green Bay

 

 

Conference Championship

Houston over Buffalo

Seattle over New Orleans

 

 

Super Bowl 54

Seattle over Houston

 

 

 

 

 

 

 

 

 

 

 

 

 

 

November 18, 2019

PiRate Ratings NFL Forecast for Week 12: November 21-25, 2019

This Week’s PiRate Ratings

Margins

Home

Visitor

PiRate

Mean

Bias

Houston

Indianapolis

4.5

3.9

3.9

Cleveland

Miami

15.1

15.1

15.5

Buffalo

Denver

2.5

3.4

3.2

Cincinnati

Pittsburgh

-5.0

-5.6

-5.7

Chicago

N.Y. Giants

12.9

9.6

9.4

N.Y. Jets

Oakland

-1.0

-0.1

-1.8

New Orleans

Carolina

13.1

10.8

10.9

Atlanta

Tampa Bay

6.5

5.0

4.3

Washington

Detroit

-6.3

-4.3

-5.3

Tennessee

Jacksonville

4.0

4.1

3.5

New England

Dallas

7.1

7.5

7.5

San Francisco

Green Bay

5.4

6.2

6.2

Philadelphia

Seattle

5.5

3.9

3.4

LA Rams

Baltimore

1.4

0.1

-0.7

 

Totals

Home

Visitor

Total

Houston

Indianapolis

45

Cleveland

Miami

48.5

Buffalo

Denver

36

Cincinnati

Pittsburgh

44

Chicago

N.Y. Giants

43.5

N.Y. Jets

Oakland

46.5

New Orleans

Carolina

48.5

Atlanta

Tampa Bay

55

Washington

Detroit

43.5

Tennessee

Jacksonville

36

New England

Dallas

43

San Francisco

Green Bay

49.5

Philadelphia

Seattle

50.5

LA Rams

Baltimore

50.5

 

This Week’s PiRate Ratings

 

A F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

New England

109.6

110.5

110.2

110.1

21

9-1

Buffalo

98.9

100.0

99.6

99.5

17.5

7-3

N. Y. Jets

93.3

94.2

93.1

93.5

21.5

3-7

Miami

87.5

87.8

87.5

87.6

26

2-8

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Baltimore

108.1

108.1

109.2

108.5

25

8-2

Cleveland

99.6

99.9

100.0

99.8

22.5

4-6

Pittsburgh

99.2

99.6

99.9

99.5

20.5

5-5

Cincinnati

91.7

91.4

91.7

91.6

23.5

0-10

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

Houston

102.4

102.6

102.3

102.5

23

6-4

Indianapolis

100.9

101.8

101.4

101.4

22

6-4

Tennessee

98.0

98.3

97.9

98.1

17.5

5-5

Jacksonville

97.0

97.3

97.4

97.2

18.5

4-6

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

Kansas City

100.4

100.9

100.5

100.6

31

7-4

LA Chargers

100.8

100.6

100.0

100.4

21

4-7

Denver

99.4

99.6

99.4

99.5

18.5

3-7

Oakland

97.3

97.3

97.9

97.5

25

6-4

 

 

N F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

Dallas

105.5

106.0

105.7

105.7

22

6-4

Philadelphia

105.2

103.6

103.3

104.0

24.5

5-5

N.Y. Giants

92.8

93.1

93.3

93.1

26

2-8

Washington

89.5

90.2

89.6

89.8

18

1-9

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Minnesota

106.6

105.2

105.5

105.8

23

8-3

Green Bay

103.6

103.7

104.0

103.8

25

8-2

Chicago

103.2

100.2

100.2

101.2

17.5

4-6

Detroit

98.7

97.5

97.8

98.0

25.5

3-6-1

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

New Orleans

107.9

105.7

106.1

106.6

24

8-2

Atlanta

99.3

99.5

99.1

99.3

25.5

3-7

Carolina

97.8

97.9

98.2

98.0

24.5

5-5

Tampa Bay

95.8

97.5

97.8

97.0

29.5

3-7

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

San Francisco

106.0

106.9

107.2

106.7

24.5

9-1

LA Rams

106.6

105.2

105.5

105.8

25.5

6-4

Seattle

102.7

102.7

102.9

102.8

26

8-2

Arizona

94.7

95.1

95.8

95.2

24

3-7-1

 

 

This Week’s Playoff Projections

AFC Seeding

1

Baltimore

2

New England

3

Indianapolis

4

Oakland

5

Buffalo

6

Kansas City

 

 

NFC Seeding

1

San Francisco

2

Green Bay

3

New Orleans

4

Dallas

5

Seattle

6

Minnesota

Wildcard Round

Kansas City over Indianapolis

Oakland over Buffalo

New Orleans over Minnesota

Seattle over Dallas

 

 

Divisional Round

Kansas City over Baltimore

Oakland over New England

Seattle over San Francisco

Green Bay over New Orleans

 

 

Conference Championship

Oakland over Kansas City

Green Bay over Seattle

 

 

Super Bowl 54

Oakland over Green Bay

 

 

 

November 4, 2019

PiRate Ratings NFL Forecast for Week 10: November 7-11, 2019

This Week’s PiRate Ratings Spreads

 

Home

Visitor

PiRate

Mean

Bias

Oakland

LA Chargers

-1.2

-1.1

0.0

Tennessee

Kansas City

-0.2

-0.3

-0.2

Cleveland

Buffalo

3.7

3.0

3.4

Tampa Bay

Arizona

5.1

7.1

7.0

N.Y. Jets

N.Y. Giants

-2.1

-1.8

-3.5

New Orleans

Atlanta

17.4

14.6

15.9

Cincinnati

Baltimore

-7.5

-7.5

-8.2

Green Bay

Carolina

5.4

5.2

4.8

Chicago

Detroit

6.6

4.7

4.1

Indianapolis

Miami

15.6

16.0

16.0

Pittsburgh

LA Rams

-5.9

-4.0

-4.0

Dallas

Minnesota

0.4

2.7

2.1

San Francisco

Seattle

7.4

8.7

9.2

 

This Week’s PiRate Ratings Totals

 

Home

Visitor

Total

Oakland

LA Chargers

46.5

Tennessee

Kansas City

47

Cleveland

Buffalo

41

Tampa Bay

Arizona

53

N.Y. Jets

N.Y. Giants

46

New Orleans

Atlanta

51

Cincinnati

Baltimore

47.5

Green Bay

Carolina

51

Chicago

Detroit

43.5

Indianapolis

Miami

48.5

Pittsburgh

LA Rams

49

Dallas

Minnesota

43

San Francisco

Seattle

50

 

This Week’s PiRate Ratings

 

A F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

New England

109.2

110.2

109.8

109.7

21.5

8-1

Buffalo

98.4

99.4

98.9

98.9

17.5

6-2

N. Y. Jets

91.2

92.0

90.6

91.3

20.5

1-7

Miami

87.6

87.9

87.6

87.7

26

1-7

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Baltimore

103.8

103.6

104.6

104.0

24

6-2

Cleveland

99.6

99.8

99.8

99.7

23.5

2-6

Pittsburgh

98.6

99.1

99.4

99.0

22

4-4

Cincinnati

93.9

93.6

93.9

93.8

23.5

0-8

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

Houston

104.5

104.8

104.6

104.7

23

6-3

Indianapolis

100.1

101.0

100.6

100.6

22.5

5-3

Jacksonville

97.9

98.3

98.5

98.2

18.5

4-5

Tennessee

97.5

97.8

97.4

97.6

16.5

4-5

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

LA Chargers

101.6

101.5

101.0

101.3

21.5

4-5

Kansas City

100.2

100.6

100.1

100.3

30.5

6-3

Denver

99.1

99.3

99.1

99.2

18

3-6

Oakland

97.3

97.4

98.0

97.6

25

4-4

 

 

N F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

Dallas

105.2

105.9

105.5

105.5

21

5-3

Philadelphia

105.3

103.6

103.4

104.1

25

5-4

N.Y. Giants

93.4

93.7

94.1

93.7

25.5

2-7

Washington

91.0

91.8

91.3

91.4

17.5

1-8

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Minnesota

106.8

105.2

105.4

105.8

22

6-3

Green Bay

103.2

103.2

103.4

103.3

25.5

7-2

Chicago

103.6

100.5

100.5

101.5

18.5

3-5

Detroit

98.9

97.8

98.4

98.4

25

3-4-1

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

New Orleans

109.4

106.8

107.3

107.8

24.5

7-1

Carolina

100.7

101.0

101.6

101.1

25.5

5-3

Tampa Bay

96.5

98.7

99.2

98.1

29.5

2-6

Atlanta

95.0

95.2

94.4

94.8

26.5

1-7

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

San Francisco

106.5

107.6

108.1

107.4

24

8-0

LA Rams

107.5

106.1

106.4

106.7

27

5-3

Seattle

102.1

101.9

101.9

102.0

26

7-2

Arizona

94.4

94.6

95.2

94.7

23.5

3-5-1

 

NFL Playoff Projections

 

AFC Seeding

1

New England

2

Baltimore

3

Houston

4

Kansas City

5

Buffalo

6

Pittsburgh

 

NFC Seeding

1

San Francisco

2

New Orleans

3

Green Bay

4

Philadelphia

5

Seattle

6

LA Rams

 

Wildcard Round

Houston over Pittsburgh

Kansas City over Buffalo

Green Bay over LA Rams

Seattle over Philadelphia

 

 

Divisional Round

New England over Kansas City

Baltimore over Houston

San Francisco over Seattle

New Orleans over Green Bay

 

 

Conference Championship

New England over Baltimore

New Orleans over San Francisco

 

 

Super Bowl 54

New Orleans over New England

 

 

 

 

 

 

 

 

 

 

October 28, 2019

PiRate Ratings NFL Forecast for Week 9: October 31-November 4, 2019

This Week’s PiRate Ratings Spreads

Margins

Home

Visitor

PiRate

Mean

Bias

Arizona

San Francisco

-9.7

-10.9

-11.1

Jacksonville (n)

Houston

-4.1

-3.9

-3.0

Buffalo

Washington

9.8

9.6

9.5

Carolina

Tennessee

5.5

5.3

6.3

Philadelphia

Chicago

4.3

5.7

5.2

Kansas City

Minnesota

-4.2

-2.2

-3.1

Miami

N.Y. Jets

-3.6

-4.1

-3.2

Pittsburgh

Indianapolis

1.5

1.1

1.8

Oakland

Detroit

0.4

1.6

1.3

Seattle

Tampa Bay

9.6

7.2

6.9

Denver

Cleveland

2.1

1.8

1.5

LA Chargers

Green Bay

-2.8

-3.1

-4.2

Baltimore

New England

-6.0

-7.6

-6.2

N.Y. Giants

Dallas

-7.3

-7.3

-6.2

 

Totals

Home

Visitor

Total

Arizona

San Francisco

47

Jacksonville (n)

Houston

42.5

Buffalo

Washington

35

Carolina

Tennessee

41

Philadelphia

Chicago

44.5

Kansas City

Minnesota

52.5

Miami

N.Y. Jets

46.5

Pittsburgh

Indianapolis

43.5

Oakland

Detroit

49

Seattle

Tampa Bay

54.5

Denver

Cleveland

41.5

LA Chargers

Green Bay

48

Baltimore

New England

44

N.Y. Giants

Dallas

45.5

 

This Week’s PiRate Ratings

A F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

New England

111.0

112.2

111.8

111.7

21

8-0

Buffalo

98.2

99.1

98.5

98.6

17.5

5-2

N. Y. Jets

92.3

93.2

91.9

92.5

20.5

1-6

Miami

86.8

87.0

86.6

86.8

26

0-7

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Baltimore

102.0

101.6

102.6

102.1

23

5-2

Cleveland

99.8

100.1

100.2

100.0

23.5

2-5

Pittsburgh

98.6

99.1

99.4

99.0

21.5

3-4

Cincinnati

93.6

93.3

93.6

93.5

23.5

0-8

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

Houston

103.4

103.6

103.2

103.4

23.5

5-3

Indianapolis

100.1

101.0

100.6

100.6

22

5-2

Jacksonville

99.3

99.8

100.2

99.8

19

4-4

Tennessee

98.0

98.4

98.0

98.1

16

4-4

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

Kansas City

99.9

100.3

99.7

100.0

30.5

5-3

LA Chargers

100.0

99.8

99.1

99.6

22

3-5

Denver

98.9

99.0

98.7

98.9

18

2-6

Oakland

96.8

96.9

97.4

97.0

24.5

3-4

 

 

N F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

Dallas

104.4

105.0

104.4

104.6

20.5

4-3

Philadelphia

105.1

103.4

103.1

103.8

25.5

4-4

N.Y. Giants

94.2

94.6

95.2

94.7

25

2-6

Washington

91.5

92.4

92.0

92.0

17.5

1-7

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Minnesota

107.1

105.5

105.8

106.2

22

6-2

Green Bay

104.8

104.9

105.3

105.0

26

7-1

Chicago

103.8

100.7

100.8

101.8

19

3-4

Detroit

99.4

98.3

99.0

98.9

24.5

3-3-1

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

New Orleans

109.1

106.5

107.0

107.5

24.5

7-1

Carolina

100.5

100.7

101.3

100.8

25

4-3

Tampa Bay

96.0

98.2

98.6

97.6

29

2-5

Atlanta

94.7

94.9

94.1

94.5

26.5

1-7

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

San Francisco

106.8

108.1

108.7

107.9

24

7-0

LA Rams

107.2

105.8

106.1

106.4

27

5-3

Seattle

102.6

102.4

102.5

102.5

25.5

7-1

Arizona

94.1

94.1

94.6

94.3

23

3-4-1

 

This Week’s Playoff Projections

AFC Seeding

1

New England

2

Indianapolis

3

Baltimore

4

Kansas City

5

Houston

6

Jacksonville

 

 

NFC Seeding

1

New Orleans

2

San Francisco

3

Green Bay

4

Dallas

5

Minnesota

6

LA Rams

 

Wildcard Round

Jacksonville over Baltimore

Houston over Kansas City

Green Bay over LA Rams

Minnesota over Dallas

 

Divisional Round

New England over Jacksonville

Indianapolis over Houston

New Orleans over Minnesota

San Francisco over Green Bay

 

Conference Championship

New England over Indianapolis

New Orleans over San Francisco

 

Super Bowl 54

New England over New Orleans

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

October 21, 2019

PiRate Ratings NFL Forecast for Week 8: October 24-28, 2019

This Week’s PiRate Ratings Spreads

Margins

Home

Visitor

PiRate

Mean

Bias

Minnesota

Washington

19.2

16.5

17.7

Detroit

N.Y. Giants

8.5

6.8

7.2

Tennessee

Tampa Bay

4.8

2.7

1.9

Chicago

LA Chargers

8.3

4.6

5.8

Atlanta

Seattle

-4.7

-4.1

-4.8

Jacksonville

N.Y. Jets

9.6

9.0

10.7

Buffalo

Philadelphia

-2.0

1.2

1.1

LA Rams

Cincinnati

13.6

12.3

12.1

New Orleans

Arizona

16.8

13.3

13.1

Houston

Oakland

10.3

10.7

9.7

San Francisco

Carolina

5.0

6.1

5.7

Indianapolis

Denver

4.0

4.7

4.6

New England

Cleveland

14.2

15.1

14.6

Kansas City

Green Bay

-0.7

-0.3

-1.3

Pittsburgh

Miami

15.1

15.2

15.9

 

Totals

Home

Visitor

Total

Minnesota

Washington

41

Detroit

N.Y. Giants

48.5

Tennessee

Tampa Bay

44

Chicago

LA Chargers

41.5

Atlanta

Seattle

52

Jacksonville

N.Y. Jets

39.5

Buffalo

Philadelphia

43

LA Rams

Cincinnati

52

New Orleans

Arizona

48

Houston

Oakland

48

San Francisco

Carolina

47.5

Indianapolis

Denver

41

New England

Cleveland

44.5

Kansas City

Green Bay

56.5

Pittsburgh

Miami

48

 

This Week’s PiRate Ratings

A F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

New England

111.0

112.2

111.8

111.7

21

7-0

Buffalo

99.4

100.6

100.1

100.0

17.5

5-1

N. Y. Jets

92.5

93.5

92.2

92.7

20.5

1-5

Miami

86.8

87.0

86.6

86.8

26.5

0-6

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Baltimore

101.7

101.3

102.3

101.8

23

5-2

Cleveland

99.8

100.1

100.2

100.0

23.5

2-4

Pittsburgh

98.8

99.3

99.6

99.2

21.5

2-4

Cincinnati

93.6

93.4

93.8

93.6

24

0-7

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

Houston

103.9

104.2

103.8

104.0

23.5

4-3

Indianapolis

100.1

101.0

100.6

100.6

22.5

4-2

Jacksonville

99.1

99.5

99.9

99.5

19

3-4

Tennessee

98.1

98.4

98.0

98.2

15.5

3-4

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

Kansas City

100.7

101.2

100.6

100.8

30.5

5-2

LA Chargers

99.5

99.7

98.8

99.3

22

2-5

Denver

99.2

99.3

99.0

99.2

18.5

2-5

Oakland

96.6

96.6

97.1

96.8

24.5

3-3

 

 

N F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

Dallas

104.1

104.7

104.1

104.3

20.5

4-3

Philadelphia

103.9

101.9

101.5

102.4

25.5

3-4

N.Y. Giants

94.1

94.5

95.0

94.5

24.5

2-5

Washington

91.2

92.2

91.6

91.7

18.5

1-6

 

 

North

PiRate

Mean

Bias

Avg

Totals

W-L

Minnesota

107.4

105.7

106.2

106.5

22.5

5-2

Green Bay

104.5

104.5

104.9

104.6

26

6-1

Chicago

104.8

101.3

101.6

102.6

19.5

3-3

Detroit

99.5

98.4

99.2

99.1

24

2-3-1

 

 

South

PiRate

Mean

Bias

Avg

Totals

W-L

New Orleans

108.2

105.2

105.6

106.3

24.5

6-1

Carolina

102.3

102.5

103.3

102.7

24.5

4-2

Tampa Bay

95.9

98.2

98.6

97.6

28.5

2-4

Atlanta

94.8

95.1

94.4

94.7

26.5

1-6

 

 

West

PiRate

Mean

Bias

Avg

Totals

W-L

LA Rams

107.2

105.7

105.9

106.3

28

4-3

San Francisco

104.3

105.6

106.0

105.3

23

6-0

Seattle

102.5

102.2

102.2

102.3

25.5

6-1

Arizona

94.5

94.9

95.5

95.0

23.5

3-3-1

 

This Week’s PiRate Ratings Playoff Projections

 

AFC Seeding

1

New England

2

Indianapolis

3

Kansas City

4

Baltimore

5

Buffalo

6

Houston

NFC Seeding

1

Green Bay

2

New Orleans

3

San Francisco

4

Dallas

5

Minnesota

6

LA Rams

Wildcard Round

Kansas City over Houston

Buffalo over Baltimore

LA Rams over San Francisco

Minnesota over Dallas

Divisional Round

New England over Buffalo

Kansas City over Indianapolis

Green Bay over LA Rams

New Orleans over Minnesota

Conference Championship

New England over Kansas City

Green Bay over New Orleans

Super Bowl 54

New England over Green Bay

 

 

 

 

 

 

 

 

 

October 7, 2019

PiRate Ratings NFL Forecast for Week 6: October 10-14, 2019

This Week’s PiRate Ratings Spreads

Home

Visitor

PiRate

Mean

Bias

New England

N. Y. Giants

17.1

17.6

16.1

Tampa Bay

Carolina

-3.1

-0.4

-0.6

Baltimore

Cincinnati

9.9

9.7

10.2

Cleveland

Seattle

-0.5

0.0

0.0

Kansas City

Houston

4.2

4.5

4.2

Jacksonville

New Orleans

-6.0

-2.1

-2.0

Minnesota

Philadelphia

2.1

2.1

2.6

Miami

Washington

-3.1

-4.5

-4.5

LA Rams

San Francisco

7.4

4.0

3.9

Arizona

Atlanta

0.2

0.0

1.2

N. Y. Jets

Dallas

-6.4

-6.2

-7.1

Denver

Tennessee

3.2

3.0

2.9

LA Chargers

Pittsburgh

5.7

5.7

4.4

Green Bay

Detroit

5.9

7.2

6.3

 

This Week’s PiRate Ratings Totals

Home

Visitor

Total

New England

N. Y. Giants

46

Tampa Bay

Carolina

52

Baltimore

Cincinnati

47.5

Cleveland

Seattle

48

Kansas City

Houston

54

Jacksonville

New Orleans

44

Minnesota

Philadelphia

45

Miami

Washington

46.5

LA Rams

San Francisco

53

Arizona

Atlanta

48

N. Y. Jets

Dallas

42

Denver

Tennessee

36.5

LA Chargers

Pittsburgh

43

Green Bay

Detroit

48

 

This Week’s PiRate Ratings

 

A F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

New England

109.0

110.1

109.4

109.5

21.5

5-0

Buffalo

99.5

100.9

100.5

100.3

18

4-1

N. Y. Jets

93.3

94.3

92.9

93.5

21.5

0-4

Miami

86.1

85.9

85.3

85.8

26.5

0-4

North

PiRate

Mean

Bias

Avg

Totals

W-L

Baltimore

101.1

100.7

101.7

101.2

23

3-2

Cleveland

99.6

99.9

100.0

99.8

23

2-3

Pittsburgh

97.6

98.0

98.3

97.9

21.5

1-4

Cincinnati

94.3

94.0

94.5

94.3

24.5

0-5

South

PiRate

Mean

Bias

Avg

Totals

W-L

Houston

103.9

104.1

103.8

104.0

23

3-2

Tennessee

99.3

99.7

99.5

99.5

16.5

2-3

Indianapolis

98.9

99.8

99.2

99.3

22

3-2

Jacksonville

98.1

98.7

99.0

98.6

20

2-3

West

PiRate

Mean

Bias

Avg

Totals

W-L

Kansas City

105.1

105.6

105.0

105.2

31

4-1

LA Chargers

100.9

101.2

100.2

100.7

21.5

2-3

Denver

99.6

99.7

99.4

99.6

20

1-4

Oakland

96.8

96.9

97.5

97.1

23.5

3-2

N F C

East

PiRate

Mean

Bias

Avg

Totals

W-L

Philadelphia

106.1

104.1

103.9

104.7

24.5

3-2

Dallas

102.7

103.5

103.0

103.1

20.5

3-2

N.Y. Giants

95.0

95.5

96.3

95.6

24.5

2-3

Washington

91.7

92.9

92.4

92.3

20

0-5

North

PiRate

Mean

Bias

Avg

Totals

W-L

Minnesota

105.2

103.2

103.4

104.0

20.5

3-2

Green Bay

103.5

103.6

103.8

103.6

25

4-1

Chicago

105.6

102.2

102.6

103.5

19

3-2

Detroit

100.0

98.9

100.0

99.7

23

2-1-1

South

PiRate

Mean

Bias

Avg

Totals

W-L

New Orleans

106.6

103.3

103.5

104.5

24

4-1

Carolina

101.6

101.5

102.2

101.8

24

3-2

Tampa Bay

96.0

98.6

99.1

97.9

28

2-3

Atlanta

96.5

97.0

96.4

96.6

26

1-4

West

PiRate

Mean

Bias

Avg

Totals

W-L

LA Rams

107.0

105.1

105.3

105.8

29

3-2

San Francisco

102.6

104.1

104.4

103.7

24

4-0

Seattle

103.1

102.9

103.0

103.0

25

4-1

Arizona

93.7

94.0

94.5

94.1

22

1-3-1

 

Playoff Projections

AFC Seeding

1

New England

2

Kansas City

3

Houston

4

Baltimore

5

Indianapolis

6

Buffalo

NFC Seeding

1

San Francisco

2

New Orleans

3

Green Bay

4

Philadelphia

5

Seattle

6

Minnesota

Wildcard Round

Buffalo over Houston

Indianapolis over Baltimore

Green Bay over Minnesota

Philadelphia over Seattle

 

 

Divisional Round

New England over Buffalo

Kansas City over Indianapolis

Philadelphia over San Francisco

New Orleans over Green Bay

 

 

Conference Championship

New England over Kansas City

New Orleans over Philadelphia

 

 

Super Bowl 54

New England over New Orleans

 

 

 

 

 

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