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Jeff Sagarin'stm Major League Soccer Ratings (MLS)


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Final 2021 MAJOR LEAGUE SOCCER ratings through results of 2021 DECEMBER 11 SATURDAY - MLS CUP CHAMPIONSHIP


this output has three parts: (1) teams listed by RATING top-to-bottom
                             (2) DIVISION AVERAGES
                                 (listed top-to-bottom)
                             (3) teams listed by DIVISIONS
                                (listed top-to-bottom within divisions)


The SCHEDULE ratings represent what the rating would have to be for a
hypothetical team to have a mathematical expectation of winning precisely 50%
of their games against the schedule played by the team in question in the games
that it has played so far.  The schedule difficulty of each given game takes
into account the rating of the opponent and the location of the game. This
is the same concept that is used in computing the WIN50% conference ratings.


 To make predictions for upcoming games, simply compare the RATINGS of
 the teams in question and allow an ADDITIONAL  .50  goals for the home
 team.  Thus, for example, a HOME team with a rating of 2.47 would be
 favored by  1.08  goals over a VISITING team having a rating of 1.89
 Or a VISITING team with a rating of 3.14 would be favored by .29 goals
 over a HOME team having a rating of 2.35

NOTE: Use whatever home advantage is listed in the output below.
      In the example just above, a home edge of .50 was shown for
      illustrative purposes. The home edge will vary during the season.
Several different home edges are shown, one for each of the several different type of ratings
directly over their respective columns.

The numbers to the right of a team's schedule strength are its rank of
schedule - (in parentheses) - and its record versus teams in these
rating's top 5 and top 10 respectively.

Teams that appear to be tied to two decimal places in a given column are actually
different when carried to more decimal places in the computer's internal arithmetic.
----------------------------------------------------------------------------------------------------------------
The PREDICTOR, is such that the score is the only thing that matters.
PREDICTOR is also known as PURE_POINTS, BALLANTINE, RHEINGOLD, WHITE OWL
and is a very good PREDICTOR of future games.
----------------------------------------------------------------------------------------------------------------
GOLDEN_MEAN also utilizes the actual SCORES of the games in a different way but is also completely SCORE BASED
and thus should be a good match for the PURE POINTS in terms of predictive accuracy for upcoming games.
----------------------------------------------------------------------------------------------------------------
The RECENT, is score-based and weights RECENT play more heavily than earlier games. Its effect will become
more pronounced the longer a season goes if a given team happens to have an upward or downward trend.
----------------------------------------------------------------------------------------------------------------
The overall RATING is a synthesis of the three different SCORE-BASED methods, PREDICTOR(PURE_POINTS), GOLDEN_MEAN,
and RECENT and thus should be a good predictor in its own right.


Predictions_with_Totals

_________________________________________________________________________________________________________________________________________________
FINAL Major League Soccer 2021 through games of 2021 December 11 Saturday - MLS Cup Championship                                                
                                RATING    W   L   T  SCHEDL(RANK) VS top  5 | VS top 10 |  PREDICTOR   | GOLDEN_MEAN  |  RECENT    
                HOME ADVANTAGE=[  0.46]                                                   [  0.45]       [  0.46]       [  0.45]
   1  New England Revolution  =   2.66   22   6   7    2.01(  15)   5  3  2 |  10  3  2 |    2.67    1 |    2.71    1 |    2.60    2  EASTERN
   2  New York City FC        =   2.64   18  11   9    2.07(   3)   4  4  2 |   7  6  4 |    2.62    2 |    2.59    2 |    2.73    1  EASTERN
   3  Nashville SC            =   2.48   13   5  18    1.94(  25)   3  2  2 |   4  3  5 |    2.48    3 |    2.50    3 |    2.46    4  EASTERN
   4  Colorado Rapids         =   2.41   17   8  10    1.91(  27)   0  1  0 |   1  4  5 |    2.41    7 |    2.40    7 |    2.41    5  western
   5  Philadelphia Union      =   2.41   16   9  12    2.04(  10)   3  5  2 |   7  5  5 |    2.43    5 |    2.41    6 |    2.37    6  EASTERN
   6  Seattle Sounders        =   2.35   17   9   9    1.99(  21)   1  0  2 |   4  3  3 |    2.48    4 |    2.47    4 |    2.16    9  western
   7  Sporting Kansas City    =   2.31   18  11   7    1.93(  26)   1  0  2 |   4  2  3 |    2.43    6 |    2.41    5 |    2.14   12  western
   8  Portland Timbers        =   2.28   20  14   4    1.96(  24)   1  3  1 |   3  5  2 |    2.21    8 |    2.20    8 |    2.46    3  western
   9  New York Red Bulls      =   2.19   13  13   9    2.08(   2)   3  5  4 |   3  6  6 |    2.16    9 |    2.16    9 |    2.23    7  EASTERN
  10  Atlanta United          =   2.15   13  10  12    2.01(  16)   0  6  4 |   0  6  7 |    2.15   10 |    2.14   10 |    2.16   10  EASTERN
FINAL Major League Soccer 2021 through games of 2021 December 11 Saturday - MLS Cup Championship                                                
                                RATING    W   L   T  SCHEDL(RANK) VS top  5 | VS top 10 |  PREDICTOR   | GOLDEN_MEAN  |  RECENT    
                HOME ADVANTAGE=[  0.46]                                                   [  0.45]       [  0.46]       [  0.45]
  11  Real Salt Lake          =   2.09   16  15   6    2.04(   8)   2  1  1 |   7  6  1 |    2.04   15 |    2.07   11 |    2.15   11  western
  12  Columbus Crew SC        =   2.08   13  13   8    2.05(   7)   2  4  5 |   4  8  5 |    2.07   12 |    2.06   14 |    2.09   14  EASTERN
  13  Los Angeles FC          =   2.06   12  13   9    2.01(  12)   1  2  0 |   3  9  1 |    2.01   16 |    2.02   16 |    2.13   13  western
  14  Vancouver Whitecaps FC  =   2.04   12  10  13    1.98(  22)   0  1  1 |   3  5  3 |    1.97   17 |    1.98   17 |    2.18    8  western
  15  D.C. United             =   2.04   14  15   5    2.05(   6)   2  8  1 |   4 10  2 |    2.08   11 |    2.06   12 |    1.97   17  EASTERN
  16  Orlando City SC         =   2.03   13  10  12    2.00(  19)   1  4  5 |   2  7  7 |    2.04   14 |    2.06   13 |    2.00   16  EASTERN
  17  Minnesota United FC     =   2.00   13  12  10    2.01(  14)   1  3  0 |   5  7  1 |    1.96   18 |    1.97   18 |    2.08   15  western
  18  CF Montreal             =   1.98   12  12  10    1.97(  23)   1  4  4 |   3  6  5 |    2.05   13 |    2.03   15 |    1.86   19  EASTERN
  19  LA Galaxy               =   1.92   13  12   9    2.00(  20)   0  1  1 |   3  6  2 |    1.91   19 |    1.93   19 |    1.90   18  western
  20  San Jose Earthquakes    =   1.78   10  13  11    2.00(  18)   0  1  1 |   1  6  3 |    1.73   20 |    1.75   20 |    1.85   20  western
FINAL Major League Soccer 2021 through games of 2021 December 11 Saturday - MLS Cup Championship                                                
                                RATING    W   L   T  SCHEDL(RANK) VS top  5 | VS top 10 |  PREDICTOR   | GOLDEN_MEAN  |  RECENT    
                HOME ADVANTAGE=[  0.46]                                                   [  0.45]       [  0.46]       [  0.45]
  21  FC Dallas               =   1.67    7  15  12    2.03(  11)   1  2  2 |   3  6  3 |    1.69   21 |    1.68   21 |    1.62   23  western
  22  Inter Miami CF          =   1.63   12  17   5    2.01(  13)   3  4  2 |   3  9  3 |    1.60   22 |    1.61   22 |    1.68   22  EASTERN
  23  Chicago Fire FC         =   1.63    9  18   7    2.12(   1)   1  4  6 |   4  7  6 |    1.59   23 |    1.59   23 |    1.70   21  EASTERN
  24  Houston Dynamo FC       =   1.45    6  16  12    2.00(  17)   0  3  0 |   2  8  1 |    1.50   24 |    1.47   24 |    1.35   25  western
  25  Austin FC               =   1.43    9  21   4    2.04(   9)   1  3  0 |   4  6  2 |    1.38   25 |    1.40   25 |    1.49   24  western
  26  Toronto FC              =   1.31    6  18  10    2.06(   4)   2  3  5 |   2  6  7 |    1.32   26 |    1.30   26 |    1.31   26  EASTERN
  27  FC Cincinnati           =   0.98    4  22   8    2.05(   5)   0  9  1 |   0 12  3 |    1.00   27 |    1.01   27 |    0.92   27  EASTERN
_________________________________________________________________________________________________________________________________________________

Divisional Rankings


There are three group ratings, the "central mean", the
"simple average" (also known as the "arithmetic mean",)
and the WIN50%.
The "central mean" gives the most weight to the middle team(s)
in the group and progressively less weight to teams as you go
away from the middle in either direction, up or down.
This tends to smooth out the effect of anomalous teams that are rated
much higher and lower than the middle team(s) in the group.  The
"simple average" ("arithmetic mean") weights each team equally
no matter where they are relative to the middle.
Here are a few examples of how the "central mean" is computed.
  4-team group ___ the weights are   1-2-2-1
  5-team group ___ the weights are   1-2-3-2-1
  6-team group ___ the weights are   1-2-3-3-2-1
  7-team group ___ the weights are   1-2-3-4-3-2-1
  8-team group ___ the weights are   1-2-3-4-4-3-2-1
  9-team group ___ the weights are   1-2-3-4-5-4-3-2-1
 10-team group ___ the weights are   1-2-3-4-5-5-4-3-2-1
 11-team group ___ the weights are   1-2-3-4-5-6-5-4-3-2-1
 12-team group ___ the weights are   1-2-3-4-5-6-6-5-4-3-2-1
 13-team group ___ the weights are   1-2-3-4-5-6-7-6-5-4-3-2-1
This is an expanded version of the "tri-mean".

The WIN50% is the rating required to win 50% of the games if playing an
infinite number of round-robins in the given group at a neutral location.
      DIVISION            CENTRAL MEAN    SIMPLE AVERAGE  TEAMS      WIN50%

   1  EASTERN                 =   2.05       2.02  (  1)     14       2.02  (  1)
   2  western                 =   2.01       1.98  (  2)     13       1.99  (  2)


      DIVISION            CENTRAL MEAN    SIMPLE AVERAGE  TEAMS      WIN50%

   1  EASTERN                 =   2.05       2.02  (  1)     14       2.02  (  1)
   2  western                 =   2.01       1.98  (  2)     13       1.99  (  2)
______________________________________________________________________________________________________

By Division

_________________________________________________________________________________________________________________________________________________

   1  EASTERN                 =   2.05       2.02  (  1)   TEAMS= 14       2.02  (  1)
FINAL Major League Soccer 2021 through games of 2021 December 11 Saturday - MLS Cup Championship                                                
                                RATING    W   L   T  SCHEDL(RANK) VS top  5 | VS top 10 |  PREDICTOR   | GOLDEN_MEAN  |  RECENT    
                HOME ADVANTAGE=[  0.46]                                                   [  0.45]       [  0.46]       [  0.45]
   1  New England Revolution  =   2.66   22   6   7    2.01(  15)   5  3  2 |  10  3  2 |    2.67    1 |    2.71    1 |    2.60    2  EASTERN
   2  New York City FC        =   2.64   18  11   9    2.07(   3)   4  4  2 |   7  6  4 |    2.62    2 |    2.59    2 |    2.73    1  EASTERN
   3  Nashville SC            =   2.48   13   5  18    1.94(  25)   3  2  2 |   4  3  5 |    2.48    3 |    2.50    3 |    2.46    4  EASTERN
   5  Philadelphia Union      =   2.41   16   9  12    2.04(  10)   3  5  2 |   7  5  5 |    2.43    5 |    2.41    6 |    2.37    6  EASTERN
   9  New York Red Bulls      =   2.19   13  13   9    2.08(   2)   3  5  4 |   3  6  6 |    2.16    9 |    2.16    9 |    2.23    7  EASTERN
  10  Atlanta United          =   2.15   13  10  12    2.01(  16)   0  6  4 |   0  6  7 |    2.15   10 |    2.14   10 |    2.16   10  EASTERN
  12  Columbus Crew SC        =   2.08   13  13   8    2.05(   7)   2  4  5 |   4  8  5 |    2.07   12 |    2.06   14 |    2.09   14  EASTERN
  15  D.C. United             =   2.04   14  15   5    2.05(   6)   2  8  1 |   4 10  2 |    2.08   11 |    2.06   12 |    1.97   17  EASTERN
  16  Orlando City SC         =   2.03   13  10  12    2.00(  19)   1  4  5 |   2  7  7 |    2.04   14 |    2.06   13 |    2.00   16  EASTERN
  18  CF Montreal             =   1.98   12  12  10    1.97(  23)   1  4  4 |   3  6  5 |    2.05   13 |    2.03   15 |    1.86   19  EASTERN
  22  Inter Miami CF          =   1.63   12  17   5    2.01(  13)   3  4  2 |   3  9  3 |    1.60   22 |    1.61   22 |    1.68   22  EASTERN
  23  Chicago Fire FC         =   1.63    9  18   7    2.12(   1)   1  4  6 |   4  7  6 |    1.59   23 |    1.59   23 |    1.70   21  EASTERN
  26  Toronto FC              =   1.31    6  18  10    2.06(   4)   2  3  5 |   2  6  7 |    1.32   26 |    1.30   26 |    1.31   26  EASTERN
  27  FC Cincinnati           =   0.98    4  22   8    2.05(   5)   0  9  1 |   0 12  3 |    1.00   27 |    1.01   27 |    0.92   27  EASTERN
_________________________________________________________________________________________________________________________________________________

   2  western                 =   2.01       1.98  (  2)   TEAMS= 13       1.99  (  2)
FINAL Major League Soccer 2021 through games of 2021 December 11 Saturday - MLS Cup Championship                                                
                                RATING    W   L   T  SCHEDL(RANK) VS top  5 | VS top 10 |  PREDICTOR   | GOLDEN_MEAN  |  RECENT    
                HOME ADVANTAGE=[  0.46]                                                   [  0.45]       [  0.46]       [  0.45]
   4  Colorado Rapids         =   2.41   17   8  10    1.91(  27)   0  1  0 |   1  4  5 |    2.41    7 |    2.40    7 |    2.41    5  western
   6  Seattle Sounders        =   2.35   17   9   9    1.99(  21)   1  0  2 |   4  3  3 |    2.48    4 |    2.47    4 |    2.16    9  western
   7  Sporting Kansas City    =   2.31   18  11   7    1.93(  26)   1  0  2 |   4  2  3 |    2.43    6 |    2.41    5 |    2.14   12  western
   8  Portland Timbers        =   2.28   20  14   4    1.96(  24)   1  3  1 |   3  5  2 |    2.21    8 |    2.20    8 |    2.46    3  western
  11  Real Salt Lake          =   2.09   16  15   6    2.04(   8)   2  1  1 |   7  6  1 |    2.04   15 |    2.07   11 |    2.15   11  western
  13  Los Angeles FC          =   2.06   12  13   9    2.01(  12)   1  2  0 |   3  9  1 |    2.01   16 |    2.02   16 |    2.13   13  western
  14  Vancouver Whitecaps FC  =   2.04   12  10  13    1.98(  22)   0  1  1 |   3  5  3 |    1.97   17 |    1.98   17 |    2.18    8  western
  17  Minnesota United FC     =   2.00   13  12  10    2.01(  14)   1  3  0 |   5  7  1 |    1.96   18 |    1.97   18 |    2.08   15  western
  19  LA Galaxy               =   1.92   13  12   9    2.00(  20)   0  1  1 |   3  6  2 |    1.91   19 |    1.93   19 |    1.90   18  western
  20  San Jose Earthquakes    =   1.78   10  13  11    2.00(  18)   0  1  1 |   1  6  3 |    1.73   20 |    1.75   20 |    1.85   20  western
  21  FC Dallas               =   1.67    7  15  12    2.03(  11)   1  2  2 |   3  6  3 |    1.69   21 |    1.68   21 |    1.62   23  western
  24  Houston Dynamo FC       =   1.45    6  16  12    2.00(  17)   0  3  0 |   2  8  1 |    1.50   24 |    1.47   24 |    1.35   25  western
  25  Austin FC               =   1.43    9  21   4    2.04(   9)   1  3  0 |   4  6  2 |    1.38   25 |    1.40   25 |    1.49   24  western
_________________________________________________________________________________________________________________________________________________
endfile

Predictions_with_Totals

These are the "regular method". _ HOME or CLOSEBY (c) team in CAPS _ both teams in lower case _ means "n" for NEUTRAL location Rating Favorite _ MONEY=odds to 100 _ FAVORITE Rating Predict Golden Recent UNDERDOG ODDS PCT% TOTAL probdraw _ ======================================================================================================================= EIGENVECTOR Analysis eigen MONEY=odds to 100 EPCT%=confidence EFAVORITE ESPREAD EODDS EPCT% EUNDERDOG endfile

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