asteroid’s initial projections (statistics explained in OP)

The last Big 12 team to play a non-conference game prior to the onset of
conference play this Saturday did so last night, and the updated Sagarin
ratings that include that game are out, so we can now do our initial season
projection for the Big 12.  Kansas opens with a 3 game lead.  Kansas State
goes from first to worst.  Baylor and West Virginia are the primary
challengers.  Texas Tech might be considered a darkhorse.  All the home
teams are favored on Saturday.  Kansas has the largest predicted margin,
which is a bit of a surprise, considering the quality of the opponent.
It'll be a key game in the race for the conference championship.  TCU
hosting Iowa State is projected to be the closest game, with Texas Tech
hosting Oklahoma State not being far behind.

                      Init.
Pred                  Proj.   Conf                          
Rank  Big XII Team    Wins   Record  Next Game   Prediction 
----  --------------  -----  ------  ---------   -----------
#  2  Kansas          14.45    0  0   WVU (Sa)   KU  by  9.3 
# 14  Baylor          10.99    0  0   UT  (Sa)   BU  by  8.4
# 16  West Virginia   10.73    0  0  @KU  (Sa)   
# 29  Texas Tech       9.33    0  0   OSU (Sa)   TTU by  3.8
# 37  Oklahoma State   8.95    0  0  @TTU (Sa)   
# 45  Iowa State       8.35    0  0  @TCU (Sa)   
# 52  TCU              7.46    0  0   ISU (Sa)   TCU by  2.0 
# 58  Texas            7.25    0  0  @BU  (Sa)               
# 55  Oklahoma         7.19    0  0   KSU (Sa)   OU  by  6.1 
# 83  Kansas State     5.30    0  0  @OU  (Sa)               

And a brief description of the statistical quantities that I've been tracking
for the last several years.

Performance is simply the average difference between the predicted scoring
margin and the actual scoring margin.  Kansas' blowout wins over Monmouth
and Kansas City (27 and 17 points above expectation, respectively) are
responsible for that large performance statistic.

Performance (points)     
---------------------    
Kansas          +4.10    
West Virginia   +1.50    
Oklahoma State  +1.49    
TCU             +0.94    
Baylor          +0.89    
Iowa State      -1.10    
Texas Tech      -1.11    
Oklahoma        -1.25    
Texas           -1.96    
Kansas State    -2.16    

Inconsistency is simply the root-mean-square of the difference between
the predicted scoring margin and the actual scoring margin.  A value of
zero would result from a team playing exactly as expected, each margin
being exactly as predicted.  Historically, the national average for
inconsistency has been about 11 points.  Baylor has played only one
game more than 9 points from expectation, which was their season opener
against Central Arkansas.  At the opposite extrene, Oklahoma State
played almost 36 points above expectation against Mississippi and
22 points below expectation against Wichita State, among others,
leading to the worst inconsistency value I've ever seen; the Cowboys
have played only two games within 7 points of expectation.

Inconsistency (points)    
----------------------    
Baylor            7.09    
West Virginia     7.53    
Oklahoma          9.46    
Kansas            9.60    
Kansas State      9.79    
TCU              10.66    
Texas Tech       10.70    
Texas            10.89    
Iowa State       12.14    
Oklahoma State   17.89    

Trend is the difference between the predicted scoring margin and the
actual scoring margin as a function of game number.  So if you play
a bunch of games above expectation early in the season and then a
bunch of games below expectation later in the season, that would
lead to a negative trend.  These values are generally not
statistically significant, which is not to say that teams don't
get better during the season.  Most teams presumably get more
comfortable with their roles and playbook as the season progresses
and therefore could be playing better in that sense, but the trend
statistic measures the improvement of a team relative to the
improvement of other teams.  If all teams improved by the same
amount, then the predicted margins would not change, and the
computed trends would remain near zero.  Texas Tech kind of stands
out in this statistic; had they not played above expectation
against Louisville, they would have seven consecutive below
expectation performances.

Trend (points per game)           
------------------------------    
TCU             +0.51 +/- 1.06    
West Virginia   +0.51 +/- 0.64    
Oklahoma State  +0.30 +/- 1.57    
Kansas          -0.02 +/- 0.96    
Kansas State    -0.04 +/- 0.86    
Baylor          -0.37 +/- 0.70    
Oklahoma        -0.76 +/- 0.79    
Iowa State      -0.97 +/- 1.02    
Texas           -1.38 +/- 0.85    
Texas Tech      -1.59 +/- 0.79    

Mental toughness is a peculiar statistic.  It is the difference
between the actual scoring margin and the predicted scoring margin
as a function of strength of opponent, for which the predicted
scoring margin is used as a proxy.  So if you blow out weak
opponents such as Kansas did to Monmouth and Kansas City, you're
getting a large above-expectation value against a large negative
predicted margin, leading to a negative mental toughness value.
Winning by more than expected against tough opponents leads to
positive mental toughness value, as would losing to weak opponents
that you're expected to beat.  That's what makes it peculiar.
These values are also not statistically significant as a general
rule.  TCU stands out here because they ran up the score against
three of their easier opponents.  The way to get a large positive
value is to either beat tough opponents by a lot more than
expected, which isn't easy, or allow weak opponents to stay close.
That's why most of the values here are negative.  It is a
dimensionless quantity (points over points, the units thereby
canceling out).

Mental toughness
------------------------------
West Virginia   +0.22 +/- 0.27
Oklahoma        +0.20 +/- 0.26
Iowa State      +0.11 +/- 0.28
Baylor          -0.03 +/- 0.19
Texas Tech      -0.04 +/- 0.32
Texas           -0.09 +/- 0.36
Oklahoma State  -0.23 +/- 0.61
Kansas State    -0.24 +/- 0.29
Kansas          -0.52 +/- 0.27
TCU             -1.04 +/- 0.51

Average offense is simply the average number of points a team
scores, though I do deduct 2 points for the home team and add
2 points to the road team to compensate for the home court
advantage.  The actual score is used for neutral court games.
Kansas State doesn't appear to be much of an offensive threat
this season.  Texas isn't much better.  Shaka Smart on the hot
seat?

Average offense (pts)   
---------------------   
Kansas          79.45   
Iowa State      79.08   
Baylor          76.27   
Oklahoma        75.17   
Texas Tech      75.17   
West Virginia   74.33   
Oklahoma State  71.17   
TCU             71.09   
Texas           68.17   
Kansas State    65.75   

Average defense is simply the average number of points a team
allows their opponents to score, with the corresponding
correction for home court advantage mentioned above.
Interesting that seven teams are within a couple points of
each other.

Average defense (pts)   
---------------------   
Baylor          61.18   
Kansas State    61.25   
Texas           61.67   
TCU             62.09   
West Virginia   62.50   
Oklahoma State  62.67   
Kansas          62.82   
Texas Tech      64.25   
Oklahoma        70.00   
Iowa State      71.75   

Total points is just what you'd expect; it's the average of
the combined teams' scores.  The home court advantage
correction has no effect here; it's taking the points out of
the left pocket and putting them in the right pocket.  The
total remains unaffected.

Total Points             
----------------------   
Iowa State      150.83   
Oklahoma        145.17   
Kansas          142.27   
Texas Tech      139.42   
Baylor          137.45   
West Virginia   136.83   
Oklahoma State  133.83   
TCU             133.18   
Texas           129.83   
Kansas State    127.00   

Scoring margin is just the difference between the average
offense and the average defense.  Keep in mind that I've
made a correction for home court advantage, so these values
will be slightly different from those computed by, for
example, Greenfield.  The correction was introduced to
recognize the fact that Power 5 teams tend to play a lot of
non-conference games at home, which tends to inflate their
scoring margins.

Scoring Margin (pts)     
----------------------   
Kansas          +16.64    
Baylor          +15.09    
West Virginia   +11.83    
Texas Tech      +10.92    
TCU              +9.00    
Oklahoma State   +8.50    
Iowa State       +7.33    
Texas            +6.50    
Oklahoma         +5.17    
Kansas State     +4.50    

Strength of schedule is taken from the Sagarin ratings.
The numerical value is shown, along with the ranking in
parentheses.  Like last season, Texas Tech has played
the weakest non-conference schedule of any Big 12 team.
Considering how highly ranked most Big 12 teams are,
conference play makes the strength of schedule rankings
improve considerably.  Everybody will be in the Top 100
by the end of the regular season.  Kansas, like Michigan
State, tends to play tough non-conference schedules,
and this season was no exception.  Having West Virginia
and Baylor among their first three conference games is
likely going to keep Kansas higher than #4 for a long
time.

Schedule Strength
---------------------------
Kansas          80.79 (  4)
Oklahoma State  77.10 ( 32)
Oklahoma        76.76 ( 39)
West Virginia   76.03 ( 50)
Iowa State      73.87 (107)
Kansas State    72.09 (196)
Baylor          71.73 (216)
Texas           71.69 (217)
TCU             70.76 (260)
Texas Tech      69.38 (314)