Using the Sagarin Ratings from USA Today and giving Butler a 2.5 point home edge here are the final four odds:

• Duke 60% chance to beat West Virginia
• Butler 67% chance to beat Michigan State
• Duke has 40% chance to win tourney, Butler 29% , West Virginia 22% and Michigan State 9%.

John Hollinger wrote today that he cannot figure out why Brandon Rush of the Pacers will average 30 minutes of Playing Time , the reason being his PER rating is poor (below 10. ) Hollinger, on the other hand gives Troy Murphy a PER of 17.7, well above average.

   As we have often stated, the box score misses a lot. When we look at how the score of the game moves and adjust for the strength of players Murphy and Rush play with we find Rush has an Adjusted +/- of around 0 and Murphy has a -7 Adjusted +/- which means  we estimate that Troy Murphy in for 48 minutes is 7 points worse than an average NBA player. So we believe Murphy must be doing some bad things that do not show up in the box score and in all likelihood Rush does many good things that do not show up in the box score.  Jim O’Brien must also believe that Rush has “hidden virtues.”

While Adjusted +/- is not perfect, we can gain insights into why the system rates Rush ahead of Murphy by looking at the following numbers:

For exmaple, we find that when Granger is in the Pacers play 2 points per game worse with Murphy in than Rush in.  When Hibbert is in, the Pacers are 12 points per game better with Murphy out than with Rush out. A bad PER does not necessarily mean you hurt the team and a good PER does not imply that you surely help the team! Adjusted +/- sorts through all these differences in team performance to obtain an estimated per minute value for a player/

I am back in class teaching 250 MBA’s spreadsheet modeling, so I will have less time for blogging. Here are ratings of NBA teams since all star break. Clearly the Magic have been the best playing 10.7 points better than average, 4.1 points better on offense and 6.7 points better on defense. The collapse of the Raptors (8 points worse than average) has bee n surprising. After their hot streak, the Mavs have fallen back in the pack. In early April I will post a review of the NBA for March.

What a first round! Most brackets are not worth the paper they are printed on (though our son is in 98.5% ile). Here are updated winning chances based on simulation with Sagarin point ratings from USA Today. For example, Kentucky has a 17.4% chance to go all the way. It looks like a 3 or lower seed has a 27% chance to win, and my best guess is 2 teams that are 3 seeds or below will make it to Indianapolis.

The following table gives the chance each team will make it to a given round. For example, Kentucky has a 48% chance of winning at least 4 games (making Final 4). Thus no team has more than a 50% chance of making the final 4. Next week should be amazing

David Berri and Martin Schmidt of  Wages of  Wins fame have just published their new book Stumbling on Wins. The authors do a great job of showing how math can help teams make better player personnel decisions and better in game decisions.  I hope you will pick up a copy.

    My favorite  chapter of Stumbling on Wins discusses the merits of various NBA coaches, They conclude that among the studied coaches,Phil Jackson is the best coach.Their methodology is to look at at every player who was traded to a coaches’ (say Phil Jackson) team and look at how the player’s productivity (as measured by Wins Produced or Win Score) changed. The coach with the highest (standardized) increase in player performance is deemed the best coach.

    We did a similar study in which we used a player’s  Adjusted +/- rating as the measure of player performance. We found Rick Carlisle to be the best coach. Mark Cuban stated that this analysis helped convince him to hire Rick Carlisle. I would love to see a similar study involving OPS, DIPS or win based baseball statistics that would analyze the merits of baseball managers. This might help use decide if Cub fans are right to blame the recent disapointing seasons on Lou Pinella.

Using the well-known and highly respected  Sagarin Ratings (found at http://www.usatoday.com/sports/sagarin/bkt0910.htm)

I have “simulated” the NCAA Men’s tourney 5000 times. For each team, the table below gives the chance of the team winning 0, 1, 2, 3, 4, 5, or 6 games.

For example, we see Kansas has a 31.9% chance of winning the tournment (winning 6 games ), a 44.6% chance of making the final game (winning 5 or 6 games) and a 60% Chance (winning 4, 5, or 6 games) of making the final 4. See below the table (or Chapter 43 of my book Mathletics) for how I ran the simulation. The table makes it clear that Kansas has by far the best chance of winning the tourney. There is around a 38% chance that a non 1 seed wins the tourney.

We assumed that the outcome of each game follows a normal random variable with mean margin = Sagarin rating of higher rated team- Sagarin rating of lower rated team and standard deviation 10 points. Then we used the simulation add-in @RISK to play out the tournament 5000 times.

If you want to see the chance a team wins at least a certain number of games look below. So 6 column is chance team wins tourney, 5 column is chance team makes it to final game, 4 column is chance team makes it to Final4, 3 Column is chance team makes it to Regional Final or beyond, 2 Column is chance team makes it to Sweet Sixteen or beyond, and 1 column is chance team wins their opening game.

The Toronto Raptors have gone 1-8 in their last 9 games and have lost 4 in a row. If the Bulls start winning, the Raptors may be out of the playoffs.  As we will see, the Raptors could be so much better!

    For the season the Raptors have played 2 points worse than average. The players who have hurt the Raptors are Nesterovich (-10 Adjusted +/-), De Rozan (-7 Adjusted +/-), Banks (-9) and Weems (-3). DeRozan’s -7Adjusted +/- means, for example, that if DeRozan played a whole game instead of an average NBA player, we estimate the Raptors would play 7 points worse. Also DeRozan (-26 points 4th quarter Adjusted +/-) and Weems (-18 points 4th quarter Adjusted +/-) have killed the Raptors in the 4th quarter.

In the 940 minutes when DeRozan, Weems, Banks, and Rasho are out the Raptors have been excellent: 5 points better than average. So reducing the minutes for the aforementioned players should help the team.  There are many other ways, however to improve the Raptors choices of lineups. All numbers below are per 48 minutes and adjusted for strength of opponent’s players on the court:

• When the core (Bargnani, Bosh and Hedo) is in, the Raptors play much better with Calderon at the point (9 points better than average) than with Jack (4 points worse than average).
• When Chris Bosh is out and  Amir Johnson is out the Raptors get killed (16 points worse than average). But when Amir replaces Bosh the Raptors are only 1  point worse than average. Breaking it down further we find that with Johnson, Bargnani and Jack in and the other two players chosen from Wright, DeRozan, Calderon , Bellinelli and Weems the Raptors are 19 points better than average in 143 minutes!
• Bargnani, Bosh and Belinelli in is great (218 minutes, Raptors play 15 points better than average). With Wright also in the Raptors are awesome (60 min, 33 points better than average per 48 minutes!).

Here is a summary of how well the most used lineups have performed for the Raptors. The key numbers for each lineup are the first number and minutes played. For example, lineup 1A has played 354 minutes and played 11 points worse than average per 48 minutes. Note 2A simply replaces Jack by Calderon and plays 15 points better than 1A. So why does lineup 1A play more often? Below we have boldfaced many of the Raptors excellent lineups that have been underutilized. For example, 8C has played 50 points better than average.       

TOR     -10.80 (   -3.33    2.09    5.42    0.44   -0.32    4.09)  354.39 minutes   99 appearances     1 A    -12.60      -93 $
Bargnani      Bosh          DeRozan       Jack          Turkoglu      25.46 years       4394_TOR_2010

TOR       5.48 (    0.37    5.16    4.79   14.05    0.25    4.28)  264.22 minutes   75 appearances     2 A      0.91        5 $
Bargnani      Bosh          Calderon      DeRozan       Turkoglu      25.88 years       4154_TOR_2010

TOR      -0.57 (    5.83   11.10    5.26   39.50    1.24    2.37)  120.57 minutes   71 appearances     3 A     -2.79       -7 $
Bargnani      Bosh          Calderon      Jack          Turkoglu      27.03 years       4378_TOR_2010

TOR       4.77 (    0.40    9.15    8.75   -3.63   -0.16    2.86)   85.13 minutes   37 appearances     4 A      2.82        5 $
Bargnani      Bosh          Jack          Turkoglu      Weems         26.08 years      12554_TOR_2010

TOR      -5.59 (  -16.76    3.47   20.23  -37.78   -2.45    4.72)   72.80 minutes   18 appearances     5 A    -12.53      -19 $
Bargnani      DeRozan       Jack          Nesterovic    Turkoglu      27.03 years       5410_TOR_2010

TOR       2.95 (   -5.00    5.41   10.41   -4.80   -0.61    4.23)   70.70 minutes   31 appearances     6 A      5.43        8 $
Bargnani      Bosh          DeRozan       Jack          Weems         24.00 years       8490_TOR_2010

 TOR      15.31 (    5.36    7.85    2.49   -1.03    0.23    2.50)   54.60 minutes   36 appearances     1 B     12.31       14 $
Bargnani      Bosh          Calderon      Turkoglu      Wright        26.98 years      20506_TOR_2010TOR      -4.99 (   -3.75    1.03    4.78  -15.82   -0.79    4.11)   54.50 minutes   25 appearances     2 B     -4.40       -5 $
Bargnani      Bosh          DeRozan       Jack          Wright        24.49 years      16682_TOR_2010

TOR      15.94 (   -0.01    8.10    8.11  -19.88   -0.63    2.91)   54.06 minutes   23 appearances     3 B     22.20       25 $
Bargnani      Bosh          Jack          Weems         Wright        25.10 years      24842_TOR_2010

TOR      23.37 (    6.37   15.36    8.99   33.20    1.19    2.24)   53.77 minutes   34 appearances     4 B     18.75       21 $
Bargnani      Belinelli     Bosh          Calderon      Turkoglu      26.55 years       4126_TOR_2010

TOR      10.90 (    3.08    5.25    2.16   10.56    0.47    2.53)   46.77 minutes   35 appearances     5 B     12.31       12 $
Bargnani      Belinelli     Jack          Johnson       Turkoglu      25.52 years       4870_TOR_2010

TOR       7.81 (    4.74    4.20   -0.53   14.84    0.70    2.87)   43.56 minutes   35 appearances     6 B     13.22       12 $
Belinelli     Bosh          Jack          Johnson       Turkoglu      25.83 years       4876_TOR_2010

TOR      24.45 (    2.67   12.28    9.61   19.58    0.62    2.38)   41.89 minutes   31 appearances     7 B     25.21       22 $
Bargnani      Belinelli     Bosh          Jack          Turkoglu      26.14 years       4366_TOR_2010

TOR       1.53 (    2.67    4.19    1.53   -5.70    0.00    2.61)   40.49 minutes   31 appearances     8 B      8.30        7 $
Bargnani      Belinelli     Jack          Johnson       Wright        24.54 years      17158_TOR_2010

TOR     -10.83 (   -2.92   -4.95   -2.03   -8.59   -0.48    4.21)   40.12 minutes   25 appearances     9 B    -16.75      -14 $
Bargnani      DeRozan       Jack          Johnson       Turkoglu      24.84 years       4898_TOR_2010

        TOR       8.38 (    8.03    6.23   -1.80   12.21    0.80    2.74)   37.95 minutes   29 appearances     1 C      8.85        7 $
Belinelli     Bosh          Calderon      Johnson       Wright        25.27 years      16924_TOR_2010

TOR       5.14 (    8.44    7.28   -1.16   28.46    1.27    2.62)   37.46 minutes   27 appearances     2 C      3.84        3 $
Belinelli     Bosh          Calderon      Johnson       Turkoglu      26.25 years       4636_TOR_2010

TOR      22.23 (    5.76    3.10   -2.67  -11.00    0.01    3.35)   36.73 minutes   26 appearances     3 C     31.36       24 $
Bosh          Calderon      Johnson       Weems         Wright        25.22 years      25112_TOR_2010

TOR       4.22 (    1.66    4.77    3.12  -14.65   -0.34    2.55)   35.55 minutes   33 appearances     4 C      5.40        4 $
Bargnani      Bosh          Jack          Turkoglu      Wright        26.56 years      20746_TOR_2010

TOR      24.35 (    2.25   11.23    8.98    3.32    0.15    2.47)   29.58 minutes   29 appearances     5 C     19.47       12 $
Bargnani      Belinelli     Bosh          Jack          Wright        25.16 years      16654_TOR_2010

TOR     -53.21 (    6.37    7.27    0.90    7.92    0.56    2.49)   29.55 minutes   24 appearances     6 C    -53.61      -33 $
Bargnani      Belinelli     Calderon      Johnson       Wright        24.96 years      16918_TOR_2010

TOR      -8.67 (    1.00   15.61   14.61   14.34    0.33    2.79)   29.02 minutes   14 appearances     7 C     -9.92       -6 $
Bargnani      Belinelli     Bosh          Jack          Weems         24.68 years       8462_TOR_2010

TOR      49.87 (    5.96   14.31    8.35   16.94    0.72    2.36)   25.09 minutes   16 appearances     8 C     47.82       25 $
Bargnani      Belinelli     Bosh          Calderon      Wright        25.58 years      16414_

Based on the ratings we posted earlier today here are projected final NBA standings.

Note the torrid race in the West for spots 2-4.

In the West it looks like there is only a 9% chance that one of Houston, New Orleans or Memphis sneaks in the playoffs.

In the East here are the playoff chances for the 5 teams fighting for spots 5-9:

• Bucks 98%
• Heat 94%
• Bobcats 91%
• Raptors 80%
• Bulls 37%.

In the three weeks since the all star break here is a summary of how well each NBA team has played.  For example, the Magic have played 10.65 points better than average. The Magic have played 2.38 points better than average on offense and 8.26 points better than average on defense. Note the Nets have really improved and the Knicks are now the league’s worst team. Kudos to the unsung Bucks, who have played great. These numbers are adjusted for strength of schedule.  Makes you think that  a Lakers-Cavs final series is not inevitable!

By the way here are the ratings based on the entire season.

The Lakers have clearly struggled on their recent 0-3 road trip. What are the problems and how can they be solved? Of course, Kobe is below par due to several injuries. Rest would probably help here. But there are other more pressing problems. 

Looking at the last two weeks our Adjusted +/- data reveals the following:

• Artest and Bynum have been playing much worse on offense.
• Brown, Farmar, and Gasol have been playing much worse on defense.

Like most teams, the Lakers often play suboptimal lineups. Here are the Lakers best lineups.

• Note that 6A and 9A rest Kobe well. For example, 6A with Brown and Odom replacing Bynum and Bryant has played an amazing 33 points per game better than average (we do adjust for strength of opponents).
•     1C , 3C and 8C do a great job of resting  Artest.
• 2B and 3C, 8C and 9C  do a great job of resting Gasol

     LAL      11.06 (    8.31    4.20   -4.11   22.78    1.42    3.55)  584.36 minutes  165 appearances     1 A      9.28      113 $
Artest        Bryant        Bynum         Fisher        Gasol         29.71 years        109_LAL_2010

LAL       8.91 (   12.79    3.78   -9.01   31.92    2.02    4.31)  380.36 minutes  144 appearances     2 A      5.17       41 $
Artest        Bryant        Bynum         Fisher        Odom          29.84 years        557_LAL_2010

LAL      11.32 (   18.44    9.37   -9.07   56.24    3.12    3.00)  233.64 minutes  146 appearances     3 A      6.78       33 $
Artest        Bryant        Fisher        Gasol         Odom          31.30 years        613_LAL_2010

LAL       9.24 (   12.13    4.08   -8.06   27.04    1.77    4.38)  138.07 minutes   85 appearances     4 A     11.47       33 $
Brown         Bryant        Farmar        Gasol         Odom          27.63 years        598_LAL_2010

LAL      32.56 (    9.20   -0.35   -9.55   27.69    1.51    3.68)   85.04 minutes   38 appearances     6 A     25.97       46 $
Artest        Brown         Fisher        Gasol         Odom          29.85 years        611_LAL_2010

LAL       8.85 (   -0.11   -9.76   -9.64  -18.67   -0.51    4.13)   74.14 minutes   35 appearances     9 A     11.65       18 $
Artest        Brown         Bynum         Farmar        Odom          25.93 years        539_LAL_2010

       LAL      19.55 (   14.77    5.55   -9.22   34.20    2.20    3.69)   59.13 minutes   56 appearances     1 B     19.48       24 $
Artest        Bryant        Farmar        Gasol         Odom          28.84 years        597_LAL_2010

LAL      23.12 (    9.12   -0.04   -9.16    9.89    1.11    4.60)   55.56 minutes   39 appearances     2 B     24.19       28 $
Artest        Bryant        Bynum         Farmar        Odom          27.38 years        541_LAL_2010

   LAL      36.14 (   15.80    7.90   -7.91   49.08    2.69    3.94)   36.05 minutes   22 appearances     1 C     30.63       23 $
Brown         Bryant        Fisher        Gasol         Odom          30.10 years        614_LAL_2010

LAL      37.71 (   10.16    2.31   -7.85   24.76    1.59    4.86)   34.84 minutes   18 appearances     3 C     37.20       27 $
Brown         Bryant        Bynum         Fisher        Odom          28.63 years        558_LAL_2010

LAL      12.31 (    5.53   -5.27  -10.80   32.25    1.30    7.05)   30.45 minutes   15 appearances     4 C     14.19        9 $
Artest        Bryant        Fisher        Mbenga        Odom          31.21 years        677_LAL_2010

LAL      12.53 (   -6.97   -7.23   -0.26  -33.42   -1.46    4.77)   29.87 minutes   16 appearances     5 C     24.11       15 $
Brown         Bryant        Bynum         Farmar        Powell        25.53 years       1054_LAL_2010

LAL      17.74 (   12.95    1.06  -11.89   36.01    2.09    4.23)   24.64 minutes   15 appearances     7 C     15.59        8 $
Artest        Brown         Bryant        Gasol         Odom          29.04 years        583_LAL_2010

LAL      34.75 (  -10.31  -11.96   -1.64  -55.64   -2.44    6.23)   23.97 minutes   12 appearances     8 C     34.05       17 $
Brown         Bynum         Farmar        Odom          Walton        25.85 years       4634_LAL_2010

LAL      19.69 (    7.31   -4.53  -11.83   11.69    0.99    4.94)   23.59 minutes   15 appearances     9 C     16.28        8 $
Artest        Brown         Bryant        Bynum         Odom          27.58 years        527_LAL_2010

Note that the lineups shown below play fairly often and have not done well.  For example, there is a 95% chance that 5A ‘s true ability level is 5 points better than average or worse. Why keep using it when there are better alternatives? For example. 3C with Fisher for Farmar (and other 4 guys same as 5A) has played an amazing 38 points better than average and is used less often than 5A. This certainly does not help the Lakers.

LAL      -9.29 (    6.49   -1.51   -8.00    2.72    0.67    5.02)  126.78 minutes   72 appearances     5 A     -9.46      -25 $
Brown         Bryant        Bynum         Farmar        Odom          26.17 years        542_LAL_2010

LAL       2.57 (   15.55   11.90   -3.65   21.29    1.98    4.04)   75.86 minutes   25 appearances     7 A      6.33       10 $
Bryant        Bynum         Fisher        Gasol         Odom          29.71 years        620_LAL_2010

LAL     -16.49 (   -0.93   -5.52   -4.59   -5.77   -0.19    2.78)   35.52 minutes   12 appearances     2 C    -17.57      -13 $
Artest        Brown         Bynum         Fisher        Gasol         28.26 years        107_LAL_2010

LAL     -30.21 (  -32.60  -25.76    6.84  -69.30   -4.55    4.69)   26.00 minutes   13 appearances     6 C    -12.92       -7 $
Brown         Farmar        Mbenga        Morrison      Powell        25.71 years       1426_LAL_2010