May 11, 2010

To Foul or Not to Foul?

Filed under: Uncategorized — wwinston @ 8:37 am

Suppose your team is up by three points. The other team has the ball and there are ten seconds left in the game. Should you foul or not? The April 23 New York Times (see http://www.nytimes.com/2010/04/22/sports/basketball/22fouls.html)

had a great analysis of this decision.

One of our top MBA”s, Sean Vinsel has done a great piece of research on this subject. Here is a summary of his results. The key insight is that the benefit of fouling depends on how good the other team is at shooting 3′s. Also it is important to note that  even with little time left in an NBA game several possessions can follow an intentional foul. We saw this on Saturday when the Lakers intentionally fouled the Jazz and the Jazz got the ball back with a chance to win the game.

Sean Vinsel’s Analysis of Fouling with a 3 Point Lead

In the Friday, April 23rd issue of The New York Times, Jonathan Abrams and Howard Beck wrote an article concerning teams up 3 points at the end of NBA games committing fouls to send the losing team to the free throw line instead of being able to attempt a game winning 3 pointer. In this article they included quotes from several coaches, most of whom oppose the idea, and statistics from Synergy Sports Technology tracking these situations over the past 2 years. According to their data, It came up 165 times. 19 times the leading team fouled, and 146 they didn’t. 18 of the 19 fouling teams won (94.7%, regulation and OT wins) and 135 of the 146 teams won after not fouling (92.5%). These samples are so small, however, that it is unclear which strategy is best, and under what scenarios.

Traditional analysis has been to simply think through this problem, leading to analysis like the following quote from the Times article:

“On the surface, it seems like an easy choice. Long-distance shooting has improved and teams cannot tie the score if they are not given the chance. Intentional fouls remove the surest route to a tie: the 3-pointer.”

However, there are so many variables in this situation (3 point %, free throw % for both teams, time to commit fouls, time to get shots, rebounding) that simply looking at actual situations won’t give you a large enough sample. But what if you could simulate many different scenarios thousands of times? We have done just that, and the results show some interesting delineations in strategy.

 

                Uising Visual Basic for Excel, we have created a model that allows the user to simulate the last seconds of an NBA game up to 100,000 times, with various parameters. To create a model to simulate the end of an NBA game, some randomness has to be simulated. The key factors included the amount of time to foul intentionally, the amount of time for a team to take a last-second shot, and the amount of time to get a rebound off of a free throw, 2 pointer, or 3 pointer. We collected data from the 2009-10 season from situations where a team was trailing by 0, 1, 2, or 3 points and fouled, or took a shot, in the last 15 seconds. Data was also collected on rebounds and the time it took to collect them. Because of precision was required to tenths of seconds, NBA.com’s game logs were used. In addition, the user was allowed to specify shooting percentages for the leading or trailing teams on free throws, 2 pointers, and 3 pointers. Defensive rebounding percentages (76.7%) were gathered from the SacTown Royalty blog, and some small randomness was built in to account for situations where the leading team fouled during the act of a shot, including a made 3 pointer. Users can select whether to foul or not, and can specify a time at which they will stop fouling. To simulate the data used by Abrams and Beck, start times were randomized between 3 and 10 seconds. The user can also exercise an option to start at the same time for every simulation.

 

During the 2009-10 NBA season, through January 9, teams were hitting 36.7% on 2 pointers and 16.7% on 3 pointers in the last 10 seconds of games where they trailed or were tied. Notice, this includes multiple shots on one possession, and games where teams were down by less than 3 or tied, so it is a slightly different data set than Abrams and Beck. When applying this season’s shooting percentages to our model, we get a winning percentage of 92.24% over 50,000 simulations when not fouling, compared to Abrams and Beck’s 92.5% (regulation and OT wins) and 93.75% over 50,000 simulations when fouling compared to their 94.7%. Although their sample sizes are smaller, the results Abrams and Beck quoted seem reasonable when we run historical data through our model. It seems like these percentages are very close to the true shooting percentages for NBA teams in the last 10 seconds when trailing or tied. The model then indicates that there is some advantage to be gained by fouling in these situations, even though the 3 point shooting percentage is so low!

This 16.7% estimate for 3 point shooting does include last second heaves at the end of games, however…perhaps we should look at higher-quality 3 point shots in the last 10 seconds. With the same set of data through January 9 as mentioned above, NBA teams shot 37 3 pointers after timeouts in the last 10 seconds, and hit 9 of them, for 24.3%. Let’s take a look at how the model performs at 20, 25, and 30 percent estimates for 3 point shooting, with 50000 simulations each:

At 20%:

Fouling: 44322 wins, 5262 overtimes, 416 losses – 93.91%

Not fouling: 41358 wins, 8642 overtimes – 91.36%

At 25%:

Fouling: 43576 wins, 6058 overtimes, 366 losses – 93.21%

Not fouling:  39275 wins, 10725 overtimes – 89.28%

At 30%:

Fouling: 44896 wins,  4878 overtimes, 226 losses – 94.67%

Not fouling: 37644 wins, 12356 overtimes – 87.64%

The winning percentages when fouling fluctuate a little more because the remaining possessions can vary wildly depending on who hits their free throws, while not fouling basically is limited to the opponent shooting a 3, then possibly a rebound and some foul shots. However, we can see that increasing the other team’s three point shooting affects our winning percentage when not fouling much more than when fouling, because their 3 point shot is going to always be taken with a chance to tie the game. When we foul, we’ll sometimes gain points, sometimes lose them, but fewer 3 pointers will be taken with a chance to tie in that case. If you think the other team is a good 3 point shooting team, that makes the case for fouling them even stronger. As Abrams and Beck suspected, there seems to be an advantage to be gained by intentionally fouling teams with a 3 point lead!

May 6, 2010

Suns Spurs Analysis thru 2

Filed under: Uncategorized — wwinston @ 7:35 pm

Still have 350 exams to grade, but here is the essence of Spurs Suns series so far. As we predicted, Dudley and Frye have been the keys.

  • With Nash in with Frye and or Dudley Suns are +32 points in 52 minutes, playing 32 points (after adjusting for opponent ability) better than average. In 37 of those minutes George Hill waso n court and Spurs were down 31 points.
  • Rest of  time Suns are -15 points playing 11 points worse than average.

For Spurs, George Hill has hurt them.

  • Hill in 64 minutes Spurs are -34 points, playing 15 points worse than average.
  • Hill out 32 minutes Spurs are +17 points playing 36 points better thn average.

So what to do? I have to grade some more, but either figure out what Hill is doing wrong, play him less or surely play him less when Dudleyand/or Frye are in hitting those 3′s!

May 4, 2010

Celtics Cavs Analysis

Filed under: Uncategorized — wwinston @ 9:14 am

As we predicted on Friday, this will be a tough series for  the Cavs. It actually looks now like the Celtics might be in the drivers seat. You don’t need numbers to tell you that Rondo has ben superb. With Rondo in the Celtics are +19 points in 87 minutes. With Rondo out they are -9 points in 9 minutes. Also the lineup of Rondo with 4 bench players (Sheed, Tony, Big Baby and Finley) was amazing +8 points in 6 minutes. When you can rest 4  starters and pick up points, you are doing something right!

  I see only one solution for the Cavs. Let’s see if they can figure out what they need  to do.

May 2, 2010

Spurs Suns Preview

Filed under: Uncategorized — wwinston @ 6:38 pm

I graded 500 spreadsheets since Thursday. I need a break so let’s look at the Suns Spurs series. This should be an exciting, long series. The Suns played better in the first round than any other team (15 points better than average) and the Spurs played 6 points better than average. All  numbers are per 48 minutes and adjusted for opponents strength.  Grant Hill got all the credit for the Suns because of his defense on Andre Miller, but the series key was that when Dudley  and Frye replaced Hill and Collins with Nash, Amare and JR the Suns were +35 points. The Spurs must be ready for this lineup.

  I believe a major reason the Spurs beat the Mavs was that Popovich stuck pretty closely to his better lineups, while Carlisle did not. Starting Dampier, Butler, Dirk, Kidd and Marion made no sense, because this lineup played poorly during the season and Butler plays poorly at the 2 guard (see our April 29th post).

   Here are the Spurs lineups that played the most (good ones boldfaced). 4A, for example, is +45 points in 95 minutes and has played 27 points better than average. 4A and 5A (Duncan, McDyess, Jefferson and Hill with Manu or Parker is the Spurs at their best.

In the Mavs series Jefferson, McDyess, Jefferson and two of Parker Manu and Hill played 17 points better than average. The rest of the time the Spurs played 2 points worse than average.

OFF     DEF  IMPACT  ZSCORE   SIGMA     PLAYING TIME                             SIMPLE      +/-
SAS      12.42 (   16.09    4.57  -11.52   38.38    2.72    4.48)  296.92 minutes  118 appearances     1 A      7.44       46 $
Duncan        Ginobili      Hill          Jefferson     McDyess       30.92 years       4904_SAS_2010
SAS       2.05 (    3.90   -4.12   -8.02   -2.66    0.28    6.08)  124.03 minutes   28 appearances     3 A      0.00        0 $
Blair         Bogans        Duncan        Jefferson     Parker        28.23 years       8715_SAS_2010

SAS      12.16 (    6.46   -3.29   -9.75   14.05    1.03    6.27)  191.20 minutes   60 appearances     2 A     11.30       45 $
Bogans        Duncan        Jefferson     McDyess       Parker        31.16 years      12810_SAS_2010

 

SAS      27.40 (   11.75   -1.65  -13.40   30.06    2.03    4.67)   94.68 minutes   39 appearances     4 A     22.81       45 $
Duncan        Hill          Jefferson     McDyess       Parker        29.96 years      13064_SAS_2010

SAS      30.61 (   18.02    9.86   -8.16   51.32    3.29    3.95)   91.27 minutes   61 appearances     5 A     25.24       48 $
Duncan        Ginobili      Jefferson     McDyess       Parker        31.72 years      12840_SAS_2010

        ACTUAL    THEORY     OFF     DEF  IMPACT  ZSCORE   SIGMA     PLAYING TIME                             SIMPLE      +/-
SAS      16.02 (   18.90    9.43   -9.46   36.13    2.90    4.78)   77.76 minutes   49 appearances     1 B     14.81       24 $
Bonner        Duncan        Ginobili      Hill          Jefferson     29.81 years        812_SAS_2010

SAS     -13.80 (    8.34    3.23   -5.11   18.27    1.34    6.58)   77.63 minutes   30 appearances     2 B    -12.99      -21 $
Bogans        Duncan        Ginobili      Hill          McDyess       30.94 years       4394_SAS_2010

SAS      10.30 (   20.82   14.72   -6.11   49.06    3.47    4.23)   58.98 minutes   47 appearances     3 B     10.58       13 $
Bonner        Duncan        Ginobili      Jefferson     Parker        30.60 years       8748_SAS_2010

SAS      -1.75 (   11.76   12.74    0.98   27.09    1.95    4.67)   57.86 minutes   38 appearances     4 B     -3.32       -4 $
Duncan        Ginobili      Hill          Jefferson     Parker        29.38 years       9000_SAS_2010

SAS     -18.38 (    4.53   -8.58  -13.11    1.11    0.46    6.44)   54.21 minutes   26 appearances     5 B    -16.82      -19 $
Bogans        Duncan        Hill          Jefferson     McDyess       30.36 years       4874_SAS_2010

        ACTUAL    THEORY     OFF     DEF  IMPACT  ZSCORE   SIGMA     PLAYING TIME                             SIMPLE      +/-
SAS      21.02 (   15.56   10.15   -5.41   47.21    2.92    4.57)   51.27 minutes   36 appearances     1 C     14.98       16 $
Duncan        Ginobili      Hill          McDyess       Parker        30.54 years      12584_SAS_2010

SAS      -2.32 (   10.34    8.02   -2.33   27.84    1.83    6.33)   50.11 minutes   18 appearances     2 C      0.00        0 $
Bonner        Duncan        Finley        Jefferson     Parker        31.48 years       8732_SAS_2010

SAS       3.43 (    0.12    4.84    4.72   -8.46   -0.22    3.10)   49.59 minutes   36 appearances     3 C      9.68       10 $
Blair         Ginobili      Hill          Jefferson     Mason         27.12 years       2849_SAS_2010

SAS      18.47 (   22.22    5.23  -16.99   62.20    4.04    3.34)   47.50 minutes   11 appearances     4 C     16.17       16 $
Duncan        Ginobili      Jefferson     McDyess       Temple        30.92 years      70184_SAS_2010

SAS       5.20 (    3.92    2.25   -1.67   11.67    0.75    3.61)   47.23 minutes   33 appearances     5 C     11.18       11 $
Blair         Ginobili      Hill          Mason         McDyess       28.28 years       6433_SAS_2010

SAS      19.61 (   12.01    2.07   -9.94   38.11    2.30    5.41)   46.86 minutes   38 appearances     6 C     16.39       16 $
Duncan        Ginobili      Hill          Mason         McDyess       30.88 years       6440_SAS_2010

SAS      21.04 (   13.94    7.36   -6.58   51.04    2.88    5.07)   45.39 minutes   28 appearances     7 C     17.98       17 $
Duncan        Ginobili      Mason         McDyess       Parker        31.67 years      14376_SAS_2010

SAS      -4.84 (    8.20   -9.73  -17.93   20.95    1.42    5.38)   44.80 minutes   19 appearances     8 C     -5.36       -5 $
Duncan        Hill          Jefferson     Mason         McDyess       30.30 years       6920_SAS_2010

SAS      24.56 (   10.27    8.51   -1.76   31.21    1.91    6.35)   41.70 minutes   24 appearances     9 C     23.02       20 $
Bogans        Duncan        Ginobili      McDyess       Parker        31.74 years      12330_SAS_2010

For the Suns, the key (besides Nash offense) is that none of the bench players hurt the team. In fact Frye and Dudley are real upgrades over Collins and Hill. Here is a summary of the Suns lineups that played the most minutes: 3A and 1B (both with Dudley) are great. Lopez is probably out so I pick the Spurs in 6, partially because Parker has dominated the Parker Nash matchup in past years.

       ACTUAL    THEORY     OFF     DEF  IMPACT  ZSCORE   SIGMA     PLAYING TIME                             SIMPLE      +/-
PHO      11.44 (   10.33   12.68    2.35   31.88    1.88    5.03)  884.62 minutes  348 appearances     1 A      8.30      153 $
Frye          Hill          Nash          Richardson    Stoudemire    31.17 years       7488_PHO_2010

PHO       4.54 (    7.04    9.89    2.85   16.36    1.11    4.77)  453.23 minutes  153 appearances     2 A      2.65       25 $
Hill          Lopez         Nash          Richardson    Stoudemire    30.19 years       7936_PHO_2010

PHO      22.20 (   17.85   18.51    0.66   33.33    2.62    2.78)  254.53 minutes  179 appearances     3 A     21.69      115 $
Dudley        Frye          Nash          Richardson    Stoudemire    28.61 years       7264_PHO_2010

PHO       6.34 (    2.92    0.19   -2.73   15.95    0.68    5.07)  202.24 minutes   61 appearances     4 A     -1.19       -5 $
Collins       Hill          Nash          Richardson    Stoudemire    32.06 years       7432_PHO_2010

PHO       3.25 (    3.64    3.16   -0.48    4.19    0.46    2.70)  166.98 minutes   95 appearances     5 A      8.91       31 $
Amundson      Barbosa       Dragic        Dudley        Frye          25.78 years        115_PHO_2010

PHO       7.92 (   -1.62   -5.38   -3.76  -12.44   -0.44    3.96)  131.12 minutes   78 appearances     6 A     11.71       32 $
Amundson      Dragic        Dudley        Frye          Hill          27.81 years        369_PHO_2010

PHO      -4.35 (    5.58    3.35   -2.22    3.49    0.66    2.65)   96.13 minutes   62 appearances     7 A     -5.99      -12 $
Amundson      Dragic        Dudley        Frye          Richardson    26.15 years       2161_PHO_2010

        ACTUAL    THEORY     OFF     DEF  IMPACT  ZSCORE   SIGMA     PLAYING TIME                             SIMPLE      +/-
PHO      22.92 (   14.56   15.71    1.15   17.81    1.85    2.77)   84.59 minutes   51 appearances     1 B     20.43       36 $
Dudley        Lopez         Nash          Richardson    Stoudemire    27.64 years       7712_PHO_2010

PHO      -0.79 (    0.33   -2.16   -2.48   -6.08   -0.16    1.61)   71.32 minutes   50 appearances     2 B      5.38        8 $
Amundson      Barbosa       Dragic        Dudley        Stoudemire    25.88 years       4147_PHO_2010

PHO      -5.94 (   10.66    9.78   -0.88   17.41    1.52    5.02)   69.25 minutes   50 appearances     3 B    -11.78      -17 $
Dudley        Frye          Hill          Nash          Stoudemire    30.27 years       5472_PHO_2010

PHO       1.74 (    8.45    3.93   -4.52   19.36    1.38    2.28)   67.32 minutes   59 appearances     4 B      2.14        3 $
Dragic        Dudley        Frye          Richardson    Stoudemire    26.17 years       6256_PHO_2010

PHO       2.21 (    4.14    6.79    2.65    5.74    0.54    4.91)   65.36 minutes   40 appearances     5 B     -3.67       -5 $
Amundson      Hill          Nash          Richardson    Stoudemire    31.25 years       7425_PHO_2010

PHO      -8.10 (    7.33    9.64    2.31   26.87    1.44    4.78)   58.80 minutes   42 appearances     6 B    -12.25      -15 $
Dudley        Hill          Nash          Richardson    Stoudemire    30.74 years       7456_PHO_2010

PHO       2.60 (    8.39   12.49    4.09   32.58    1.67    5.15)   57.62 minutes   32 appearances     7 B      2.50        3 $
Barbosa       Frye          Hill          Nash          Stoudemire    30.79 years       5442_PHO_2010

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