NBA Analysis Volume One: Possessions Per Game Vs. Wins

We hear it all the time when it comes to the NBA: Champions play a half-court game. Thanks to the recent success of teams like the Spurs, and the Celtics' six game victory over the much quicker Lakers in the 2008 NBA Finals, the results show that teams that play slow, win.

Or do they?

That was the question that I asked myself when looking over statistics from the 2007-2008 NBA season. Because of this, I bring you the first edition of my NBA Statistical research: Do possessions per game have an effect on a team's performance?

I came into this study with the hypothesis that slower paced teams did attain more success in terms of wins than faster paced teams. Originally, the data seemed to support this finding.

Team	Wins	Pace
DEN	50	99.7
GSW	48	98.8
IND	36	97.7
PHO	55	96.7
SEA	20	96.3
LAL	57	95.6
MEM	22	95.3
SAC	38	94.7
ORL	52	93.4
UTA	54	93.2
CHI	33	93.0
LAC	23	92.1
MIN	22	91.9
CHA	32	91.8
NYK	23	91.6
NJN	34	91.5
MIL	26	91.3
ATL	37	91.1
BOS	66	90.9
HOU	55	90.4
PHI	40	90.4
DAL	51	90.2
CLE	45	90.2
TOR	41	90.2
MIA	15	90.2
NOH	56	89.9
WAS	43	89.5
SAS	56	88.8
POR	41	87.9
DET	59	87.3

Eleven of the bottom 13 teams on this chart made the playoffs in 2007-08, and three of the four conference finalists (Boston, Detroit, San Antonio) were in the bottom 12 of the league in pace. Out of those bottom 13, only Miami had a losing record. In turn, four of the top 10 in pace had sub .500 records.

So my original hypothesis is correct? Not so fast.

Finding the means of both the wins column (41) and the pace column (92.3866...), I used this information to help me find the covariance. In the next table, x is Wins - Mean Wins, y is Pace - Mean Pace, and xy is the product of the two columns.

Team	x	y	xy
DEN	9	7.313	65.820
GSW	7	6.413	44.893
IND	-5	5.313	-26.567
PHO	14	4.313	60.387
SEA	-21	3.913	-82.180
LAL	16	3.213	51.413
MEM	-19	2.913	-55.353
SAC	-3	2.313	-6.940
ORL	11	1.013	11.147
UTA	13	0.813	10.573
CHI	-8	0.613	-4.907
LAC	-18	-0.287	5.160
MIN	-19	-0.487	9.247
CHA	-9	-0.587	5.280
NYK	-18	-0.787	14.160
NJN	-7	-0.887	6.207
MIL	-15	-1.087	16.300
ATL	-4	-1.287	5.147
BOS	25	-1.487	-37.167
HOU	14	-1.987	-27.813
PHI	-1	-1.987	1.987
DAL	10	-2.187	-21.867
CLE	4	-2.187	-8.747
TOR	0	-2.187	0.000
MIA	-26	-2.187	56.853
NOH	15	-2.487	-37.300
WAS	2	-2.887	-5.773
SAS	15	-3.587	-53.800
POR	0	-4.487	0.000
DET	18	-5.087	-91.560

The sum of the xy column divided by 30 gives us the covariance of the sample, which is -3.18. This number by itself does not tell us much about the sample, however, by finding the variance of the x and y column, we can find the coefficient of correlation between the data.

The variance of wins can be found by finding the sum of squares in the x column and dividing by 30; the same can be found in the pace column. The variance of wins is 184.8, and the variance for pace is 9.684.

The coefficient of correlation is a number between 0 and 1, where 0 shows no relation between the data and 1 being perfect (i.e. a straight line). To find this number, take the square of the covariance and divide it by the product of the two variances. Doing the math (-3.18)(-3.18)/[(184.8)(9.684)] gives us a coefficient of correlation of 0.00565.

This is surprising, as the low number indicates very little, if any, correlation between the data. This is supported after an inspection of the data in graphical format.

The previously mentioned coefficient of correlation can be found in the equation on the top left hand corner.

This research was very surprising for me, and brought me to a new conclusion in basketball: style of play is irrelevant as long as it is the style your team is most adept to using.

As this is the first of many articles I will write on this series of basketball statistics, I welcome any suggestions for further research, especially weighed against the only real statistic that matters in the NBA; wins and losses.

Next Analysis: Offense vs. Defense.