May 19 2009

# The Distribution of Play Ending Events in the NBA

I have come to the realization that I really don’t understand the NBA game all that well.

Sure I have a general knowledge of basketball, but as I work toward building a realistic simulation of the NBA, I realize that I don’t understand the dynamics of the game that impact a team’s chances of scoring points.

By quantifying the distribution of play ending events, I will be taking the first step in the direction of understanding the dynamics of the game.

What is a play?

The terms possession and play get thrown around a lot, so I want to be clear on the definition of a play that I am using here:

• play – period of play before a play ending event

Ok so that really doesn’t help. The real understanding comes in the definition of a play ending event:

• play ending event – all shot events, any event that stops play or gives the opponent the ball, and any event that creates a free throw opportunity

In general, play ending events can be broken down into four basic categories: fouls, shots, timeouts, and turnovers.

The General Distribution of Play Ending Events

The general distribution of these four basic categories is as follows:

 Season Location Foul% Shot% Timeout% Turnover% 08-09 Away 8.5% 75.4% 5.5% 10.5% 08-09 Home 8.7% 75.5% 5.5% 10.3% 07-08 Away 8.3% 75.6% 5.4% 10.6% 07-08 Home 8.3% 76.0% 5.4% 10.2% 06-07 Away 9.2% 74.2% 5.6% 11.0% 06-07 Home 9.2% 74.1% 5.8% 10.9%

This data was compiled from 137,706, 140,343, and 136,108 away play ending events, and from 136,971, 139,543, and 135,805 home play ending events from the 08-09, 07-08, and 06-07 seasons, respectively.

I believe I need to make it clear that I consider shooting fouls a component of shots, and thus I have grouped them with Shot% and not Foul%. Also, I group offensive foul turnovers with Foul% instead of Turnover%. These distinctions will be made clear below.

One result from this table that interests me is the difference between Foul% and Shot% when comparing the 06-07 season to the other two seasons.

There are enough events to say these are statistically significant from each other, so I’m interested to know if 1) some rule change caused this, 2) some other explanatory reason made this happen that I’m missing (such as the distribution of play starting events, which I will cover in the future), 3) this really was just by chance, or 4) I have some perl code not working as desired.

That said, these general categories give us an idea how plays end, but they don’t really tell us how play ending events for home versus away teams differ. Digging into more detail will shed some light onto this.

Distribution of Fouls

The percentages below are on a per play basis. So this means they are not conditional on knowing there was a foul, which is why they do not sum to 1.

 SEA LOC CP D3S DP DT FT1 FT2 OFF PF TECH MISC 08-09 A 0.02% 0.30% 0.013% 0.027% 0.025% 0.003% 1.54% 6.22% 0.28% 0.04% 08-09 H 0.03% 0.31% 0.010% 0.029% 0.030% 0.005% 1.49% 6.47% 0.30% 0.03% 07-08 A 0.02% 0.32% 0.011% 0.026% 0.027% 0.001% 1.55% 6.09% 0.25% 0.02% 07-08 H 0.03% 0.30% 0.014% 0.020% 0.033% 0.001% 1.48% 6.17% 0.27% 0.02% 06-07 A 0.03% 0.40% 0.007% 0.028% 0.032% 0.004% 1.91% 6.45% 0.33% 0.02% 06-07 H 0.03% 0.39% 0.005% 0.020% 0.035% 0.003% 1.77% 6.65% 0.31% 0.03%

Abbreviations: SEA: Season; LOC: Team Location, A=Away and H=Home; CP: clear path; D3S: defensive 3 seconds (includes all “illegal defense” events for the 06-07 play-by-play); DP: double personal; DT: double technical; FT1: flagrant type 1; FT2: flagrant type 2; OFF: offensive foul; PF: personal fouls; TECH: technicals; MISC: all other fouls.

Distribution of Shots

The percentages below are also on a per play basis.

2 point shots:

 Season Location Make% Miss% Make+SF% Miss+SF% Blocked% 08-09 Away 23.4% 23.3% 1.93% 6.96% 4.26% 08-09 Home 24.4% 23.5% 1.88% 6.65% 3.69% 07-08 Away 23.5% 23.6% 1.96% 7.08% 4.20% 07-08 Home 24.7% 23.7% 1.81% 6.83% 3.58% 06-07 Away 25.3% 28.0% 2.10% 7.10% 4.10% 06-07 Home 26.2% 28.0% 2.03% 6.76% 3.57%

3 point shots:

 Season Location Make% Miss% Make+SF% Miss+SF% Blocked% 08-09 Away 5.60% 9.73% 0.025% 0.113% 0.109% 08-09 Home 5.65% 9.56% 0.023% 0.101% 0.092% 07-08 Away 5.46% 9.68% 0.022% 0.101% 0.094% 07-08 Home 5.55% 9.65% 0.029% 0.105% 0.087% 06-07 Away 2.93% 4.57% 0.021% 0.096% 0.051% 06-07 Home 3.02% 4.48% 0.013% 0.099% 0.030%

Distribution of Turnovers

Like the other distributions above, the percentages below are also on a per play basis.

 Season Location Steal% Dead Ball% 08-09 Away 6.2% 4.3% 08-09 Home 6.1% 4.1% 07-08 Away 6.2% 4.4% 07-08 Home 6.1% 4.1% 06-07 Away 6.1% 4.8% 06-07 Home 6.1% 4.7%

Summary

The distributions presented above are simply one component of plays in the NBA. The next step is to examine how plays start, as this has a role in how a given play ends.

From there, the ultimate goal is to then quantify the distribution of how plays end based on how they started. This will help answer questions like, “What proportion of plays end with a 2pt FG make + shooting foul when the play starts on a steal?” or “Does the data provide evidence that there is a positive or negative relationship with this proportion and playing at home?”

These are simply a couple of examples of the many questions that I want to be able to answer to help better understand how the game works.

### 4 Comments on this post

1. Conditioning the Distribution of Play Ending Events Given How the Play Starts wrote:

[…] last post took a very general look at how plays end in the NBA. To better understand how the game works, […]

May 31st, 2009 at 12:22 pm
2. The Time Distribution of Events in the NBA wrote:

[…] data is represented as the number of seconds elapsed from the start of the play to the time of the play ending event, all conditional on how the play […]

June 28th, 2009 at 8:57 pm

1. Gabe said:

“One result from this table that interests me is the difference between Foul% and Shot% when comparing the 06-07 season to the other two seasons.”

Wasn’t 06-07 when they tried that new synthetic ball for half the season? That might have had something to do with it.

May 22nd, 2009 at 8:59 am
2. Ryan said:

That’s a good point Gabe. The underlying shot% differs for the 06-07 season a good bit.

I’m going to look at the conditional distributions based on how the play started, so maybe that will give a better indication of maybe poor shooting.

May 22nd, 2009 at 10:29 am