APBRmetrics

[gravityandlevity]

I have a painfully naive question, so please forgive my ignorance. But I don't understand what it means to "simulate" a basketball game. If this question has already been covered somewhere else on this forum, feel free to just send me a link and ignore everything below.

It's actually probably more correct to say that I don't understand why one needs to simulate a basketball game. In my mind, "simulating" means "repeatedly drawing random numbers from a given probability density function" (PDF). But, as far as I can tell, the PDF must be part of the input to the simulation (you, the programmer, must tell the computer how likely different things are). So why not just work analytically with the PDF's? What does the simulation tell you that you didn't know at the time of writing it?

To be concrete, I can imagine a simple "simulation" of a game between the Timberwolves and the Lakers. I might know (or hypothesize) that the Timberwolves' scoring is a Gaussian distribution with mean 90 and standard deviation 5, and that the Lakers scoring is also Gaussian with mean 100 and standard deviation 7. I could then "simulate" the game by randomly drawing from both distributions and seeing how many times the Timberwolves had the larger score. But this doesn't tell me anything I didn't know already: I could have just calculated the probability of the T-Wolves winning from what I assumed about the PDFs at the beginning. (In this simple example, it's just over 12%).

Am I misunderstanding something?

Or is it just a matter of terrible analytical complexity when you have a very detailed description of what's relevant in a basketball game? I can imagine that if you're trying to describe the net outcome of 100 individual possessions, then analytically you would have to chain together 100 conditional PDFs. So maybe that's too unwieldy to work with, as opposed to just drawing lots of random numbers in succession. Is that the basic idea?

Thanks for your help.

[Ryan J. Parker]

[gravityandlevity]

Thanks Ryan.

I'm actually pretty familiar with Monte Carlo methods. Usually, Monte Carlo calculations are used when the "set of all possible outcomes" is so enormously large that you have no hope of evaluating them all analytically. Is that the motivation for using them in basketball? (Naively, it would seem to me that a basketball game is much more limited in its possibilities than, say, the configuration of a large galaxy).

Successful Monte Carlo calculations also usually have some strong heuristic built into them (in my experience). For example, there might be a rule to preferentially explore configurations with lower energy (like the Metropolis algorithm ). Otherwise, exploring the set of all possibilities can be unwieldy even as a process of pulling random numbers.
Is there some equivalent "rule of thumb" for simulations of basketball games?

[Ryan J. Parker]

I thought you might be.

So basically I view the game as probably most of the members of this forum do: complex enough to be unwieldly for an analytical solution.

But if you come up with something better, do let me know.
_________________
I am a basketball geek.

[bchaikin]

I don't understand why one needs to simulate a basketball game...

for the purpose of performing what-if scenarios...

What does the simulation tell you that you didn't know...?

the outcome of a potential real-life scenario such you don't have to actually perform that real-life scenario...

To be concrete, I can imagine a simple "simulation" of a game between...

what if one of the team's star players, who had played in all their games up to the point of you running your sim, slips on a bar of soap and is out before that next game you are about to simulate?...

as opposed to just drawing lots of random numbers in succession...

random number generators work great...

it would seem to me that a basketball game is much more limited in its possibilities than, say, the configuration of a large galaxy...

correct - your typical large spiral galaxy has upwards of 100-500 billion stars if not more, with large elliptical galaxies even more. there are far fewer variables in nba hoops...

[Ed Küpfer]

[gravityandlevity]

Thanks everyone. I'm glad to know that I roughly understand the problem.

My curiosity turns now to what, exactly, gets simulated. Bob, I particularly appreciate you taking time to answer questions, since I understand you're a serious expert in the field.

I understand your point about the power of simulating "what if" scenarios, but one's ability to predict such scenarios depends on knowledge of various statistical distributions describing the player and the plays. Without giving away any trade secrets, can you give me a sense of what sort of assumptions (hopefully justified by data) have to go into "simulating a basketball game"?

When people say that they're "simulating a game", what do they generally mean? Are they simulating each individual possession? Are they simulating each individual shot, rebound, foul, etc?

[bchaikin]

can you give me a sense of what sort of assumptions (hopefully justified by data)...

hopefully...

When people say that they're "simulating a game", what do they generally mean? Are they simulating each individual possession? Are they simulating each individual shot, rebound, foul, etc?

i can't speak for people, but i simulate every shot, pass that has an opportunity to be an assist, FT, foul (both aosf and nsf), rebound, steal, turnover, blocked shot, etc based on player's real life abilities. basically every player touch other than passes that do not have an opportunity to be an assist (backcourt passes without any defense nearby, handoffs, basically any pass where had the player receiving the pass shot and scored an assist would not have been awarded)...

the sim does not (yet) account for technicals, double fouls, things that occur only rarely (but does account for team turnovers)...

there's an old thread here entitled "shouldn't possession usage count all potential assists" that goes into some of the thinking behind the sim...

[acollard]

Speaking of simulating a basketball game, occasionally when I am reading an old APBR site or article, I see a reference to a free download of the B-BALL simulation software. However, I notice that it is no longer available from bballsports.com. Is it still available anywhere on the internet, for free or otherwise? I think it would be exceedingly fun to play around with.

[bchaikin]

However, I notice that it is no longer available from bballsports.com...

correct...

Is it still available anywhere on the internet, for free or otherwise?

there was an old DOS version available at the old yahoo APBR or APBR analysis site in the files section, but i don't know if that is still there...

[haralabob]

[mtamada]

[Kevin Pelton]

[bchaikin]

...those same obstacles and unknowns hinder all of our attempts to model basketball...

not quite all....