- --- In APBR_analysis@y..., "Michael K. Tamada" <tamada@o...> wrote:
> Mike G's critique I think makes a number of worthwhile points. One

of the

> most important ones is the linkage, or lack thereof, between and

This was my initial main point to him as well, and the one he seems

> individual player's performance and his team's performance.

>

to understand the least. I'll try to run the APBR_A words past him.

I was struggling to explain exactly why what he did was wrong. My

best explanation (I felt) was, while his team model is linear, some

of the parameters in that model aren't linear, especially PPS and

ASTO. The sum of PPS and Ast/TO over all players does not lead to

the team value. Assuming that the weights on team efficiency

parameters apply at an individual scale assumes linearity in the

parameters, not only in the model. (I think this is effectively what

MikeT says below.) Berri also mentioned to me that ASTO was not

necessary in his team regression (it did not explain any more

variation in team pts than without it), but he felt it should be in

there for the extrapolation to individuals; I think this also points

out the lack of connectedness between the team regression and the

individual value.

> But, as Mike G pointed out, it is almost surely a mistake to apply

these

> team weights to individual players. Points scored and PPS (or FG%)

being

> the prime example, one which several of us have mentioned before.

A 55%

> FG% player such as Bo Outlaw or the elderly Artis Gilmore may sound

great,

> but if they're only scoring 8 points a game, they aren't really

helping

> the offense very much. Conversely, an Alan Iverson can be helping

his

> team, even with his wretched 42% FG%. (Although he still did not

deserve

> that MVP award he won last year.)

This type of argument worked little with Berri..

>

lack of

>

> What is missing from Prof Berri's article is a true model of how

> individual players' contributions lead to overall team success (or

> success). This is IMO the Holy Grail of sports statistics

research, most

> especially basketball research. It is unfortunately exceedingly

are a

> difficult. Even without fancy statistics or models though, there

> couple of obvious features that such a model must have:

Let me interrupt and put in what I think the Holy Grail must be able

to do:

1. Honor conservation of possessions. A team and its opponent have

the same number of possessions in a game (+ or -2) - that's pretty

much a definition. If you're hypothetically putting 5 high scoring

guys together, your model better acknowledge that they aren't all

going to score so high. There just aren't enough possessions to go

around. Their opponents would have to also speed things up, but that

is unlikely to occur unless you have Paul Westhead as coach.

2. Honor conservation of wins. The sum of a team individual wins

and losses should be pretty close to the team total. If you are

putting together a team of 5 guys who each have individual win/loss

records of 19-1, you aren't going to end up with a team that is 95-

5. (I'm not even sure you end up with a team that wins 95% of its

games, but that is not a _rule_.)

3. Be context-sensitive. The (point or win) values of assists,

rebounds, and blocks should depend on what else is happening on the

team. Assists are most valuable on teams with many players who can

shoot. Teams can be successful without assists if only a few guys

shoot well, something you see at lower levels of basketball in

particular. The value of a defensive rebound also varies. If you're

forcing a ton of missed shots, but not getting defensive boards, the

boards you get are highly valuable. If you're not forcing any missed

shots, it is better to expend energy forcing misses. This gets at

why you can't have a team of 5 PGs or 5 PFs.

4. With "normal" substitution patterns, be close to additive. It

would be nice that this model, when used with normal substitution

patterns, be easy to use and not require a computer to calculate.

You have some statistic for individuals that you can add to say how

many net points you will be up on your opponent. (Net points are

what I'm personally going for because it is easily convertible into

wins/losses.)

5. Account for fatigue. We're not even trying on this one, I don't

think. We typically assume that player performance is independent of

how much time they spend on the court. If it truly were independent,

everyone's best players would play 48 minutes each.

> In its simplest form, if "Q" is the quantity of output produced in

a given

> period of time, "L" the amount of labor used, and "K" the amount of

so

> physical capital used, then the Cobb-Douglas form assumes that

>

> Q = b * L^a * K^(1-a)

>

> It's usually more convenient to take logarithms of these variables,

>

production

> ln(Q) = ln(b) + a*ln(L) + (1-a)*ln(K)

>

> which is a nice simple linear equation which has a number of nice

> mathematical characteristics. Probably too nice, as real world

> functions are more complex than what is contained in these

equations.

> For example it assume that there are constant returns to scale, and

thus

> no economies of scale.

Prof. Berri has mentioned that he is on one side of a rather

substantial Economics of Sports debate about the appropriate form of

the model for wins and points in basketball (and attendance, I

believe). It sounds like we all are on a 3rd side that doesn't

believe either the linear or Cobb-Douglas forms (at least for winning

and points). (Coming from a stochastic hydro background, I know how

you can _assume_ nice models that don't capture any of the "how",

because the models that capture how things work are quite challenging

to work with, especially when you assume statistical variations.)

I have generally been trying to improve the communication between

that academic side that Berri represents and us. As I've mentioned

to him, his goals are good (evaluating compensation, racism, etc.),

but if the method that underlies his evaluations is so flawed to not

pass the laugh test, no one who can make a difference is going to

listen to his conclusions.

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