# The Payoff

Posted on 04/03/2011 by

Cost–benefit analysis is tool used by governments, companies to evaluate the desirability of an action. The goal of the analysis is to see whether the benefits outweigh the costs. The trick for applying this analysis is to figure what constitutes value and what exactly is your cost.

The game of basketball is about turning possessions into points. It is thus extremely easy to identify possessions, the currency of the game, as cost and point margin creation as value. The word margin being the critical one in that equation because we know that the ability of a team to generate point margin is the truest measure of the quality of a team.

Over the past week, I’ve spent a lot of time looking at usage or the percent of the possessions available that a player uses for his team. You might ask me why? It may seem like a devout jew preaching the glory of bacon. I might even answer you.

I think this'll end better than that. (Image courtesy of xkcd.com)

Simple enough. Wins Produced (go  here for details) gives me the value produced by a player (or a reasonable approximation). Usage tells me the cost of that production. In essence it gives me a sense of perspective. If a player produces .2 wins in a game it’s generally a good game but if he uses 40% of the possessions for his team? Not quite so good.

Let’s get some numbers on the table.

Total Wins Produced for the Season so far (thru April 1st): 1126

Total Points for the Season so far (thru April 1st): 225,240

Total Possessions for the Season so far (thru April 1st):238,102

Points per possession: .942                                 per 20 possessions: 18.856

Wins Produced per possession:  .0047          per 20 possessions: .0942

What do these numbers mean? Remember what I said about point margin? The goal for the NBA is to generate more points than the opposition and to do it consistently. The more you do it the more you win . This is why scorers get all the love. The problem lies in the fact that if we focus just on scoring (i.e. value) and not on usage (i.e the cost) we can miss the boat.

Let’s address that. We want to win games over .500. The end goal is then to be better than average.

Thus I came up with the above average rankings.Using all game samples >= 24 Minutes Played and looking only at players with more than ten games, I worked out:

• Average of Usage Rate
• Sum of Player Possesions
• WP48 & Wins Produced
• Break even win return on 20 possesions (see above)
• Expected Break Even Wins Produced return on Possesions: this is the player possessions used times avg wins produced per possession
• Marginal Wins (Wins over .500 generated) : Wins Produced -Expected Break Even Wins Produce
• Break even point return on 20 possesions: this is the player possessions used times avg points per possession
• Point Return on 20 possesions: Points Produced by player over Break even per 20 possessions
• Points over average generated: Points Produced by player over Break even total
• Estimated Marginal Wins over .500 from Scoring: Points over average generated divided by 31.1 (full explanation for that is here)
• And I ranked everyone by WP, Usage, Marginal Wins  and Marginal Wins  from Scoring

How does that look? Let’s look at it three ways:

First comes use:

Now comes points:

And finally marginal wins:

Heh. You’ll note that use does not track to winning (or even wins from scoring). You’ll also note that Melo and Amare are both high usage above average scorers. The problem is that they don’t do the other things that help you win.

The point to this? Simple, to win in the NBA you need guys from the top of List #2 (efficient scorers) but you need to pair them with guys from the top list three (marginal win producers) . Guys on both lists? Superstars. Too many from List #2 ( scorers) and your team becomes one dimensional (NY). You can survive guys from the bottom of list 2 (Rondo,Kidd) if they bring enough else to the table and you have stud scorers (Allen,Dirk,Pierce) on your team.

Oh and if you have a high usage, borderline efficient scorer who brings nothing else to the table?

Go Raptors.

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