Saturday, July 19, 2008

On the Value of Field Goal Percentage

The author of the Women's Sports Blog has been following the Pleasant Dreams blog. (Go to the blog. It's a good read.) However, the author is puzzled by the use of Wins Score and asks, "if Wins Score is a better metric than Efficiency because it doesn't take into account field goal percentage, then why do you report field goal percentage at all when talking about the Dream and the teams it plays?"

Let's first get into the details about field goal percentage and why some people like Wins Score better than Efficiency. The primary point is that to a certain degree, both are linear metrics -- each good thing you do gives you points; each bad thing you do loses you points.

Field goal percentage is equal to the number of field goals you make divided by the number of field goals you attempt. Therefore, any stat that is counting field goals made and field goals attempted is incorporating field goal percentage in some manner.

Both metrics count field goals attempted, but only Efficiency counts both field goals made and field goals attempted, whereas Wins Score skips the "field goals made" part completely, incorporating it into "Points". Why is this bad?

I'm going to repeat the article written by DJ at The Wages of Wins Journal. Let's look at, say, Chioma Nnamaka coming off the bench. She tries three field goals and makes one of them in her five or so minutes of play.

Efficiency has (Field Goal Attempts - Field Goals Made) and subtracts all of that from "Points". Nnamaka made two points. She had three attempts, and made one shot.

2 - (3 - 1) = 2 - 2 = 0.

So Nnamaka wasn't hurt at all by her 33 percent field goal percentage. It's an additive metric, so all we've done is add "zero" to the final total.

Let's assume she took four shots instead of three. One was a three pointer that went in, the other three were misses.

3 - (4 - 1) = 3 - 3 = 0.

In this case, Nnamaka isn't hurt by a 25 percent field goal percentage.

The problem is that these are very low percentages for success. The problem with Efficiency is not that it counts field goal percentage; the problem is that it places too high a value on it. In Effiency, anything above a 25-33 percent field goal percentage (depending on how many threes are taken) will be rewarded in the final results. This is a very very low standard to set.

Wins Score avoids the problem by not tallying up the number of field goals made. With Wins Score, field goal attempts are subtracted out, and Nnamaka would have earned 2 - 3 = -1 point for her crappy shooting.

Is Wins Score more reasonable than Efficiency? Part of the results have to do with a "smell test". I can count just about anything I want to, height, age, shoe size, add it up using some bizarre calculus and claim the results mean something. It would be circular reasoning to claim that the results verify what you set out to prove, when you claim that things are being added to or subtracted from the metric because they give you good results.

Wins Score passes the smell test to me more than Efficiency, which is why I use it.

(* * )

This then gets to the question, "So why are you including field goal percentages at all in the report if some metrics overvalue them?"
Victory". Efficiency and Wins Score are combined metrics and individual metrics. They are primarily designed to measure what one single player brings to a team, and they measure the totality of the combination.

Dean Oliver's Keys, however, looks at the entire team and is looking at pieces, not an entire combination. Efficiency and Wins Score says, "Which player has the best overall game?" and players can be compared across teams. The Four Keys to Victory ask, "what parts must an individual team do well to win an individual game?" They are essentially separate questions.

Field goal percentage is important at the individual game level because a team only gets a certain number of possessions during a game. Every time you take a shot, miss, and don't get the offensive rebound, you've given the other team a chance to score. If you miss a lot of shots, you give the other team a lot of chances to score. At the game level, it hurts.

However, in a way, both the Keys to Victory and Wins Score link up. Both say, "We're not going to reward a team/player for shooting 33 percent from the field." It's amazing how separate things begin to fit into a larger picture once you look at them. One problem that both Efficiency and Wins Score have is that neither values offensive rebounding very well, which Oliver's metric does.

I hope this answers the question. If it doesn't...well, I would go to blogs like Rethinking Basketball or Swanny's Stats or Storm Defense. There are a lot of guys who can explain this stuff better than I can.

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