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.

The Mann/Bales Trade and More Crazy Stats

I was very much influenced by a post at Rethinking Basketball that was used to evaluate rookie talent in the WNBA. The point of the post was to determine which rookies had the potential for success given their limited playing time and which were likely to fail. This inspired me to do the same regarding Mann and Bales. Neither gets starters minutes so the tools used by Q to test rookies could be useful.

The first tool I want to develop is something called "Wins Score". "Wins Score" is what we call a linear metric. All that means is that Wins Scores is one of those tools that gives a player x points for something something good, y points for doing something bad, and adds all the points together for a final total. (Remember 3x - 2y in algebra? Just like that.)

If you just can't stand not knowing the metric, here it is:

(Points + Rebounds + Steals + ½Assists + ½Blocked Shots – Field Goal Attempts – Turnovers - ½Free Throw Attempts - ½Personal Fouls)

The WNBA uses a similar metric called "Efficiency"

((Points + Rebounds + Steals + Assists + Blocked Shots) - ((Field Goal Attempts - Field Goals Made) + (Free Throw Attempts - Free Throws Made) + Turnovers))/Games

There are two differences in the two formulas. The second divides by "games" at the end. All this does is reduce the second formula to a "per game" basis.

The other difference is that Wins Score only gives half credit for assists and blocked shots. It ignores field goals and free throws made, only gives half credit for free throw attempts, and unlike Efficiency, Wins Score takes points away for personal fouls whereas Efficiency ignores personal fouls.

Most Basketball APBRmetricians like "Wins Score" a lot better than they do "Efficiency". When I switched to "Wins Score" the following results popped up.

Betty "Noox" Lennox: 26th in Efficiency, 55th in Wins Score
Ivory Latta: 40th in Efficiency, 58th in Wins Score
Tamera Young: 51st in Efficiency, 53rd in Wins Score

Furthermore, Stacey Lovelace pops up to 56th in Wins Score, above Ivory Latta. Why does everyone take such a hit in Wins Score?

First, Wins Score doesn't care how well you shoot, as opposed to Efficiency. Wins Score just cares how many points you put on the board. Secondly, turnovers hurt you in Wins Score, and they don't hurt you in Efficiency.

Betty makes a lot of turnovers for the points she makes. As the end of 2007, she was 12th in turnovers all time in the WNBA. Wins Score appropriately devalues her overall worth to the team. With Tamera Young the highest overall Wins Score leader for the Dream -- at 53rd in the wNBA -- it's no wonder that the Dream is 0-17.

All right. Let's assume that we agree that Wins Score does a better job than Efficiency in predicting a player's worth. Where do we go from there? What does this mean both for Kristen Mann and for Alison Bales?

The first thing we need to do is create some way to answer the question, "if these two players played starters minutes instead of sub minutes, what is their potential for upside?" As it turned out, this question had already been answered by a man named Kevin Broom.

He created something called a "Diamond Rating". The point was to find "diamonds in the rough" which had been overlooked, players who might be able to make something happen if they had playing time.

The formula is a bit more complex, so I'll just summarize how it works. I changed Broom's formula and assumed that a WNBA starter would play 33 1/3 minutes per game. (His formula is an NBA formula, and he uses 40 as the starter's benchmark.)

a) Figure out what the Wins Score would be if the player played 33 1/3minutes and divide that by games played,
b) Subtract their current Wins Score per games played,
c) Add the difference between their win score per 33 1/3 minutes divided by games played and the league's average win score per 33 1/3 minutes divided by games played.

A and B determines how close the player comes to a starter. C gives them credit if they're producing more than an average player.

We then exclude certain groups of players. Anyone who's playing less than 2.5 minutes per game is chopped off -- we don't have enough data on them. Anyone playing more than 21 minutes per game is chopped off -- they're earning close to starter's minutes already.

WNBA leaders in PADR (Petrel Adjusted Diamond Rating)

CON Danielle Page 39.83
HOU Sancho Lyttle 19.28
MIN Vanessa Hayden 13.25
NYL Tiffany Jackson 10.95
WAS Crystal Langhorne 10.52
PHX LaToya Pringle 9.89
SAC Crystal Kelly 8.96
LAS Sidney Spencer 8.54
CON Tamika Raymond 6.98
MIN Kristen Rasmussen 6.66

As it turned out, Sancho Lyttle is lighting the league up now that she's had a chance to play. She lit up the Dream for 18 rebounds on Thursday. (Danielle Page is an outlier, as she barely makes the 2 1/2 minutes per game cutoff. I'd ignore her.)

Let's look at the Diamond Ratings of Alison Bales and Kristen Mann.

Bales 6.31 12th
Mann -0.61 67th

According to the Diamond Rating, Bales might have something extra to offer if you give her time. (We don't know yet where the cutoff in Diamond Rating for the WNBA rests. In the NBA, "diamonds in the rough" usually score eight or better in Diamond Rating.) Whereas Mann, according to Diamond Rating, doesn't have much to offer if you give her extra time.

Is Bales a real "Diamond in the Rough?" Is this going to be one of those trades that's going to work out very well for the Dream in the end and help us turn things around? The only way we'll know is that if Alison Bales is given significant minutes on the floor. We probably won't see that happen in todays Sky/Dream game, but we might see it later on in the year.

And just remember...sometimes the statistics lie...!