Advanced Metrics Handbook, Vol. 1: Effective Field Goal Percentage
by Evan Dunlap on Aug 11, 2010 8:00 AM EDT
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Part of an occasional series explaining some of the advanced statistical terms employed at Orlando Pinstriped Post. Today's topic: effective field goal percentage, or eFG% for short.
On November 4th, 2009, Orlando Magic forward Mickael Pietrus scored 15 points in a victory over the Phoenix Suns, but shot just 4-of-10 from the floor, for 40%. Conventional analysis would hold that 40% shooting isn't acceptable at the NBA level, but it'd be a bit misguided. Traditional field goal percentage doesn't really tell the whole story, which is why former L.A. Clippers head coach Mike Dunleavy developed eFG%, a better measure of shooting proficiency, during his playing days in the early 1980s.
The formula:
(FG + 0.5 * 3P) / FGA
In plain English:
Dunleavy believed that shooting percentages should reflect the fact that three-point shots are worth more than two-point shots. eFG% accomplishes this task by multiplying the number of three-pointers made by 1.5
What it's for:
Evaluating volume three-point shooters, like Pietrus, whom traditional FG% underrates. For his career, Pietrus has shot 43.5% from the field. However, Pietrus' tendency to let fly from beyond the arc--46.2% of his shots come from long range--boosts his eFG% to 51.8%. In contrast, it won't tell you anything new about Magic center Dwight Howard, who's made just one three-pointer in his six-year career.
The takeaway:
Pietrus indeed shot 40% in Orlando's win against Phoenix, but looking at the bigger picture, you'll see he was more efficient than what raw FG% indicates. Three of his four field goals came from beyond the arc. Plugging his numbers from that game into the formula, we see that Pietrus registered an eFG% of 55.0%, which is slightly higher than his season average o 54.0%.
Additionally, eFG% is a proven measure of team success, as the noted statistician Dean Oliver identified it as one of the four factors of winning in his book Basketball On Paper. It's not a novelty or a curiosity, in other words. It's a relevant, respected component of modern basketball analysis, though it's not even the best advanced shooting metric available, as we'll see in a later installment in this series.
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Boo stats
Physical Attributes >Quantifiable Evidence
ORL★NDO M★GIC
-SEMINOLES-;;-►
by Wally Balls 407 on Aug 11, 2010 1:14 PM EDT reply actions
So is True Shooting % better?
Do you know which one SVG uses more?
"A man has got to have a code." -Bunk, Season 1; Omar, Season 4.
TS% is better, but eFG% is good too.
They’re usually used to supplement each other.
I know that Van Gundy uses both.
I write for Magic Basketball and have a Twitter account.
TS%
Accounts for free throws too. They tell you different things; both are useful.
by eltharion_doa on Aug 11, 2010 10:25 PM EDT up reply actions
so how come it only rewards the 3 pt shot made but doesn’t punish the higher risk miss?
and, stats are cool, but what about the SC porn standard…you know it when you see it?! sure it’s important, but let’s not make it such an objective numbers game that the human element, say 4th quarter free throw misses in the playoffs, gets thrown out with the bath water.
by thejugs on Aug 11, 2010 5:32 PM EDT reply actions
You've made up your mind and nothing I say is going to sway you. Clearly.
If Dean Oliver says it matters, OK, it flipping matters.
why so defensive? i never said it doesn’t matter…
but im sure we can agree that it’s not the SOLE measure of a player or team?!
by thejugs on Aug 12, 2010 5:09 PM EDT up reply actions
can you measure and predict basketball solely on stats?
by thejugs on Aug 12, 2010 5:12 PM EDT up reply actions
I'd trust stats more than "hearsay"
If I see notice something when I’m watching NBA, and I want to provide evidence, I use statistics.
A missed field goal is a missed field goal
You don’t lose a point for missing a three.
by eltharion_doa on Aug 11, 2010 10:27 PM EDT up reply actions
a miss is just a miss but one make is worth more than another make?
just saying, all misses are not equal. some are worse shots than others…
by thejugs on Aug 12, 2010 5:10 PM EDT up reply actions
you get 0 points for missing a 2 point shot or a 3 point shot
you get 2 points for making a 2 point shot and 3 points for making a three point shot
by MagicMark on Aug 12, 2010 6:05 PM EDT up reply actions 2 recs
Statistically, it is a miss from 10-15ft.
Please don't simply ignore the stats when making your case, 'cause "...your eyes lie to you sometimes..."
Stats Education::
Advanced Stats 101 @ MBN | Basketball Reference | Basketball Prospectus | 82games
by magicfaninTN on Aug 12, 2010 10:29 AM EDT up reply actions
lighten up....it was a joke.
Please don't simply ignore the stats when making your case, 'cause "...your eyes lie to you sometimes..."
Stats Education::
Advanced Stats 101 @ MBN | Basketball Reference | Basketball Prospectus | 82games
by magicfaninTN on Aug 14, 2010 11:45 AM EDT up reply actions
since 3pt fg percentage is generally lower than fg percentage, this formula only rewards more 3 pt shots, without punishing the extra missed attempts.
example: ever see an up fake, one dribble step inside the line, and an open 2 pt shot?
by thejugs on Aug 12, 2010 5:11 PM EDT up reply actions
The “extra missed attempts” are punished by the fact that your shooting percentage drops. Let’s see if I can illustrate this in a different way:
- in eFG% last year was Dwight Howard. He shot .612 from the field, .000 from 3 (0-7). He hit 510 shots (worth 1,020 points) out of 834 shots taken (worth 1,668 points). Thus, he scored 0.612% of all possible points.
- was Channing Frye. He shot .451 from the field, and .439 from 3. He hit 145 2-pointers and 172 3-pointers (806 points) out of 703 shot attempts (1,406 points). He scored 0.573% of the expected points if every shot was a 2-pointer and he hit all of them. Frye’s overall shooting percentage is .161 lower than Howard’s, but his eFG% is only .039 lower because he scores almost as many points per shot as Howard due to the 3-point shot.
eFG% is looking at how many points the player scored compared to how many shots they took. In effect, Howard’s being rewarded for taking high-percentage 2 point shots and hitting them. Frye’s being rewarded for being good at hitting the more valuable three-point shot.
Honor is no substitute for victory.
Excellent examples
Orlando Magic... 2010 Eastern Conference Finalist
Chicago Blackhawks... 2010 NHL Stanley Cup Champions!!
by Mike from Illinois on Aug 13, 2010 4:23 PM EDT up reply actions
Risk is a part of everything that we do, even when we corss the street.
eFG is a simple calculation which makes perfect sense with some caveat. All business decision makers, researchers, statisticians, etc., factor risks in, most of the time. Meanwhile, they all make assumptions for the sake of practicability. There are two types of risks; negative (pure risk) and positive (opportunity). in fact, 3-point shot is a classic example of two types of risk; making it (opportunity), missing it (risk). thejugs is right about the risk factor in taking a 3-point shot since the probability of making a 3-pointer is less than a 2-pointer. If we go back and calculate the difference – say 40% v. 50% – therefore, reward a 3-pointer only 0.4 instead of 0.5? Big deal! I would say not worth it. But I am not going to blast the guy who is persistent on making it more accurate.
a missed shot cannot ever be anything more than 0 points
a made shot can be either 2 or 3 points
the only “risk” associated with shooting threes is if you aren’t very good at it and do not shoot a high enough percentage
and making it .4 instead of .5 is asinine because it is worth 1.5 as many points, hence the 1.5 multiplier.
Talking statistically - if that is what you want to do - your statement of
“the only "risk" associated with shooting threes is if you aren’t very good at it and do not shoot a high enough percentage” is inaccurate. You cannot measure it based on whether one is good or bad. You have to measure it based on the average of 3-pointer v. 2-pointer. And no matter what since the probabilty of making a 3-pointer is less than making a 2-pointer, that is a negative risk.
im not a math science guy but isn’t it opportunity cost?
like, the cost of using vacation time isn’t just the transportation, hotel, food, etc. you also have to factor in the cost of alternative courses of action, like going to work and getting paid.
the cost of a lower percentage 3 pt is not just 0 points if the alternative of a higher percentage mid range pull up is factored in?
by thejugs on Aug 12, 2010 8:56 PM EDT up reply actions
how difficult is it to understand that a 3 point shot is a higher percentage chance to score points than a mid-range pull up?
that is the entire point of EFG%
shots at rim = highest % shots = good
shots behind 3 point line = worth extra points = good
mid-range shots = same amount of points as shots at rim at a significantly lower average % = bad
this is as simple as it gets
Looking at last year statistically, for the NBA as a whole:
Multiplying FG% by the points earned on the shot:
At rim: 1.222 points/shot
< 10 feet: 0.884 points/shot
10-15 feet: 0.798 points/shot
16-23 feet: 0.794 points/shot
>23 feet: 1.068 points/shot
Unless you can get to the rim, on average you will score the most points by taking threes. Even short jumpers from less than 10 feet score fewer points in the long run than shooting threes. The odds of hitting an individual shot are higher (0.442 to 0.356), but the odds need to be at least 50% higher for a 2 to score more in the long run than a 3.
Honor is no substitute for victory.
These are excellent historical data
I assume that they are based on 2009-10 averages; right? I initially thought that the difference between averages of made 3-pointers v. made 2-pointers was around 0.10, and these numbers confirm that assumption. I still believe, as I initially mentioned, that eFG% is a very effective instrument even without conditioning it (ever so slightly down) for the difference in averages of 3-pointers and 2-pointers made. Thank you for providing the data.
Yes, that was based off last year’s NBA averages per HoopData. It would vary some by team, based on what their players specialize in. For example, the Magic’s numbers for last year are:
At rim: 1.256 points/shot
< 10 feet: 0.930 points/shot
10-15 feet: 0.828 points/shot
16-23 feet: 0.804 points/shot
>23 feet: 1.126 points/shot
Honor is no substitute for victory.
The point is
That you compensate for the lost opportunity cost of giving up a potential 2 point shot with the far greater reward of a potentially successful 3 point shot.
You’re getting a 50% higher return on your investment, if you like, so you’re happy to accept a lower chance of being successful on any individual investment because you’ll get a greater average return taking the higher risk.
by eltharion_doa on Aug 13, 2010 2:10 AM EDT up reply actions
This is not as simple as you think.
I learnt a lesson long time ago when I was introduced to this old adage: don’t take yourself so seriously becuase nobody else does. That was when I gave up looking at issues in absolute terms. You need to research the principles of risk management, buddy.
It's just basketball, brochacho.
One does not need to understand risk management to know whether or not a certain type of shot is efficient.
Actually, understanding risk management is pretty useful
But the point is that the 3 point is efficient even after considering risk management. You risk a greater chance of failure, but have a chance at a higher reward. If the higher reward is sufficient enough to compensate for the higher risk, it’s the correct decision.
Understanding efficiency is basically the whole point of risk management. It’s making sure that when you take a higher risk, you’re getting a greater reward as compensation, and deciding on the magnitude of the greater reward that you need to compensate you for the higher risk. This is exactly what the 3 point shot does, and why we talk about efficient shooting. Indeed, basketball – because we can statisfically determine risk, and precisely quantify the reward – allows far more precision in risk/benefit analysis than you’ll find in business.
by eltharion_doa on Aug 13, 2010 2:14 AM EDT up reply actions 1 recs
as a forgotten factoid in the discussion, the team that scores more points usually wins. This often has a high correlation with scoring more points per possition or points per shot taken. I think we can end this discussion if we do like preschollers and just quit keeping those meaningless statistics of final score and wins versus losses.
"We have a great bunch of outside shooters. Unfortunately, all our games are played indoors." - Weldon Drew
I'll tell ya about the Magic It'll free your soul but it's like trying to tell a stranger 'bout rock n roll
"This dude is huge....I've got to go home and eat like five chickens and put a lot of weight on. It's going to take a couple months, but seriously." - Marcin Gortat about Shaq.
by NC Magic Fan on Aug 13, 2010 11:48 AM EDT up reply actions
This is a sound argument
You mentioned “3 point is efficient even after considering risk management”. No doubt about it, but the question in a quantitative assessment is how much more efficient? I was not trying to make it more complicated than it should be. The point which I was trying to get across was that it is not as simple as “while a made 3-pointer is worth 3 and a made 2-pointer worth 2, a missed shot from either range is just 0; end of story”.
The point i was arguing was this:
Someone was attempting to say that a missed 2 and a missed 3 are somehow different. you get exactly 0 points in both situations, so they are exactly the same in that respect. I guess the point you were trying to make is that shots closer to the basket are supposedly “easier” to make, and thus the risk is less for those, but in taking that point, the opportunity cost you take is that your shot is only worth 2 points, whereas a long ball is worth 3.
35% @ 3pt = 52.5% shooting from anywhere inside the arc. We have had 4-5 players that were close to 40% the past few years, so the efg for the 3’s they shoot is close to 60%. This last season we shot a slightly lower percentage as a team – I believe we ended somewhere in the mid 38%’s as a team.
As stated above, a two point shot inside 10 feet but not at thee rim results in .884 points per shot. A three point shot results in 1.068 points per shot. Therefor, a three point shot is 20.8% more efficient than a less than 10 foot shot.
Following that logic, a three is 33.8% more efficient than a 10-15 foot shot and 34.5% more efficient than a 16-23 foot shot.
"We have a great bunch of outside shooters. Unfortunately, all our games are played indoors." - Weldon Drew
I'll tell ya about the Magic It'll free your soul but it's like trying to tell a stranger 'bout rock n roll
"This dude is huge....I've got to go home and eat like five chickens and put a lot of weight on. It's going to take a couple months, but seriously." - Marcin Gortat about Shaq.
by NC Magic Fan on Aug 13, 2010 3:27 PM EDT up reply actions
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