Regressed Career Three Point Shooting

(Bump for sometimes some of us forget how good Chris Hill was.)

After yesterday's post in which I gave the regressed three point shooting for the B1G Ten conference since the 2001-02 college season, SpartanDan commented he'd be more confident in this applied to individual players. So that's what I did.

For all of the back story on the method (simple regression), I'll just quote what I've already written:

Tom Tango, consultant to nearly every NHL team, a few MLB teams, author, and noted advanced baseball statistician blogger laid out regression very well in a post on his blog here. His post was on NBA free throw percentage and how much skill exists in that (a lot). I may appear to somewhat know what I'm talking about mathematically, but it's really more of a smoke screen. I didn't possess the knowledge to do something that turns out to be relatively simple, provided you've got a spreadsheet handy. Tom's post sparked my mind which prompted me to grab the shooting data for the Big Ten teams as far back as I could get them. It also sparked Matt Snyder, author of To Maroon and Gold, a blog on the Calvin Knights -- a D3 school in Michigan -- who ran a regression to estimate true talent team three point defense. (You may also know Matt from his wonderful baseball writing at Motor City Bengals on the Tigers.)

I extracted all the data from Sports Reference's College Basketball section, which gave me individual data from the 1998-99 season through yesterday.

First, let's take a look at the best three point shooters in this time frame by raw three point percentage. I'm using a cutoff for these leader boards at 500 attempted three's in a 'career'. I figure an average of 125 three's attempted per year in a four year career would be a good bench mark for the real shooters in the league. Onward to the data!

I tend to forget just how good of a three point shooter Chris Hill was. I remember him being good, but he's all-time good. There's Jon Diebler, who in my article yesterday, I mentioned likely wasn't a true talent 50% three point shooter even though he went 110-for-220 this year. His career three point percentage is closer to his real talents.

Here's the top ten in regressed three point shooting:

Everyone is regressed downward and we see that basically, the best of the best are still just hitting around 40% of their three's. The level of regression on these guys ranges from 14% (Diebler) to over 20% (Luke Recker [22%], Kirk Penny [20%] and Danny Morrissey [20%]).

The amount of regression is based in the number of attempts. Given that, it makes sense that the individual season is regressed more. Let's focus on Jon Diebler. Diebler in his first two seasons was 260-for-673 which is 38.6% from deep. If we plug those in, we'd need to regress his numbers to about 18% towards league average. Basically, it's saying that 4/5ths of his skill from the three point line is Diebler and 1/5th is some sort of random variation -- be that luck, good coaching, playing with players who get him good looks -- or what have you.

This year, Diebler is 110-for-220 from three. If we look at his 2010-11 season alone, we would need to regress it 40% towards the league mean. Essentially, this is saying that this year, 60% of his three point prowess is attributed to Diebler with the remaining 2/5ths being attributed to some random variation. For his career, it looks like this:

3P REG is the amount of regression you need to apply for that particular season. r3P% is his regressed three point shooting percentage. The Delta is the difference between his regressed three point percentage and his actual three point percentage. As you can see, his career r3P% isn't far from his raw career 3P%. Still, three point shooting is volatile enough that you need to regress a players career total -- even someone like Diebler who's shot nearly 900 treys in his career -- around almost 15% to the league mean.

So, how much do you regress at various levels? Well. . .

This is the amount you should regress based on the number of attempts taken by a player in either a season or career. You can click the image to enlarge. Basically, 1/5th of a players three point percentage once they reach 500 attempts is random variation/luck dragons/quality teammates/what have you, while 4/5ths is skill.

However, in a given season, you're likely to see around 250 attempts from your teams best three point shooter, which would mean you should regress their percentage a little over 1/3rd to the league mean. The amount of regression gets steeper the closer you get to 50 attempts.

This makes intuitive sense. Let's say you've got a standard coin. One side is heads and one side is tails. You flip it 75 times and it comes up heads just 29 times (38.7%) while it's tails the remaining 46 times (61.3%). The coin only has two sides so there's a 50-50 chance of flipping heads or tails. Yet, in this run of 75 coin clips, you've managed almost a 60-40 slant towards tails. This, is just random variation or luck or anything you'd like to call it.

For basketball, there's more randomness in shooting a three then there is in flipping a coin. Mike Tisdale is 29-for-75 from three point land in his career and given the small number of shots, we'd estimate his true talent at being a 36.6% three point shooter rather than a 38.7% shooter he is on the surface. If you look at the graph, 75 attempts would be regressed about 65% towards the league mean, which is exactly what I'm regressing Tisdale to. He is likely a bit above-average three point shooter (league average is around 35%), but we are fairly uncertain at just how much above-average (if at all) he is.

Below are the top 15 single-seasons by regressed three point percentage, with a minimum of 100 attempts.

Lots of familiar names given the people we saw on the career leader board. In case you were wondering, Illinois' Jamar Smith had the largest difference between his r3P% and his actual 3P%, getting docked 6.5%. He shot 66-of-137 from three in 2005-06 which was 48.2%. His regressed 3P% was 41.7.

Here is a spreadsheet with career regressed three point percentages (min. 50 attempts) as well as individual seasons (min. 10 attempts). The data is on two separate tabs. To download, click the link and go to File > Download As > your medium of choice.