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# Just How Extreme Was Markus Howard’s Three Point Shooting?

Fun math! No, wait, come back, it’s more fun than math. We promise.

I can already tell you that I misled you a little bit in the title. It was for a good reason, though, because it sets the foundation for what I’m going to talk about. The misleading part was that there are different ways to describe extreme. It’s all based on your parameters for it. When it comes to three point shooting, there are really four ways you can be extreme. Here’s a little figure to visualize it.

Each of those four quadrants show how you can be extreme. Roy Hibbert was an extreme three point shooter. He shot 100% for his career at Georgetown. He also had three total attempts. That would put him in the top left corner: Above average, but not qualified because of his low number of attempts.

The bottom left is reserved for those schmoes who only played in one game because they were benchwarmers and only existed to serve the purpose of making sure no one got hurt, but they couldn’t even make the one three the crowd was begging them to take. Those cheers were out of pity, Brett Olson. Have fun telling your kids about the two threes you didn’t make.

The bottom right is probably the most rare extremity. You’d have to somehow convince you coach to let you play and shoot enough threes, but miss almost all of them. I want to meet the person at the farthest point on the bottom right and shake his hand. He’s a hero in my eyes.

The top right, as you can see, is where the elite live. We are going to zoom in on that region.

There are two main factors at play here: accuracy and attempts. Accuracy determines if you are below or above average (y-axis) while attempts determine if you’re qualified or not qualified to be considered as one of the greats (x-axis). Qualified is defined as a 2.5 threes made per game and at least 75% of the team’s games played, but we’ll do a little more investigation on that later. What I want to do now is properly weigh those two main factors in order to determine where Markus Howard, who had one of the best three point shooting years in history while he was 17 years old, ranks among the elite. To do that, I will need to do some math. I’ll start being more math-intensive after this paragraph and I’ll make a line where it ends, in case an explanation of methodology either bores or confuses you and you’d like to skip it. I don’t think it’s too earth-shattering, so I invite you to join along anyway. I’ll even ease the load by doing an example calculation through the process.

Hey everyone. Alright we finally weeded out the others. After this I’ll give them some lip service and welcome them back, but it’s really you that I care about. We’re sticking together all the way through.

To start this off, I thought a lot about that grid and what it means (#deep). More specifically I thought about that middle point. Is the solution as easy as just plotting percentage and attempts on that grid and finding the Pythagorean distance to that center point? Maybe that could help, but the ranges of these two axes are way different. Players can shoot as many as 300 long range shots a season, but they can’t go over 100%, even if that was feasible. Finding the distance to that center would give more weight to how many threes they take than I was comfortable with. I even thought about multiplying the percentages by 1.5 to account for the risk in taking a three, a la effective field goal percentage, but that wasn’t enough still. I had to rethink what I was going after a bit. Even if I did compute those distances, what does the number itself even tell me? I wanted more specific units.

Boiling everything down to its simplest question, the ultimate goal when a player shoots the ball is points scored in a more efficient way than their opponent. When we’re just looking at three pointers, I want to find who best scores points relative to the average elite player. I could just multiply 3*3P%*3PA and give a fairly accurate ranking, but

1. We’d be comparing these players to everyone on that grid. I want to compare them to a higher standard to give a better context.
2. There’s a bias against players on slower-paced teams (think Virginia) and teams that play less games due to scheduling or being on worse teams that don’t make it to the postseason

So I’ll just add a couple things to that equation above. I’m going to subtract average values from a player’s 3P% and 3PA stats and then divide that whole result by possessions. That’s the big picture. Let’s get more into the minutia.

For attempts, you can just look at the difference between a player’s 3PA and what the qualifying mark for the individual player is. That formula would be

Where 3PA is three point attempts, 3P% is three pointers percentage, and G is games played. 2.5*G equals the required amount of three pointers made to qualify and dividing that by the percentage gives you the unit of three point attempts required to qualify. Everyone’s favorite heart attack Ashton Gibbs, for example, attempted 208 threes at a 49% clip over 31 games in 2011. Plugging those numbers into the displayed equation, we get around 50, which means he exceeded the qualifying mark by 50 shots.

Everyone with me still? Let’s take a break actually. It couldn’t hurt. Remember this game? Let’s watch the highlights again. We’ll get back to this when the video is done.

What a night. Anyway, now we need to figure the average 3P%. This is tricky. Do I compare the player to the league’s average for his particular season or do I keep it as one baseline for everyone. I personally like keeping it to one standard because no matter what the standard is, the difference will at least be consistent all around. Ultimately my standard for average was the 2017 league percentage of 35%. Three point percentage across the league doesn’t change too much across years anyway, by like a percentage at most, so it probably wouldn’t differ too much if you did it on an individual basis. The math here is easier; for the Ashton Gibbs example we simply take 49 minus 35 to get 14 (will be .14 for future equations to keep units consistent), which means that he shot 14 percentage points better than league average.

So now we have a percentage relative to average and attempts relative to average. We can easily convert those to “points from three above average” by multiplying 3P%*3PA*3. For Gibbs, this would be 50*.14*3 to give us 21 points above average. Again, this is simply raw points. We want to make this a rate statistic to avoid that second bias.

I don’t want to do per possession actually. Those numbers are teeny tiny, and it’s hard to grasp what a player accomplished over a whole season just by looking at it one possession at a time, so let’s look at this on a per-100-possession basis (100 possessions is just a nice round number. It’s the equivalent of about a game and a half). So now we just take our points above average number, 21 for Gibbs, that we just determined and divide that by a team’s possession rate per game times the amount of games a player appeared in, multiplying that end result by 100. That was dense, so to finish the example, the 2011 Pittsburgh Panthers averaged 63.6 possessions over Gibbs’ 31 games, which would give 1971.6 possessions over the year (possession rates are adjusted for opponents, hence the decimal). 21 over that gives .01062, but since it’s per 100 possessions, just shimmy that decimal over a couple spots and you have 1.062 points per 100 possessions. Just remember we’re comparing this to the qualifying mark, so don’t get too underwhelmed.

I only have possession data going back to 2002 through KenPom, so for all years before that I’m just going to guess what the league average for the year was with a regression line (y=-.0993x+266.63 if you’re curious) based on all the available years I have, and say that his team was average. It’s not perfect, but it’ll have to work.

Overall this part may seem petty, but a difference of 14 possessions a game (the difference between Stephen Sir’s Northern Arizona team and Robert Nyakundi’s SMU team) over 30 games can mean a 420 (heh) possession advantage where a player can attempt and make more threes. Also note that minutes and usage data doesn’t exist for everyone either. In a perfect world, we’d incorporate that for every player.

Alright I think we can bring the others back now. I really don’t want to. They’re probably going to tell me to get back in my mom’s basement in the comments for bringing math into sports. I’ll just tough it out I guess.

Welcome back everyone else! We made a secret club in between the horizontal lines and you’re not invited. But to recap, I basically walked through my thought process for making an Excel sheet where I determined the best way to determine a player’s three point ability is to take his points above average from three per 100 possessions, with an example calc sprinkled in. Now I just need to plug in the information I need, which would definitely not take as much time as it did if I had the ability to create custom tables and export them, but that’s a rant for another day. Because of this, I limited myself to only insert data until I got tired. Without any further ado, here is the full file. I’d drop it in here as a table, but it would just distract us from our full point.

Since his name is in the title of this article, I know you’re looking for Markus Howard. He’s down at row 25. He sucks! I’m going to do some surprise math on you all now by calculating his z score. The hyperlink gives a better definition than I could, but basically it’s a way of measure how far away he is from the average, with positive numbers being above and negatives being below. Markus’ z score is -.75. He needs to be benched until he can figure this out! If you’re thinking about how he could be so high on the all time rankings and so low here, look at the attempts above average. Essentially, had he taken 9 less threes than he did, he wouldn’t have even qualified for the ranking. Plus Marquette was only 1 of 6 on the ranking to exceed 70 possessions a game.

Honestly, though, the fact that we’re even talking about this and raising the question to the point where you all definitely thought he had a shot at #1 speaks to how insane his previous season was. He was 17! (Take a drink.) Look back at the grid I posted up at the top and remember that the pool of players I chose from were already in that very top right elite group (like Joe Flacco), so it was just a matter of how elite they actually were. Markus Howard essentially had the 25th best three point shooting year since they started keeping track of this officially. He was 17! (Take a drink.)

Alright, so we’ve spent a lot of time talking about Markus in comparison to the other players on this elite zone. Let’s zoom out and look at the whole grid. What is he doing relative to that center dot? Specifically, let’s look more closely at that 2.5 makes per game qualifier. It makes a lot of sense for a situation like before when we’re comparing elite players. We don’t want to include a guy with 40 makes over 30 games because that’s not a big enough sample to determine whether or not it’s an all time great, but that doesn’t mean this information isn’t valuable. So let’s adjust this qualifying number a bit to see what he actually provided with his threes.

We’re really only asking one more question here: How many threes does the average player make a game? I’d say roughly 8 players play in any given game and the median for made threes per game by a team last year was 7.3, so each player makes .9125 threes a game. I’m going to plug that number into the formula I displayed in the methodology section and adjust the final result to show points per 70 possessions instead of 100 since that’s how many Marquette averaged a game. That’s it. This won’t affect Howard’s ranking at all, but it will show that, just from three pointers, he provided an extra 1.87 points per game above average. It may not seem like much, but remember the context of this. This is the average player. The dreaded standard that drags everyone to mediocrity at some point or another. He’s almost two points better than that every time he steps out on the court. That’s why he’s up at 25.

What does this mean going forward? Well, you’ll see there’s only one player on that table who was listed twice. Many of them took increasingly more shots at a higher percentage leading to a breakout senior season, but the rest, except for Stephen Sir, took more shots the next year at a lower percentage. I think we can expect that from Howard. He’ll have a much bigger role on the team with ample opportunities to shoot at will, which he definitely should, but it would be unreasonable for us to raise our expectations so high that 44% would be a disappointment. Luckily, the team shouldn’t need him to produce at that level. The production of Andrew Rowsey and Sam Hauser may stutter a bit in a similar way to Howard’s, but at worst, the team should have three effective long range shooters. Back in April, Brewtown Andy already did the logical walkthrough and did a tremendous rundown about what we should/could expect, but I finally want to look a little more specifically at how much “worse” Howard can afford to be in order to keep up with the pace he set last year.

We’ll just work backwards here. Let’s say Wojo lets Howard fire off around 7 threes a game to give him 225 for the year. It’s definitely within the realm of possibilities. With that many attempts, just to match the extreme level he was at last year, he’d have to make 46.75% of his threes. Again, this probably is not a reasonable expectation for us, so please don’t circle that percentage as your goal for him. This is mainly meant to show that the more Wojo unleashes his stroke, the more the team can afford a dip in percentage. Plus, that’s 75 shots that are in the upper stratosphere of production. They’d likely be replacing merely above-average shots with the way this offense can go, but Markus Howard launching threes will be the best chance at raising the bar for how high this offense can go.