Da’Monte. Can. Shoot.

By now, it’s no secret that Da’Monte Williams has been an elite three-point shooter this season. Entering Saturday’s game against Purdue, he has made 16 of his 23 attempts from distance, and his three-point percentage of 69.6% leads the country among players with at least 12 attempts. He went 2 for 3 from outside against Indiana, and that lowered his three-point percentage. This would be extraordinary for any player, but the craziest part is that Williams was never even an average shooter in the past. His previous career high for threes made in a season was 13, and in his first three seasons, he never made even a third of his three-point attempts. His improvement from distance has been impressive to say the least, and people have started to take notice. At halftime of last Saturday’s game, I tweeted about it.

But after the game, I got to thinking: I said that I wasn’t exaggerating, but is that true? His complete turnaround as a shooter has been amazing, but did it actually account for half of the team’s improvement? As I was thinking, I realized that there is a quantifiable answer to this question, so I had no choice but to write an article about it.

Buckle up, folks. We’re about to do some #math.

Before we start, I should clarify what exactly we are about to calculate. I want to take last year’s Illini and replace Williams’ three-point shooting statistics with his shooting from this season. Here are my assumptions:

1. Da’Monte will shoot (and make) threes as often per 100 team possessions (while he is on the floor) as he has in the 2020-21 season.
2. He will play the same amount of minutes as he did in the 2019-20 season.
3. Everything else about the team — rebounding, pace, etc. — will be the same as it was in 2019-20.

All we’re doing here is taking last season’s team and replacing Williams’ shooting ability. He will take more threes, and he will make more of them, but he will not play any more minutes, and everything else about both him and the rest of the team will remain unchanged.

WARNING: The next section will be extremely heavy on numbers and math. I’m including it because I want people to be able to check my work, and I also want to help Illini fans get a better understanding of analytics. But if math isn’t your thing, skip it. Seriously. Jump to the last bolded equation, and I’ll start to speak English again after that.

Got all that? Great, let’s start.

The first thing we need to do is to calculate the points per possession on possessions that Da’Monte takes a three. This is fairly straightforward, but we need to account for points on his missed shots as well, i.e. from potential offensive rebounds. And remember, everything but his shooting will be the same as in the 2019-20 season, so we will use the team’s offensive rebounding percentage from last year. Here’s our equation:

(16/23) * (3 points) + (7/23) * (35.6%) * (1.109 points) = 2.207 points per possession

On 16 of 23 attempts, Da’Monte will make a three. 35.6% of his 7 misses will be rebounded by the Illini, and they will score 1.109 points per possession on those offensive rebounds. This adds up to 2.207 points per possession on Williams’ three-point attempts.

Next, we need to see how often Da’Monte is taking threes this year. More precisely, we need to find the percentage of possessions that Williams takes a three when he is on the floor.

(23 attempts) / ((739 possessions) * (64.5%)) = 4.825% of possessions

Illinois has had 739 offensive possessions this season, and Da’Monte has been on the floor for 64.5% of them. During these possessions, he has taken 23 threes. So Da’Monte has taken a three on 4.825% of Illinois’ possessions while he has been on the floor.

Now, we need to calculate the real version of each of these numbers for the 2019-20 season.

First, points per possession on Williams’ three-point attempts:

(11/41) * (3 points) + (30/41) * (35.6%) * (1.109 points) = 1.094 points per possession

On 11 of 41 attempts, Da’Monte made a three. 35.6% of his 30 misses were rebounded by the Illini, and they scored 1.109 points per possession on those offensive rebounds. This adds up to 1.094 points per possession on Williams’ three-point attempts.

Next, the percentage of the time that Da’Monte took a three:

(41 attempts) / ((2102 possessions) * (53.3%)) = 3.660% of possessions

Illinois had 2102 offensive possessions last season, and Da’Monte was on the floor for 53.3% of them. During those possessions, he took 41 threes. So Da’Monte took a three on 3.660% of Illinois’ possessions while he was on the floor.

Now, we need to find the difference in points per possession between the possessions where 2020-21 Da’Monte would have taken a three and the 2019-20 possessions where he actually took a three. The problem is that there are more possessions of the former, so we need to add a few possessions where Williams did not take a three to the 3.660% where he did. Here’s how we’ll do that:

((3.660%) * (1.094 points per possession) + (4.825% - 3.660%) * (1.109 points per possession)) / (4.825%) = 1.097 points per possession

For 3.660% of possessions while he was on the floor, Da’Monte Williams shot a three, and Illinois scored 1.094 points on these possessions on average. There were also [4.825 - 3.660]% of possessions while he was on the floor where he did not shoot a three, but 2020-21 Da’Monte would have. The Illini scored 1.109 points on these possessions on average. In total, on the 4.825% of possessions where 2020-21 Williams would have taken a three, Illinois scored 1.097 points per possession.

We can now compare this with the points per possession on three-point attempts that 2020-21 Da’Monte would have scored on the 2019-20 team.

(2.207 points per possession) - (1.097 points per possession) = 1.110 points per possession

If we keep everything else the same about 2019-20 but plug in the shooting of 2020-21 Da’Monte Williams, the possessions where he shoots improve by a massive 1.110 points per possession.

But that improvement is only on a small percentage of the team’s total possessions, so we need to calculate how much Da’Monte’s shooting shooting helped the team overall.

(1.110 points per possession) * (4.825%) * (53.3%) = 0.029 points per possession

In our scenario, Illinois scores 1.110 more points per possession on Da’Monte’s three-point attempts, but he only shoots them on 4.825% of possessions while he’s on the floor, and he’s only on the floor 53.3% of the time. Still, the 2019-20 Illini would have scored 0.029 more points per possession with 2020-21 Da’Monte’s shooting instead of 2019-20 Da’Monte’s shooting. That sounds small, but it’s the difference between an offense just outside the top 25 in the country and one in the top 10.

We’re almost done, but we still need to see how big this improvement is compared to the team’s improvement in other areas. First, let’s note that 0.029 points per possession is equal to 2.9 points per 100 possessions. Now, we can find the difference between the adjusted net efficiency of the 2019-20 team with that of the 2020-21 team. The one issue is that Bart Torvik’s ratings include his preseason ratings for about 15 games of the season. Illinois has played 10 games so far, so the preseason ratings account for about a third of the total. The other two-thirds are what we’re interested in. Luckily, Bart Torvik’s preseason ratings are publicly available, so it just takes a bit of algebra to figure out how efficient Illinois has actually been this season, but I’ll spare you all from that. If you feel so inclined, I encourage you to check my work. Anyway, here’s the difference:

(25.25 net points per 100 possessions) - (17.1 net points per 100 possessions) = 8.15 net points per 100 possessions

Adjusted for opponent strength, Illinois has outscored its opponents by an average of 25.25 points per 100 possessions this season, compared with 17.1 points per 100 possessions in 2019-20. That makes for an improvement of 8.15 points per 100 possessions.

Da’Monte Williams’ shooting accounts for an improvement of 2.9 points per 100 possessions, and the team as a whole has improved by 8.15 points per 100 possessions. So here’s our final answer:

(2.9 points per 100 possessions) / (8.15 points per 100 possessions) = 35.6%

By my math, 35.6% of Illinois’ improvement this season can be attributed just to Da’Monte Williams’ improved three-point shot.

Now, I don’t think that 35.6% number is really accurate. A lot of calculations went into that number, but we can only calculate what we can measure. There are other factors that can make this number wrong.

It could actually be higher, because Da’Monte making threes means that defenders need to stay with him on the perimeter. This opens up driving lanes for the rest of the guards, and makes the offense more efficient. Just the threat of Da’Monte shooting the ball helps the offense, even if he doesn’t take many shots.

The number could also be lower though, because the rest of the team improving means that Williams’ shots might be more open. Ayo Dosunmu, Trent Frazier, and Andre Curbelo are probably better at creating open looks for their teammates than Dosunmu, Frazier, and Andres Feliz were last season.

So part of the improvement of the rest of the team can be attributed to Da’Monte Williams’ improved shot, but part of the improvement of Da’Monte Williams’ shot can be attributed to the rest of the team improving as well. My gut says that the former has a larger effect, and that the 35.6% number is low. Maybe it’s really somewhere in the forties. I actually have no idea though, so I’ll just stick with the 35.6% number.

There are a couple other possible explanations for Williams’ improved shot, but I don’t think either of them hold up to scrutiny. Three-point shooting percentages have held steady across college basketball, sitting at 33.3% both this season and last. And offense as a whole has actually gone down a bit in college basketball. Da’Monte hasn’t been helped by a better offensive environment. And Illinois has actually faced a tougher slate of defenses (22nd in the country vs. 26th, per KenPom) this year than last, so it’s not like Da’Monte is just making threes because nobody is guarding him.

It seems that a number somewhere close to 35.6% is the “real” answer. But I want to emphasize that all of the calculations I did are somewhat rough. I did my best to make them as accurate as possible, but there are lots of places where the numbers I used may be somewhat inaccurate for one reason or another. So I should probably stop saying “35.6%,” and really say something like “over a third.”

But for a team that improved by as much as Illinois has, one player’s improvement of one skill accounting for over a third of the team’s improvement is crazy! There are five returning players from last year’s rotation, and we would expect a couple of them to each account for over 20% of Illinois’ improvement. Ayo turning himself into an All-American probably accounts for at least a third of the team’s total improvement, for instance. But that’s a combination of all of Ayo’s skills, not just his shooting. Ayo is a better shooter, passer, rebounder, and defender than he was last season, and he’s getting to the free-throw line more often. And he’s doing all of that while carrying a greater load on offense. When a player gets better at everything there is to do on a basketball court, and he also has the ball in his hands all the time, he’s going to play a huge role in improving his team.

Da’Monte has also played a massive role in improving the Illini, but it’s taken far less for him to do it. Ayo has gotten better at everything, and the offense runs through him. Da’Monte’s improvement of his shot alone has accounted for over a third of the team’s improvement, and he barely ever touches the ball! He has gone entire games without taking a three, and his shooting is still responsible for such a large share of the team’s overall improvement. I seriously cannot emphasize enough just how remarkable this is.

I think to really put this in perspective, it’s better to look at the effect Williams’ improved shot has had on the team by itself, rather than as a percentage of the team’s improvement. We calculated that if we replaced the shooting of 2019-20 Da’Monte with the shooting of 2020-21 Da’Monte, the team would have improved by 2.9 points per 100 possessions. As it was last season, Illinois was already a very good team, ranking 29th in the country according to Bart Torvik. But if we add 2.9 net points per 100 possessions, Illinois jumps all the way up to 12th in the country. That’s the difference between a team that’s a 7-seed or an 8-seed and a team that’s a 3-seed or a 4-seed in the NCAA Tournament. Illinois would jump four seed lines based just on the improved shot of a player who barely touches the ball. I said it before and I’ll say it again: I cannot emphasize enough just how remarkable this is.

Even so, it turns out that I really was exaggerating a little bit. It doesn’t look like Da’Monte Williams’ improved shot actually accounts for half of Illinois’ improvement, just a little over a third. I was wrong, and I’ll be the first to admit it. But I don’t think I was wrong because I overestimated the effect of Da’Monte Williams’ shooting. He has turned into a knockdown shooter, and Illinois is a far better team because of it. I just underestimated how much the team has improved overall.

Now, Da’Monte will not continue to shoot 70% from distance over an entire season. That would be the greatest three-point shooting season of all time. The regression monster is always lurking, and sooner or later it will bite. I want to make that clear. Shooting 70% from three-point range is just not sustainable for thirty games. Still, Da’Monte Williams’ improvement from three has been one of the most impressive feats I’ve ever seen from a college basketball player. It’s time to give him the recognition he deserves.