The current record holder for three-point accuracy in a season is Glenn Tropf who made 52 of his 82 attempts (63.4%) for Holy Cross in the 1988 season. Arizona’s Derrick Williams has made 27 of his 40 attempts so far this season, which is good for 67.5%. Of all the things Williams has done this season, that is the most amazing to me. It’s not that Williams is a great outside shooter, because he’s probably not “great”. But clearly, he’s good and nearly all of his 40 shots have been high-quality looks. Williams’ sparkling numbers have resulted from a combination of good touch and good fortune.

This got me curious as to the chances of Williams – potential first round-pick for reasons that don’t have much to do with his ability to make 20-foot jump shots – breaking the three-point accuracy record. The only way to investigate this is to run the rest of Arizona’s season over and over. I did it one million times! And now I am exhausted.

First, let’s look at the assumptions I used…

Williams has a 40% chance of making any three-point shot. It’s impossible to know what the true percentage should be, but we have some clues. He actually only made 4 of 16 three-point attempts last season. He’s made 40 of 90 (44.4%) mid-range two-point attempts this season. And he’s a 75% free throw shooter, so he has above-average shooting touch. Given his discriminating shot selection, 40% seems about right.

Williams’ three-point attempt frequency is based on the past. He’s taken no threes in five games, one three in nine games, two threes in nine games, three threes in three games, and four threes once.

– The number of games Arizona plays is also important. I’ll give them an 80% chance of winning in the first round of the Pac-10 tourney and a 70% chance of winning in the Pac 10 semifinals. For the NCAA tourney, I’ll give the following chances of winning in the first five rounds: 90/70/60/50/40. (These chances are appropriate for a three-seed, which may be optimistic by a line or two. Also, for the purposes of this simulation, it’s irrelevant whether the Wildcats win either title game.)

After running the simulation, there are two issues to consider: first, whether Derrick Williams gets to the minimum 50 attempts to qualify for the record and second, whether he makes enough shots to break the record. It turns out getting to 50 attempts isn’t trivial. But in 88.1% of the trials, he took at least 10 three-pointers in what’s left of the season.

What you really want to know is how often Williams broke the record (reaching the minimum attempts). This occurred 16.9% of the time.  A one-in-six chance is better than I expected. It’s realistic, though not likely.

There’s no need to stop here, though. Let’s check out some of the more unusual seasons Derrick Williams had.

Season #120581: Things could actually get better for Williams. In this season, where Arizona falls in the Pac 10 semis and the 2nd round of the NCAA’s, Williams makes 15 of his next 16 attempts and puts the record out of reach at 75%, the best percentage of any of the simulations.

Reg    #28 3-4
Reg    #29 1-1
Reg    #30 0-0
Reg    #31 2-2
P10     R1 4-4
P10  Semis 2-2
NCAA    R1 1-1
NCAA    R2 2-2
Total     42-56 75.0%

Season #661026: On the flip side, in this sim Williams goes 2-for-31 down the stretch, although this includes runs to the Pac-10 and NCAA title games. I didn’t make any connection between Williams’ ability to hit shots and Arizona’s chance of advancing although there’s surely a loose one. However, the chance of Williams breaking the record is inversely related to Arizona’s number of games since the more attempts Williams has, the less likely it is he will keep his percentage above 63.4.

Reg    #28 0-0
Reg    #29 0-4
Reg    #30 0-1
Reg    #31 0-3
P10     R1 0-3
P10  Semis 0-1
P10  Final 0-3
NCAA    R1 0-4
NCAA    R2 0-1
NCAA   S16 1-2
NCAA    E8 0-4
NCAA    F4 0-4
NCAA Final 1-1
Total     29-71 40.8%

Season #6155: This was Williams’ worst effort for the rest of the season. He misses all 20 of his attempts.

Reg    #28 0-2
Reg    #29 0-2
Reg    #30 0-4
Reg    #31 0-2
P10     R1 0-2
P10  Semis 0-3
P10  Final 0-2
NCAA    R1 0-1
NCAA    R2 0-2
NCAA   S16 0-0
NCAA    E8 0-0
Total     27-60 45.0%

Season #254994: This was one of two seasons where Williams shuts it down. In both cases, the Wildcats didn’t win a tournament game.

Reg    #28 0-0
Reg    #29 0-0
Reg    #30 0-0
Reg    #31 0-0
P10     R1 0-0
NCAA    R1 0-0
Total     27-40 67.5%

Season #89420: Williams took the most shots in this season, finishing with 76 attempts. This is a total that would surely prevent him from threatening the record.

Reg    #28 2-4
Reg    #29 0-3
Reg    #30 2-3
Reg    #31 1-2
P10     R1 1-2
P10  Semis 0-2
P10  Final 2-4
NCAA    R1 1-4
NCAA    R2 0-1
NCAA   S16 0-1
NCAA    E8 2-3
NCAA    F4 2-3
NCAA Final 1-4
Total     41-76 53.9%

Derrick Williams continues his improbable attempt at immortality tonight at USC. It’s especially incredible considering that of the top 25 three-point shooting percentages since the arc became real, only three have occurred since 1995 and none since 2001. And he’s doing it with one more foot of distance than everyone else.