An Analytical Evaluation of Jaden Ivey’s Shooting Improvement

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Jaden Ivey has taken a massive leap in his sophomore season, as he has become one of the best players in college basketball. Ivey has bee on an incredible journey the past couple of years, going from the 89th ranked recruit and not starting the first half of last season to now being arguably a top-5 player in college basketball. While he has certainly improved in many facets of his game, an area which a lot of people like to point to is his 3-point shooting improvement.

Shooting is one of the most misunderstood areas in all of basketball from the perspective of the average fan. A large reason for this is the misunderstanding of what a subsequent sample size is. Per research done by Daryl Blackport, 3-point shooting percentage does not stabilize until 750 attempts. Even at 750 attempts, a player’s 3-point shooting percentage is about 50% because of their shooting ability and 50% because of randomness/luck. In college basketball, no player has ever even gotten close to 750 attempts in a season (most was 394 by Marshall Henderson).

Another reason 3-point shooting percentages aren’t as robust of a measurement of shooting talent as people think is because it doesn’t take into account context. Not all 3-point shots are the same. Raw 3-point percentage doesn’t take into account the fact that self-created shots or contested shots are more difficult than catch and shoot or open shots. Raw 3-point percentage also doesn’t take into account distance, which is especially harmful to players that shoot a few more end of half heaves than others.

Last season, Jaden Ivey shot 25.8% on 97 attempts. This season, Ivey has shot 43.8% on 73 attempts. While the 18% improvement has been enough evidence for most to crown him as a much improved shooter, I’m a little bit more hesitant to do so. Remember, 750 attempts is the number at which 3-point percentage somewhat stabilizes. Ivey is now at 170 attempts for his career, which is not nearly enough to make any large conclusions.

While the shooting percentage has significantly improved for Ivey, some of the general indicators have not. Free throw percentage is generally a better proxy for shooting talent than actual 3-point percentage for NBA Draft evaluation because it usually has a much larger sample and there is far less variance in the statistic. Ivey’s free throw percentage has slightly decreased from last season, going from 72.6% to 71.4%. Another helpful metric is 3-point attempts per possession, as better shooters will generally take more shots. Ivey is actually shooting fewer 3s per 100 possessions than last season despite the larger role. He is shooting 10.0 3s per 100 possessions this season, and last season he was at 10.5.

Before further exploring Jaden Ivey’s shooting percentage improvement, it is important to see if the context of his shots are the same from last season to this season. This is difficult to do without access to data on splits of open vs. contested shots, but we can use some different indicators. Whether or not a 3-pointer was assisted can be a decent indicator of shot quality. Last season, 84.0% of Jaden Ivey’s 3-point makes were assisted. This season that number is slightly down to 81.4%, which is not significant enough of a difference to make a determination on the quality of shots he is taking. We can also look at Ivey’s shot charts to see if there is a major difference in where he is shooting 3’s from:

Chart per cbbanlytics | Hexagon size indicates volume of shots | Blue to red indicates increasing accuracy

Based on the two shot charts, there doesn’t seem to be a major difference in location of his shots. Because the amount of self-created shots and the locations of the shots are similar, we can assume that the 3-point shot profile for Ivey is similar based on the data we have.

Lastly before digging into the numbers more, it’s important to look at Ivey’s shooting mechanics to see if we can spot a significant change. The video below shows his mechanics from this season to last season:

Ivey’s mechanics look very similar from last year to this year. There is a very slight difference in the timing of his dip, as he has been better at planting his right foot when he’s at the bottom of his dip. The release point looks to be the same, and the upward motion of his arms and angle of his elbow on the shot look the same. I will also mention that his lower body is really inconsistent on his jumper, which could lead to inconsistent results.

To dive deeper into Ivey’s shooting numbers, I used simulations to see the likelihood that Jaden Ivey has not improved at all as a shooter. I first ran simulations for Ivey’s first season, in which he took 97 attempts. To do this, I simulated 97 shots 10,000 times for each 3-point percentage from 20 to 50. The goal of this was to see the chances of shooting 25.8% or worse from 3 at different percentages. Here were the results:

The graph shows the chance that a shooter of different percentages could shoot 25.8% or under. For example, a 30% 3-point shooter has about a 20% chance of shooting 25.8% or worse on 97 attempts.

Our next simulation looks at the chances of shooting 43.8% or greater on 73 attempts with a variety of different percentages:

To see if the chances that Ivey did not improve as a shooter at all, we can simply multiply the odds of shooting 25.8% or worse by the odds of shooting 43.8% or better at each shooting percentage we simulated. Results are shown in a table below:

As you can see, the most likely scenario if Ivey had not improved as a shooter is that he is a 33% 3-point shooter. However, the chances of a 33% 3-point shooter making 25.8% or less of their first 97 attempts and 43.8% or more on his next 73 attempts are just 0.29%. This means that it is likely Ivey is an improved shooter this season. Next, I wanted to look at how much he has improved.

The graph above shows the percent chance of shooting 25.8% or worse and shooting 43.8% or better at different amounts of improvement in 3-point percentage. For example, a player that improves their 3-point shooting 10% from one season to the next has about a 7.5% chance of shooting less than 25.8% their first season and greater than 43.8% the next season. For a player to have that large of a gap in shooting percentage is an incredible anomaly, even if Ivey did improve as a shooter by 18% (the chances of seeing that season-to-season improvement would only be around 30%). The most likely scenario to me is that Ivey was not as bad as a 25.8% shooter, nor is he as good as a 43.8% shooter. Both are very noisy numbers on a small sample of shots, so determining how much better Ivey has gotten is very tricky (and… impossible?).

While this article has mostly focused on looking at the past, isn’t it more important to look at the future? What is Jaden Ivey as a shooter right now? In order to attempt and predict this, we are going to use Kostya Medvedovsky padding method. The padding method simply adds a number of average 3-point attempts to the existing sample of a players’ attempts in order to cancel out the noise in their own percentages. As the sample size rises, the padding has less of an effect on the predicted 3-point percentage. The formula for the padding method is shown below:

expected_fg3_pct = (3PM + X*league_average_fg3_pct)/(3PA + X)

For Jaden Ivey, the formula would be as follows:

expected_fg3_pct = (57 + 240*0.331)/(170 + 240) = 33.3%

*The linked article explains why X is 240 | Average 3-point percentage in college is 33.1% as of the 2019-20 season

Padding is a value mechanism for evaluating small samples because we see far less variance over smaller samples for stats such as 3-point percentage. The chart below shows Ivey’s raw 3-point percentage over time in green, and his padded expected 3-point percentage in orange:

As you can see, the padded percentage stays much more constant throughout Ivey’s career than just his raw 3-point percentage.

If we wanted to use the padding method for Jaden Ivey as a 3-point shooter using all the data we have available (High School, FIBA U19, College), Ivey’s shooting projection would be as follows:

expected_fg3_pct = (189 + 240*0.331)/(506 + 240) = 36.0%

Since we said that it was likely that Jaden Ivey improved as a shooter during the offseason, it would be reasonable to use his shooting numbers from this season to make a prediction:

expected_fg3_pct = (32 + 240*0.331)/(73 + 240) = 35.6%

Using the difference of Ivey’s padded expected 3-point percentage from last season to this season, we can try and calculate how much he has actually improved as a shooter:

expected_fg3_pct _diff = (32 + 240*0.331)/(73 + 240) – (25 + 240*0.331)/(97 + 240) = +4.61

Is this measurement perfect? Absolutely not. +4.61 is simply a measurement in the change of expected 3-point percentage from last season to this season, which is not the same as his improvement. It is more so giving us better numbers to compare against each other. A 4.61% improvement is much more reasonable than a 18.0% improvement, and an improvement of that magnitude using the padding method is a very hopeful sign for Ivey’s shooting projection going forward.

The larger scope of this article is to get a sense of how small sample sizes can drastically impact our perception of players and even teams. From a game to game and even season to season level, basic statistics which are generally freely referenced have major sampling flaws that rarely get discussed. A sample of one 40 minute game is not enough to perform an evaluation on a team. Even a sample of 35 different games is not enough to perform a proper evaluation based on record. One of the largest issues in sports analytics in general is lack of proper sample size, and it impacts far more than just 3-point percentage.

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