NBA Does the NBA play favourites - a FTr analysis

[ambchang]

So after watching Luka shoot 7 free throws in the 1st quarter yesterday, I thought to myself, "Is it because he's Luka, or is it because he's a Laker?", and so I spent this noon hacking out a regression model of a player's FTr, taking into account their shot profile (0-3/3-10/10-16/16-3pt/3pt) and their team.

I did a similar analysis back a few years during that Kobe-Nash-Dwight season where they were close to misisng the playoffs, only to come storming back. I noticed something and did an analysis, then confirmed that not only did the Lakers FTA increased dramatically during that stretch where they went from like 10th seed to 7th seed (don't remember exactly the seeding), but the team directly above them in the standings see their FTA DECREASE dramatically, until they are surpassed by the Lakers, then their FTA went back to normal. it was one of the most hilarious things I have seen, but we already knew what was going on.

Anways, some background:
Luka last season was traded from the Mavs to the Lakers. His FTr with the Mavs was .313, but increased to .445 once he became a Laker. So happened to Unibrow? Well, the opposite (or is that the same?) happened, his FTr was .423 with the Lakers, then dropped to .316 with the Mavs (only 9 games though). Speaking of Unibrow, his prime and most dominant was with the Pels, he scored close to the paint much more with the Pels/Hornets than he did with the Lakers, and yet the two seasons he had the highest FTr was with the Lakers. Go figure.

Rui Hachimura? .179 with the Wiz, then .235 with the Lakers. (the season he was traded). Ayton FTr has been cratering since he was with Portland (went from a regular low to mid .2s to low .1s, but mostly because he is playing like wuss away from the basket. This year so far, his FGA% is LOWER than he had last year with the Blazers, and yet his FTr went up from .128 to .172. So I am like ... does playing for the Lakers really give you more FTs?

So this is what I did. I looked up all player-team combinations from last year, and did a regression model of a player's FTr as a dependent variable, then the following as the independent variables: FGA% from 0-3/3-10/10-16/16-3P/3-P, and finally the team. (1 for belong to a certain team, 0 for not), so say Wemby will be 1 for Spurs but 0 for all other teams. This isn't the best as there are just too many boolean variables, but alas. The other problem is that my analysis pack only accepts up to 16 independent variables at a time, so with the 5 mandatory fields filled up by the shot profile, I have to divide up the model into 3 groups (ATL to GSW, HOU to NYK, and finally OKC to WAS), and there are issues with this as the coefficients to each batch is different even for the shot profile. I ran a fourth regression model without any team details as a reference.

Comparing the numbers, the intercepts are fairly reliable for all four batches, at around 0.00045, which basically means that you get 0 FTs with 0 shots, which is quite on the ball, batch 3 has 0.048, which is a bit high for my taste but not something I will lose sleep over. All four models have the shot profile having high absolute t-Stat numbers and low P-value numbers for 0-3 (0.00005 to 0.0003) and 3-10 (0.01 to 0.04), which basically shows the shot profile from close range has a large impact on the FTr, which isn't a surprise at all. Note that I am using the FTr and shot profile (% of attempts) and not the raw numbers, which means that an end of the bench guy who played 4 minutes all season will count as much as an all-star or even a superstar who get superstar calls. I did that on purpose as I wanted to look at impact of team, not players, so this will remove the bias of superstars skewing the numbers for a team.

I cannot, for the life of me, figure out why all shot profile, other than 16-3P, have +ve coefficients with the FTr, I would have thought the further you go, the lower the number gets and will be negative for anything 10+, but for 16-3P, only the 4th batch has a -ve number, but at the same time, the P-value is quite high for 3P (0.08 to 0.18) and 16-3P (0.20 to 0.31), which I am not surprised by as those should have lesser impact than say 0-3, which consistently showed numbers approaching 0. In other words, shots from 16+ feet doesn't have any significant impact on the FTr. So I am relatively comfortable with the model.

One final thing, 10-16 has by far the lowest P-value, whcih means it has the most signficant impact on the FTr AND it has the highest Coefficient, which means that it is closely tied. The Coefficient I can understand as these are just percentages. Most players have low FTr and low 10-16 shots, so they have a high Co-efficient. It doesn't mean that they are closely tied by any means. What I cannot get is why they have such a low P-value. (9.2 x 10^-6 to 5.2x10^-5), which are far lower than the 0-3 numbers. But overall, I am comfortable with the model itself.

Now to the teams.

 

[ambchang]

Overall the numbers indicate that there is a very low probability of a non-zero impact being on a particular team has on your FTr. In fact, only 1 single team has a P-value of less than 0.05 (The Wolves at 0.00011), which has a coefficient of 0.173, which is a huge deal. There is a 95% CI that if you are a Wolf, you FTr will increase between 0.085 to 0.260, which is an INSANELY high number. The ONLY team that has a +ve lower 95% bound were the Wolves, at 0.0854. I never would have thought that.

The only other team that has a P-value less than 0.25 are ...... the Lakers, and it has a coefficient of 0.05, which means that if you are a Laker, you have a 95% chance of shooting between 3% less to 13% more FTs than if you are not a Laker. Again the P-value is relatively high, but I would say it's not that low as it really should be close to 1.

I wanted to past the table in but wasn't able to, I will see if I can link it to a google sheet or something.

For those who are curious, the Spurs have a P-value of 0.598 and a co-efficient of -0.023.

While the P-values are low, I would like to point out teams with +ve co-efficients are DAL, GSW, HOU, IND, LAC, LAL, MEM, MIA, MIL, MIN, NOP, OKC, PHO, UTA AND WAS. So if there's smoke ......

I added another element by using minutes played as a proxy to see the "benefits" of a team gained through the entire 24-25 season. I felt this way we factor in the actual game plan impact based on minutes, but would still manage the bias in superstar calls accordingly. I am not sure if the logic is sound in this one so check me on it.

• I calculated the expected FTr of each individual player-team combination, then multiplied that by the number of minutes played
• I then calculated that weighted (by minutes) average for each team and compared it to the unweighted average of each team. The rationale is that the longer on the floor the more impact you have on the floor. My take is that FTr cannot be added but can be averaged.

I looked to see which team benefited the most by the difference between the actual FTr with the expected FTr.


The results are:

• Dallas had a pretty healthy lead as the #1 in increase in FTr compare to the 2nd team, Orlando. 0.0315 vs. 0.0254, it means that for every 1000 shots the Mavs took, they have 31.5 FTs more than what you would expect form them, and a 6 FT advantage over the Magic. Given they took 87.7 FGA as a team last year and shot 77% from the line, it translates to 2.8 more FTs and 2.1 PTs more a game. Extrapolating to 100 possessions for O/D/Net Ratings using pace, and everything else being equal, that pushed their ORtg and NetRtg up from -3.33 to -1.2 If Dallas was to get the expected FTr as the league average (including themselves), their ORTG and subsequently NRTG would have dropped to -3.33 , and that would have dropped their 19th ranked NETRtg last year to 24, which is somewhere between the 36-46 Suns and 30-52 Raptors, they don't get those ping pong ball combinations to get Cooper Flagg, bumping every one down a spot (well theoretically), which would have been ...... Atlanta's pick that was traded to the Spurs, and we'd have the #1 pick. But then we would be bumped up one spot and never have gotten Harper. Ironically, that spot would have likely be taken by the Mavs as that net rating likely would have had them below 34 wins as well. ahhh, the joys of parallel universes.
• #2 is Orlando, which enjoyed an increased FTr of 0.0253, which gave them a 1.69 points per game and NETRtg increase of 1.89, moving them from 17 to 20, bumping them up 3 spots.
• Spurs are #20 on the list, with a decreased FTr of 0.0067, which is minimiscle. Thi has a net rating impact of -2.8, which didn't move our rank in the league at all.
• Surprise surprise, the team with the most negative impact? OKC. Their weighted deviation meant their FTr dropped 0.0533, which is VERY impactful as it made them score 4 less points than they otherwise would have (4.94 less FTs a game). This would push their historical NetRtg even higher, from 12.8 to 16.85. I actually had to double check this to make sure. The thing is that even though Shai enjoyed an increase of FTr of an increase 0.12 based on his shot profile, high minutes players like Cason Wallace (-0.17), Aaron Wiggins (-0.12), Dort (-0.12), Hartenstein (-0.13), and Isaiah Joe (-0.08) more than offset that advantage Shai (and Chet, who was at +0.12) got. To be fair, Shai shot a hell lot more than all of them, so ....
• My favourite team, the Lakers, are ranked #6 with a +0.0170 increase over expected, giving them a 1.45 FTA and 1.14 PT advantage every game. This bumped up their NetRtg by 0.06, which bumped their NETRtg from 17th in the league to their actual 14th.
• The previous champs, the Wolves, is now only #8 after the rates are weighted by minutes. Still gave them a 0.84 PT advantage a game ad bumped their NRtg rank from #8 to #4.

Next, I will see if I have time to check the Mavs pre and post Doncic.

 

[ambchang]

@scott, if you have time, see if you have time to see what the hell I am talking about, and whether my approach is logical. Thanks.

 

[scott]

Will do! Look forward to digging into this over the weekend!

 

[scott]

I haven't had time to dig in too much, but I think it would be interesting to only look at active players who have played on the Lakers and another team, and then run a simple analysis of the delta on the FTr of those guys. You could do the same for other high profile teams (NYK, BOS, GSW). If you have time, it would be fascinating to do that across all teams and you could develop a "FTr Premium" for each team.

 

[Area 51.247]

Statistical analysis like this are difficult for me to wade through, although they are fascinating.

Thanks for trying to clear the fog from around a common preconception, that free throws are adjusted to benefit certain teams.