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[OC] How much money are VanVleet, Gallinari and Montrezl gonna get this offseason? Attempting to predict free agent contracts this offseason using machine learning

After attempting to predict the MIP using machine learning, I switched my focus to trying to predict this offseason's free agent contracts. I hope y'all enjoy! (There's a TL;DR at the bottom)


Day 1 of NBA free agency is by far the biggest day of the offseason for the league. It was a doozy last season, with seismic shifts in the league's power structure. Arguably 2 of the top 5 players (when healthy) in the league, as well as an additional 3 within the top 25, changed teams.
This year's class? Not as highly regarded as last year. Anthony Davis is the crown jewel, while Brandon Ingram is the best restricted free agent available. The hype of this class was further deflated when players like Kyle Lowry and Draymond Green signed extensions with their current teams.
What I wanted to do was predict what contracts this year's free agent class might get based off previous offseasons. Stars generally get star-type money, but in tiers below, contracts of comparable players usually come up in discussing contract value.


  • statistical data (regular season totals and cumulative advanced stats) from Basketball-Reference
    • I do understand that some players get paid on the strength of playoff performance
  • historical free agents (2016-2019) and salary cap history also from Basketball-Reference
  • 2020 free agents from Spotrac
  • historical contract info from Capology, Spotrac and Basketball-Insiders
    • Capology = main source, but inconsistent with min/near-min contracts
    • Spotrac requires a premium login to view contract cap hits beyond the last and current contracts, but the cash earnings are free to view
    • When player was near-minimum & played for multiple teams in one season, Basketball-Insiders had transaction history in team salary archives (needed player's first team of season)
    • set contract years to zero and salary to zero for players who went overseas, had explicitly non guaranteed first years in their contracts (training camp deals, two ways, ten days, exhibit 10s) or had blanks in their contract terms cell
    • included option years and partially guaranteed years in my calculation of contract years (looked at it as both player and team intending to see out the contract)

Preprocessing the Data

I started off with contract year stats, because there's anecdotal evidence that players exert more effort in their contract year. I initially wanted to use totals to bake in availability/body fragility, but the shortened season would cause the model to declare all players to be fragile and underestimate their contract. Stats other than games played, games started, and the advanced stats (OWS, DWS and VORP) were converted to per game. Percentages were left alone. Games played, games started, and the advanced stats were scaled to have a normal distribution (mean of 0 and standard deviation of 1).
In addition to using contract year stats, I summed the past two years and the contract year. Why did I settled on 3 years?
  • Players do get paid on past performance, so just using contract year stats was out of the question
  • 2 years opens up the possibility of a fluke year
    • Kawhi would have his nine game season bring down his averages significantly from his Raptors season: adding another year somewhat lessens this effect
  • On the other hand, it's quite unlikely that teams factor in stats from more than 4 years ago, a lot would have changed (the Knicks didn't pay Derrick Rose to recapture his form of his MVP year)
Another reason I settled on 3 years is that I can keep the same model for restricted free agents:
  • my thought is that the rookie year is a bonus: great if you did well, but doesn't matter in the grand scheme of things if you did poorly
  • For example, if Donovan Mitchell had a worse rookie year but had the same level of play that he has achieved in his second and third year (as well as next year), I highly doubt that Utah would offer Mitchell a significantly less amount of money due to a substandard rookie year
I performed the same processing on the three-year totals, using the three-year game total as the denominator for converting to per game. I had to calculate the three-year percentages, and also re-engineered the win shares per 48 minutes metric.
  • removed categories that were linear combinations of one another (total rebounds = offensive + defensive rebounds)
  • kept age and experience as predictor variables, but removed position because I felt it would ultimately reflect in the stats

Data Visualization

Relationship between targets (first year salary as % of cap and contract years)
  • box and whisker with transparent layer of actual points (added random variation to see all points)
  • correlation coefficient is 0.77 (strongly and positively correlated)
  • median value of first year cap % (middle line in each box) increases w/increase in contract length
Relationship between win shares as first year salary as % of cap
  • shouldn't be too groundbreaking: better players get paid more
Distribution of contract length by offseason
  • no surprise that as contract length increases, the percent of contracts of that length given out decreases
  • in 2016, the amount of players who didn't receive contracts was lower than the amount who received 1, 2, or 4 year contracts
    • 2016 was the year the salary cap spiked from $70 million to $94 million
    • Similar to a lot of people with new-found money, teams spent somewhat recklessly.

Dealing w/Target Correlation

As mentioned, the target variables are correlated with a Pearson correlation coefficient of 0.77. My method to combat this:
  • predict one target first without the other as a predictor
  • choose the best model (be that a single model or an ensemble of multiple models)
  • use the first target's predictions as an input to predict the second target
So I will have a model that predicts years first and salary second, as well as a model that predicts salary first and years second. I know it's not the greatest method (correlation does not imply causation!), and I'm open to hear alternative ways y'all would have gone about it!
One potential problem is compounding errors. If there's an incorrect year prediction, it might lead to an incorrect salary prediction and vice versa.

Algorithms to Train

  • a linear regression model as a baseline
  • a k-nearest neighbors model: take the distance between the statistics of two players (the absolute value of the difference) and then take the average of the outcome variable of the k nearest neighbours
A very simple example:
Player PPG RPG Contract
A 25 7 4 yrs, $90 million
B 24 8 ?
C 6 0.3 1 yr, $2 million
D 5 0.5 ?
With a 1 nearest neighbour model, you can clearly see that B is most similar to A, and D is most similar to C. Therefore, B's predicted contract is 4 years and $90 million, and D's predicted contract is 1 year and $2 million.
  • a decision tree model: maybe as a player passes certain statistical thresholds, their contract increases?
    • only using for predicting the contract years; since there are so many different salary percentages, a solitary decision tree would either be useless or far too complicated
  • two random forest models: better than decision trees in that they reduce instability by averaging multiple trees
    • unfortunately, the cost is we don't get an easily interpretable tree
  • a support vector machine: attempts to separate classes with a hyperplane
    • support vectors are the points closest to the hyperplane, named as such because the hyperplane would change if those points were removed
    • Here's an image from Wikipedia.svg) that I believe succinctly explains SVMs

Testing the Models

Years First, Salary Second

years performance metrics
  • Mean absolute error is the measure of the average difference between forecasts, while the residual mean squared error penalizes large errors
  • The random forests provide by far the best performance, being above 80% accuracy when no other model is above 60%. However, they have a hard time distinguishing max contract year players.
    • This is somewhat understandable, as the fifth year is only accessible to players resigning with their current team.
    • The models could get confused seeing similar players in stats, but one signed for five years and one signed for four.
To alleviate this, I propose that if a player is predicted by ANY model to be a 5 year player, their contract year prediction is 5. Else, use a median of Rborist, ranger and SVM.
Why am I including SVM? Well, it has the best performance among the other models. I’m assuming that the random forest models will generally agree with each other. In the off chance they don’t, I’ll rely on the SVM to break the tie.
years decision tree
The decision tree maximizes its prediction when a player does all of the following:
  • has above average offensive win shares in the contract year
  • plays more than 28 minutes per game in the contract year
  • shoots better than 41% from the field in the contract year
  • has less than 9 years of experience
The decision tree minimizes its prediction when a player does all of the following:
  • has below average offensive win shares in the contract year
  • has at most slightly above average defensive win shares in the contract year
  • steals the ball less than 0.56 times per game in the contract year
  • is an unrestricted free agent
  • has played almost half a standard deviation less games than the average in the last 3 years
salary performance metrics
  • With the MAEs being relatively similar, I’ll take the median of the models.

Salary First, Years Second

salary performance metrics
  • The MAE range for the salary-first model is much smaller than the equivalent for the salary second model.
  • I’ll take the median, as I did for the previous.
years performance metrics
  • All models achieved at least the same if not a better correct prediction percentage than when predicting years first.
  • The number of max year predictions has substantially increased (and in the linear model’s case, has outstripped the actual number of max contracts given out).
  • I’ll take the median of all models except KNN, which has the lowest prediction accuracy by around 8%
years decision tree
  • The singular decision tree again has trouble with predicting max contract length.
  • Salary makes up 50% (4 of 8) of the decisions in the tree.
  • The decision tree minimizes its prediction when a player has a predicted salary of less than 0.76% of the salary cap.
  • The decision tree maximizes its prediction when a player is less than 31 years old and their predicted salary is above 16% of the cap.

Evaluating the Models

Here's a google sheet of all predictions separated by whether a player had a player option or not!
  • Totals are based on a $115 million salary cap (might not happen, but is a concrete number we have at our disposal) and 5% annual raises

Selected Player Option Decisions

I was unsure how to deal with club options, but players who decline player options become unrestricted free agents.
player Y1S2 Cap % yrs_Y1S2 total_Y1S2 S1Y2 Cap % yrs_S1Y2 total_S1Y2 2021 Option
Gordon Hayward 0.1788988921 3 64.86 0.1812429743 3 65.71 34.19
Andre Drummond 0.2221571423 3 80.54 0.2000980177 4 99.18 28.75
Anthony Davis 0.3014811978 5 191.58 0.2868035625 3 103.98 28.75
Otto Porter 0.08297334043 2 19.56 0.07925015245 2 18.68 28.49
DeMar DeRozan 0.2781873551 3 100.85 0.2657556943 3 96.35 27.74
Nicolas Batum 0.01857416549 1 2.14 0.02604507845 1 3 27.13
Evan Fournier 0.213951204 4 106.05 0.1969257167 4 97.61 17
James Johnson 0.02424448669 1 2.79 0.03168259373 1 3.64 15.83
Jerami Grant 0.132122261 3 47.9 0.1139293428 3 41.3 9.35
Stanley Johnson 0.01658695123 1 1.91 0 0 0 3.8
While some might be surprised at the DeRozan and Drummond projections, we have to note that the model doesn't take into account intangibles like playing reputation, team fit, or willingness to take a reduced salary to be on a championship contender.
If Anthony Davis re-signs with the Lakers, he is eligible for eight percent raises rather than five. That would bring the Y1S2 total to $202 million, which is exactly what he is eligible for. In terms of the three year projection, Davis could sign that shorter contract with the last year being an option in order to be eligible for the 35% max contract after 10 years of service (but the model wouldn't know that).
Jerami Grant and surprisingly (to me at least) Evan Fournier look like players set to cash in after declining their option. Players like Nicolas Batum, James Johnson, Otto Porter and Stanley Johnson (who's predicted to be out of the league by the S1Y2 model) would be wise to accept their option.

Selected Free Agents

player Y1S2 Cap % yrs_Y1S2 total_Y1S2 S1Y2 Cap % yrs_S1Y2 total_S1Y2
Brandon Ingram 0.2548324081 4 126.31 0.2465662829 4 122.21
Danilo Gallinari 0.2173187706 3 78.79 0.2149018106 3 77.91
Fred VanVleet 0.1961214299 4 97.21 0.1888455092 4 93.6
Montrezl Harrell 0.19201499 3 69.61 0.1782262995 4 88.34
Hassan Whiteside 0.1941521099 3 70.39 0.1723290935 3 62.48
Assuming Brandon Ingram (a first-time All-Star this season) doesn't make one of the three All-NBA teams, his first year contract salary is capped at 25%, which is right in line with predictions. However, I (among many others) expect Ingram to get the full five year extension.
The Heat wanted to acquire Danilo Gallinari from the Thunder this trade deadline, but ultimately were unable to broker a deal. Gallinari's career has been marred by injuries, but he has played over 80% of games the past two seasons. He's averaging 19 points per game this year, on 44% field goal shooting and 40% three-point shooting.
After his breakout in last year's Eastern Conference Finals and NBA Finals, Fred VanVleet has blossomed again in a starting role this season. Even so, Masai Ujiri and Bobby Webster might balk at paying him $24-25 million per year.
Montrezl Harrell and Hassan Whiteside are the first cases of dissension between the two models. The S1Y2 model projects Harrell to get 4 years, while the Y1S2 model only projects three. For Whiteside, the difference is almost 8 million dollars less in salary under S1Y2.
player Y1S2 Cap % yrs_Y1S2 total_Y1S2 S1Y2 Cap % yrs_S1Y2 total_S1Y2
Marcus Morris 0.1675722624 3 60.75 0.1587575186 3 57.56
Joe Harris 0.1539417297 3 55.81 0.1586893002 3 57.53
Serge Ibaka 0.1536284642 3 55.7 0.1416514857 3 51.35
Bogdan Bogdanović 0.1284454435 3 46.57 0.1216267861 3 44.09
Jordan Clarkson 0.1357167335 3 49.2 0.1062462145 3 38.52
Marcus Morris reneged on a verbal 2-year, $20 million contract with the Spurs last offseason to sign a 1-year, $20 million deal with the Knicks. He was the focal point of the Knicks offense and a hot commodity at the trade deadline, ultimately ending up with the championship-contending Clippers.
In February, Zach Lowe on his Lowe Post podcast thought that Joe Harris had a chance to double his current salary of $8 million. The models are even more optimistic, projecting his first year salary as over $17 million.
Bogdan Bogdanovic has been mentioned as the second-best RFA in the class. He might be squeezed out of Sacramento, considering the recent contracts to Buddy Hield and Harrison Barnes as well as upcoming contracts to De'Aaron Fox and Marvin Bagley III.
Jordan Clarkson has the largest discrepancy in salary ($11 million) between the two models.
player Y1S2 Cap % yrs_Y1S2 total_Y1S2 S1Y2 Cap % yrs_S1Y2 total_S1Y2
Dāvis Bertāns 0.1170676039 3 42.44 0.1080289004 3 39.16
Goran Dragić 0.1030787964 2 24.3 0.1104918333 2 26.05
Dario Šarić 0.1045436656 3 37.9 0.1021354069 3 37.03
Christian Wood 0.1121053606 3 40.64 0.0925855695 3 33.57
Derrick Favors 0.09816080257 2 23.14 0.1064310171 3 38.59
Davis Bertans has shot the lights out this season, earning himself a raise over his current salary of $7 million.
Christian Wood has flashed star-like potential since being inserted into the starting lineup in place of the departed Andre Drummond. But the key here is 12 games started. Wood played limited minutes in the first four months of the season. His contract situation, as well as that of Malik Beasley (who flourished after being traded to Minnesota mid-season), are intriguing to say the least.

Limitations, Methodology Changes and Future Work

  • unable to quantify intangibles like playing reputation, team fit, or willingness to take a reduced salary to be on a championship contender
  • also can’t determine which team will sign which player
    • highly depends on a sequence of events: if Team A signs this player, they don't have enough money to resign Player B, who then goes to Team C for less money, etc
  • due to the shortened season and the uncertainty of the cap, higher-tier players might take shorter deals to give them more flexibility
Methodology Changes
  • maybe I should have predicted them as a tuple instead of sequentially
    • unfortunately, caret doesn't have that capability of multi-target regression
  • maybe should have implemented a time factor or weighted recent years more heavily, as team decision makers may have gotten smarter
  • wanted the models themselves to perform feature selection and determine what the most important variables were
Future Work
  • looking at the contract years as a classification problem with 6 classes (0, 1, 2, 3, 4, 5)
  • try more models, like boosting (in which models are added sequentially, with later models in the sequence attempting to correct the errors of earlier models)
  • predicting a third target: whether a contract will end in an option year
    • Star players are more likely to demand the last year of their contract as a player option in order to take ownership of their future.


  • Attempted to use machine learning on NBA free agents from 2016-2019 to predict contract length & first year salary as % of the salary cap for 2020 free agents
  • Used contract year stats as well as summed last-three-year stats (converted to per game)
    • games played and cumulative advanced stats (WS & VORP) were scaled due to the shortened season
  • since targets were correlated, I predicted one target first and then used its predictions to predict the second target
    • Six models were tested: linear, k-nearest-neighbors, decision tree, two random forest algorithms and a support vector machine
  • Anthony Davis is the only player predicted to get a five year deal
  • Models can't quantify intangibles like playing reputation, team fit, or willingness to take a reduced salary to be on a championship contender; also star players more likely to take shorter deals to maintain flexibility in this uncertain season
I did the analysis in R, and the GitHub link is here. Hope y'all enjoyed this!
submitted by cilantro_samosa to nbadiscussion


Game Ready Driver 451.67 FAQ/Discussion

Game Ready Driver 451.67 has been released.

New feature and fixes in driver 451.67:

Game Ready - This new Game Ready Driver provides the latest performance optimizations, profiles, and bug fixes for Death Stranding. In addition, this release also provides optimal support for Horizon Zero Dawn: Complete Edition and F1 2020.
G-Sync Compatible Display - Added the following G-Sync Compatible Display:
  • Dell S2721HGF
  • Dell S2721DGF
  • Lenovo G25-10
Game Ready Driver Fixes (For full list of fixes please check out release notes)
  • The refresh rate of 144Hz-capable HDMI displays cannot be set above 120 Hz. [3038540]
  • [Kepler GPUs]: With SLI/multi-GPU and G-SYNC enabled, TDRs may occur soon after launching an application. [200628981]
  • [Detroit: Become Human]: The game may randomly crash. [3037846]
  • [Adobe Premiere]: Adjustments in Lumetri color panel causes video to appear noisy. [3038602]
  • [Notebook][GeForce GTX 1050 Ti]: Blue-screen crash, application hang, or system hang may occur. [3038621]
  • [Notebook][The Witcher 3 WILD HUNT]: The game remains minimized when the NVIDIA Control Panel >3D Settings >Manage Display Mode is set to Automatic or Optimus, and cannot be restored to full screen. [200628973]
  • [Notebook][G-SYNC]: Graphical corruption occurs when windowed G-SYNC+V-Sync is On while running applications in Clone/Duplicate mode. [200628911]
  • [Notebook]: LVDS-display goes blank upon rebooting the system after driver installation on some systems. [200627952]
Game Ready Driver Important Open Issues (For full list of open issues please check out release notes)
  • Windows 7 Only [Notebook][H-Clone]: With the integrated graphics processor as the clone source, display settings cannot be changed from the NVIDIA Control Panel. [200594188]
  • Windows 10 Only [Mechwarrior 5 DirectX 12]: The game crashes randomly with TDR and "Video driver crashed and was reset” error. [200634109]
  • Windows 10 Only [Shadow of the Tomb Raider][DirectX 12]: The game may crash when launched if Hardwareaccelerated GPU scheduling is enabled. [3037544]
    • To workaround, disable Hardware-accelerated GPU scheduling.
  • Windows 10 Only [Horizon Zero Dawn Complete][DirectX 12]: Colored corruption occurs during the game-load menu if Image Sharpening is enabled. [200633655]
  • Windows 10 Only Several games randomly freeze for a few seconds during gameplay. Affected games include Assassin's Creed Origins, Planetside 2, Assassin’s Creed III, Assassin’s Creed Odyssey, and Assassin’s Creed Syndicate. [3038632]
  • Windows 10 Only [Sunset Overdrive]: The game may display random green corruption if Depth of Field is enabled from in-game settings. [2750770]
  • Windows 10 Only [VR}: HDCP errors occur with Valve Index VR. [2967616]
  • Windows 10 Only [Call of Duty: Modern Warfare]: Color banding can occur in the game after enabling Image Sharpening from the NVIDIA Control Panel. [2889337/3028436]
  • Windows 10 Only [Call of Duty - Warzone]: Freestyle does not work. (200593020)
  • Windows 10 Only [Forza Motorsport 7]: The curb may display a black strip during a race on certain tracks. [2781776]
  • Windows 10 Only [Zombie Army: Dead War 4][Ansel/Freestyle]: The Ansel & Freestyle tabs are unselectable. [2810884]
  • Windows 10 Only [Tom Clancy's Rainbow Six Siege][Vulkan][G-SYNC]: When playing the game in Vulkan mode with G-SYNC enabled, flickering occurs after switching the game between full-screen and windowed mode.[200578641]
    • To work around, either disable G-SYNC or play using an API other than Vulkan.
  • Windows 10 Only [Notebook]: Some Pascal-based notebooks w/ high refresh rate displays may randomly drop to 60Hz during gameplay. [3009452]

Driver Downloads and Tools

Driver Download Page: Nvidia Download Page
Latest Game Ready Driver: 451.67 WHQL
Latest Studio Driver: 451.48 WHQL
DDU Download: Source 1 or Source 2
DDU Guide: Guide Here
DDU/WagnardSoft Patreon: Link Here
Documentation: Game Ready Driver 451.67 Release Notes
Control Panel User Guide: Download here
NVIDIA GeForce Driver Forum for 451.67: TBD
RodroG's Turing Driver Benchmark: TBD
Computermaster's Pascal Driver Benchmark: TBD
Lokkenjp's Pascal Driver Benchmark: TBD
NVIDIA Discord Driver Feedback for 451.67: Invite Link Here

Having Issues with your driver? Read here!

Before you start - Make sure you Submit Feedback for your Nvidia Driver Issue
There is only one real way for any of these problems to get solved, and that’s if the Driver Team at Nvidia knows what those problems are.So in order for them to know what’s going on it would be good for any users who are having problems with the drivers to Submit Feedback to Nvidia. A guide to the information that is needed to submit feedback can be found here.
Additionally, if you see someone having the same issue you are having in this thread, reply and mention you are having the same issue. The more people that are affected by a particular bug, the higher the priority that bug will receive from NVIDIA!!
Common Troubleshooting Steps
  • If you are having issue installing the driver for GTX 1080/1070/1060 on Windows 10, make sure you are on the latest build for May 2019 Update (Version 1903). If you are on the older version/build (e.g. Version 1507/Build 10240), you need to update your windows. Press Windows Key + R and type winver to check your build version.
  • Please visit the following link for DDU guide which contains full detailed information on how to do Fresh Driver Install.
  • If your driver still crashes after DDU reinstall, try going to Go to Nvidia Control Panel -> Managed 3D Settings -> Power Management Mode: Prefer Maximum Performance
If it still crashes, we have a few other troubleshooting steps but this is fairly involved and you should not do it if you do not feel comfortable. Proceed below at your own risk:
  • A lot of driver crashing is caused by Windows TDR issue. There is a huge post on GeForce forum about this here. This post dated back to 2009 (Thanks Microsoft) and it can affect both Nvidia and AMD cards.
  • Unfortunately this issue can be caused by many different things so it’s difficult to pin down. However, editing the windows registry might solve the problem.
  • Additionally, there is also a tool made by Wagnard (maker of DDU) that can be used to change this TDR value. Download here. Note that I have not personally tested this tool.
If you are still having issue at this point, visit GeForce Forum for support or contact your manufacturer for RMA.
Common Questions
  • Is it safe to upgrade to ? Fact of the matter is that the result will differ person by person due to different configurations. The only way to know is to try it yourself. My rule of thumb is to wait a few days. If there’s no confirmed widespread issue, I would try the new driver.
Bear in mind that people who have no issues tend to not post on Reddit or forums. Unless there is significant coverage about specific driver issue, chances are they are fine. Try it yourself and you can always DDU and reinstall old driver if needed.
  • My color is washed out after upgrading/installing driver. Help! Try going to the Nvidia Control Panel -> Change Resolution -> Scroll all the way down -> Output Dynamic Range = FULL.
  • My game is stuttering when processing physics calculation Try going to the Nvidia Control Panel and to the Surround and PhysX settings and ensure the PhysX processor is set to your GPU
  • What does the new Power Management option “Optimal Power” means? How does this differ from Adaptive? The new power management mode is related to what was said in the Geforce GTX 1080 keynote video. To further reduce power consumption while the computer is idle and nothing is changing on the screen, the driver will not make the GPU render a new frame; the driver will get the one (already rendered) frame from the framebuffer and output directly to monitor.

Remember, driver codes are extremely complex and there are billions of different possible configurations. The software will not be perfect and there will be issues for some people.For a more comprehensive list of open issues, please take a look at the Release Notes. Again, I encourage folks who installed the driver to post their experience here... good or bad.

submitted by Nestledrink to nvidia