NBA Salary Predictions

• Goal: Use different modeling techniques to try and accurately predict what the yearly salary of a player would be based on as seasonal player stats from the last 20 years
  • Hidden Goal - To be that guy that uses advanced Machine Learning models to predict salary worth when a friend complains that the Bucks overpaid for a player

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Getting the Data

• Was able to get game/season stats using Sports Reference API that pulls from Sportsreference.com and it took a lot of wrangling to pull together

  • Feature Descriptions

    • Some strange categories that end with _percentage (besides Field-Goals) are referring to {Stat} per 100 possessions
    • Features include: assist_percentage, block_percentage, defensive_rebound_percentage, offensive_rebound_percentage, steal_percentage, total_rebound_percentage, turnover_percentage, usage_percentage

• Sports Reference API no longer is working (for getting Teams data anyways), might want to look into just connecting with this dataset from Wyatt Walsh

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Exploratory Data Analysis

• These functions that were partially taken from this Towards DataScience Article and also modified by myself to get all the info I needed to create created two DataFrames:

  • Season DataFrame (Mainly used this one):

    • 61 Columns (29 null columns that were removed)
    • Target Feature = Avg_Salary
    • Salary gives career earnings in total up to that season, so for the target value I divided the Salary by the amount of years played at that point
    • 13,235 Rows (Season data for players: Vince Carter claims most with 22 years)
    • 2,033 Unique Players

  • Career DataFrame (Used mostly for EDA):

    • 61 Columns (29 null columns that were removed)
    • 2,040 Rows
    • 2,033 Unique Players (Down to 1923 players after removing players without salaries)

• Highest Paid: LeBron James $17.2M

• Lowest Paid: Kirk Penney $4.5K

Trying to get an idea of what features contribute to a higher salary

• Showing average salaries over time:

• Features compared to Average Salary:

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Linear Regression

• Training:

  • Mean absolute error = 240,457.84
  • Mean squared error = 127,441,167,125.65
  • Median absolute error = 172,839.44
  • Explain variance score = 0.42
  • R2 score = 0.42

• Residuals plot:

• Training Plot:

• Testing:

  • Mean absolute error = 234,554.68
  • Mean squared error = 123,912,975,078.46
  • Median absolute error = 169,628.39
  • Explain variance score = 0.44
  • R2 score = 0.44

• Residuals plot ():

• Test Plot:

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Applying Neural Network to predict Salary of player

• Initially just tried a simple DNN that used 3 Dense Relu layers and msle as log function, ran over 10,000 epochs, results are shown below:

• Then tried running multiple DNN's using the following loss Functions:

loss_functions = ['mae', 'mse', 'mape', 'msle', 'huber', 'logcosh']

• Model features (first_hidden is 20% of the numbers of rows in X_train):

def build_and_compile_model(loss):
  model = keras.Sequential([
      layers.Dense(first_hidden, activation='relu', input_shape=[X_train.shape[1]]),
      layers.Dense(first_hidden//4, activation='relu'),
      layers.Dense(first_hidden//16, activation='relu'),
      layers.Dense(first_hidden//32, activation='relu'),
      layers.Dense(first_hidden//64, activation='relu'),
      layers.Dense(1, activation='linear')
  ])

  model.compile(loss=loss,optimizer=tf.keras.optimizers.Adam(0.0001),
                metrics=['mae'])
  return model

• Results of Training over 500 epochs:

mae had a final val_loss of 202289.53125

mse had a final val_loss of 142236286976.0 # Squared error: 377,142.26

mape had a final val_loss of 68.57567596435547 # Percentage

msle had a final val_loss of 154.00787353515625 # Log error

huber had a final val_loss of 219148.109375

logcosh had a final val_loss of 201331.84375

• Log_cosh ends up slightly edging out the with it's final val_loss over mae

• In practice it seems that these models consistently predict about 7 times less than actual for your average player & up to 18 times less for those outlier players with a super max deal

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Who shall we test with?

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Conclusions

• Without doing things like clustering, identifying salary limitations of the team that the player is on and removing outliers it's a bit hard to make a super accurate prediction
• A DNN will make a more accurate prediction than simple linear regression, however for most players it's really not going to make a reasonable difference

References

• Used functions to create DataFrames from this Towards DataScience Article

• Players that are not currently playing do not have contract data, but can find contracts using spotrac

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If only I had more time...

• Cluster NBA players into different positional categories based off season stats, then train Neural Network to predict something like win percentage (or perhaps have it categorize into something like [Great Team, Good Team, Okay Team, Bad Team, Awful Team])
  • Unfortunately the results I was getting using KMeans Clustering don't make any sense to me. Tried using both career totals, per game averages and scaling the data, but KMeans was suggesting between 2-3 clusters & decided that wouldn't make for a good proof of concept, hence the pivot to salary predictions
  • Regardless, here are some Scree Plots I'd created using PCA:

• And one of many Horizontal Bar Charts of the most common suggestions of clusters