Teams in the NBA are always looking to get an edge over their opponent. They will seize opportunity of any chance to gain a competitive advantage over their rivals in order to bring their city a championship. Free agency is one event on the basketball calendar that these teams use to bolster their squads and complete their roster puzzle. They can use free agency to sign superstars or critical role players. However, the real winners of free agency are those who can find productive players for little money. Signing players to bargain deals can help a team exceed expectations while using little cap space, allowing them to contend with financial flexibility. Additionally, smart free agent additions can allow an already contending team to upgrade with the small amount of money they have available. This brings the question, who are the best value free agents this year and how do we find them? (Note: If you don’t care about the methods, skip down to the findings section.)

## Methods

In order to start finding the best value free agents, I had to figure out a way to project each upcoming free agent’s deal they would sign. To do this, I gathered the stats of players in their contract year, as well as their new contract average salary. Ideally, I would use the player’s contract year stats to find the projected salary amount in one step, but one factor which prevents this is the changing NBA salary cap. The salary cap has increased at a rate disproportional to inflation, making an adjustment to the average salary of a deal necessary. To control this, I calculated each past free agent’s Relative Cap Percentage (RCP), which is found by taking their average salary divided the NBA salary cap for the year that they signed.

After adjusting for the salary cap, I used a multiple regression model to project each player’s RCP in their new deal. Then, I tested out several models, finally deciding on one which used 8 inputs, including basic stats such as age and minutes played as well as advanced stats such as PER and DBPM. The next step was to apply the model to the 2020 free agents. I used $115 million as the projected salary cap for next season (although no one really knows what it will be due to the coronavirus interrupting the NBA season). Finally, I found each upcoming free agent’s (exluding those with a pending team/player option) projected salary by multiplying the projected RCP by the projected salary cap.

The next step was to find the best value free agents, meaning those who will most likely exceed the value of their salary. For this step, I needed a measure of each player’s total value. I chose win shares per 82 games, a metric that attempts to assign the number of wins each player is responsible for, for this task. Since win shares have a bias towards specific positions (primarily centers), I standardized them for each position. Then, in order to take regression to the mean and age into account, a used a linear regression predicting the next year’s projected standardized win shares with the previous year’s standardized win shares per 82 games and age as inputs. Lastly, I converted the standardized value back into the win shares units by multiplying times the standard deviation and adding the mean.

The final steps of the project were to plot the predicted win shares versus the projected salary. While I thought using win shares per million dollars would have been a logical way to evaluate the players, I found that they do not both increase at the same ratio. For example, a player with a $10 million projected salary is expected to have 4 win shares per 82 (0.4 WS/$million), while a player with $20 million projected salary is expected to have about 6.5 win shares per 82 (0.33 WS/$million).

After finding the best fit regression line, I used the residual plot to find the best and worst value free agents, which the best value players being those with the greatest residuals while the worst value players are the ones with the least residuals. Additionally, I added the probability of a given player exceeding the deal they earn using normal distributions of projected salary and expected win shares.

## Findings

### Who Will Get the Most Money

#### Brandon Ingram, PF, NOP (Age 22)

- Projected Salary: $31.0 million
- Predicted Win Shares: 7.15
- Category: High Cost, Low Value
- Probability of Exceeding Deal: 15.1%

#### Fred VanVleet, PG, Tor (Age 25)

- Projected Salary: $29.1 million
- Predicted Win Shares: 8.93
- Category: High Cost, Medium Value
- Probability of Exceeding Deal: 44.9%

#### Danilo Gallinari, PF, OKC (Age 31)

- Projected Salary: $24.6 million
- Predicted Win Shares: 7.52
- Category: High Cost, Medium Value
- Probability of Exceeding Deal: 43.1%

#### Montrezl Harrell, C, LAC (Age 30)

- Projected Salary: $22.7 million
- Predicted Win Shares: 7.55
- Category: High Cost, Medium Value
- Probability of Exceeding Deal: 51.0%

#### Hassan Whiteside, C, Por (Age 30)

- Projected Salary: $21.3 million
- Predicted Win Shares: 8.82
- Category: High Cost, High Value
- Probability of Exceeding Deal: 74.1%

Others Include: Marcus Morris, Davis Bertans, Joe Harris, Serge Ibaka, Bogdan Bogdanovic

Ingram, while a restricted free agent, will likely remain with the Pelicans as he is expected to gain the most money during free agency. Most of the projected highest payed players are as expected, but this method helps to put a specific monetary value on each player. Of the most likely top paid players, Whiteside is the most likely to exceed the expectations of his deal. Meanwhile, Ingram is one person who are likely to get big money but disappoint over the length of his contract. While the it would be a controversial move for the Pelicans to let go of Ingram, it may be the most beneficial in the long term future.

### Who Are the Most Undervalued

#### Rondae Hollis-Jefferson, SF, Tor (Age 25)

- Projected Salary: $10.3 million
- Adjusted Win Shares: 6.87
- Category: Medium Cost, High Value
- Probability of Exceeding Deal: 86.1%

#### Michael Carter-Williams, SG, Orl (Age 28)

- Projected Salary: $6.3 million
- Adjusted Win Shares: 5.19
- Category: Medium Cost, High Value
- Probability of Exceeding Deal: 80.6%

#### George Hill, PG, Mil (Age 33)

- Projected Salary: $16.2 million
- Adjusted Win Shares: 7.81
- Category: High Cost, High Value
- Probability of Exceeding Deal: 78.2%

#### Wes Iwundu, SF, Orl (Age 25)

- Projected Salary: $3.6 million
- Adjusted Win Shares: 3.27
- Category: Low Cost, High Value
- Probability of Exceeding Deal: 66.8%

#### Torrey Craig, SF, Den (Age 29)

- Projected Salary: $3.7 million
- Adjusted Win Shares: 3.20
- Category: Low Cost, High Value
- Probability of Exceeding Deal: 64.8%

Other Include: Justin Holiday, Pat Connaughton, Hassan Whiteside, Nerlens Noel, Christian Wood, Chris Boucher

These listed players are best suited for contenders strapped for money who are trying to further improve their team. Young, improving players such as Christian Wood, Wes Iwundu, and Chris Boucher will likely outplay their deals and improve a team for little cost while providing a good outlook for the future. Additionally, players such as Hill, Carter-Williams, Craig, and Noel would be best suited as key pieces for contending teams as they are inexpensive (with the exception of Hill, who will likely resign with the Bucks).

### Who are the Most Overvalued

#### Carmelo Anthony, PF, Por (Age 35)

- Projected Salary: $9.7 million
- Adjusted Win Shares: 0.5
- Category: Medium Cost, Low Value
- Probability of Exceeding Deal: 10.6%

#### Isaiah Thomas, PG, Was (Age 30)

- Projected Salary: $5.2
- Adjusted Win Shares: 0.57
- Category: Medium Cost, Low Value
- Probability of Exceeding Deal: 22.8%

#### Markieff Morris, PF, LAL (Age 30)

- Projected Salary: $6.2 million
- Adjusted Win Shares: 1.25
- Category: Medium Cost, Low Value
- Probability of Exceeding Deal: 27.2%

#### Serge Ibaka, C, Tor (Age 30)

- Projected Salary: $18.0 million
- Adjusted Win Shares: 4.59
- Category: High Cost, Low Value
- Probability of Exceeding Deal: 26.4%

#### Davis Bertans, PF, Was (Age 27)

- Projected Salary: $18.4 million
- Adjusted Win Shares: 4.85
- Category: High Cost, Low Value
- Probability of Exceeding Deal: 29.5%

Others Include: Dwayne Bacon, Kent Bazemore, Aron Baynes, Tristan Thompson, Marc Gasol

Finally, there are the players who are the most overvalued. Of these players, only Ibaka and Bertans, and Thompson are likely to get very lucrative deals (Carmelo Anthony will likely get less than projected due to his age). However, teams should be careful to sign these players, each of whom have a very small chance of exceeding their deal. Additionally, if a team does decide to sign one of these players, it should be on a short team deal so they don’t get tied up with a bad deal. One important thing to take away is that while signing veterans is usually a good idea for competing teams, Anthony and Thomas should be avoided as they have a very small chance of exceeding the value of their deal.

## Summary

The most highly paid players during this year’s free agency will likely be Brandon Ingram, Fred VanVleet, and Danilo Gallinari. Using projected average salary as well as predicted win shares, I was able to find the most undervalued and overvalued free agents, including the chance that they exceed their expectations. Of the highest paid players, George Hill, Hassan Whiteside, Jae Crowder, and Christian Wood are the most likely to exceed their deals and should be targeted by all NBA teams that are not planning to tank. Additional undervalued players that can improve a team but are cheap include Michael Carter-Williams, Torrey Craig, and Wes Iwundu. These players should be pursued by teams that want to improve while spending the least amount possible. Lastly, the most overvalued players who will likely get large deals are Brandon Ingram, Serge Ibaka, and Davis Bertans. While these players may seem appealing at first, teams should rethink their decisions to sign them as their stats predict that they will not live up to their deal. The NBA has actually shown that they value free agents at what they should, meaning that finding high impact players for very little money is a difficult thing to do (see Salary vs Production graphic above). I will end off this article by mentioning some things which could have improved this project. I believe that using more than 5 seasons of data, separating into a train and test set, and using a better metric for player quality (such as 538’s Raptor ratings) would have improved the results. The most overvalued and undervalued free agents can be found using statistics.

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