Introducing LEBRON: Longevity Estimate Based on Recurrent Optimized Network

Introduction

Although he’s in his 17th season in the league, LeBron James is putting up All-NBA first team-quality numbers. Every year, we wonder whether this will be the year that LeBron finally declines. After all, very few players even last 17 seasons, let alone dominate in each of them.

LeBron’s incredible longevity raises questions as to how we predict a player’s career arc. In signing players, general managers pay for not only current performance but also future expectations. For young players, the future expectation centers around the hope that they’ll flourish into stars. Meanwhile, for old players, the hope is that they’ll last the entire contract before breaking down.

However, so many variables affect NBA player performance, making longevity incredibly hard to predict. Players regress or progress in a seemingly random way over the course of their careers. Even if we (somehow) hold injuries, team changes, coaching changes, and more factors that can have large direct effects on player performance, it’s hard to predict a player’s career arc.

For example, let’s look at Roy Hibbert’s career. Hibbert made the 2012 and 2014 All-Star teams. He was also selected to the All-Defensive 2nd team for the 2013-14 season and helped anchor the Pacers’ strong defense when the team made it to the conference finals twice in a row. In the 2011-2012 season – when he made his first All-Star team – Hibbert was 25 years old. The All-Defensive 2nd team selection came when he was 27 years old. Conventionally, we say that players hit their prime around 27 or 28 years old. So, Hibbert seemed to be entering his prime in a promising position. However, two years later – in his age 29 season – his point total fell almost in half (10.6 to 5.9) as he moved to the Lakers. He retired at age 30. Hibbert seemed to suffer no injuries during this time (he missed a maximum of 5 games between the 2011-12 and 2015-16 seasons). Though Hibbert switched teams and the league moved away from his type of player, Hibbert’s regression seems unexpected.

There are several more examples of unexpected progressions and regressions. Again, projecting career arcs is very hard. However, here we’ll try to create a new metric that will give us a better estimate of a player’s career arc.

LEBRON (longevity estimate based on recurrent optimized network) uses a deep learning sequence model to project a player’s career arc. LEBRON predicts future All-NBA probability (which we determine using some models discussed later). It is far from perfect. Certain factors – like injuries -are impossible to predict when projecting a player’s future. However, LEBRON can give us a better idea of a player’s career arc than assuming all players follow the typical age/performance curve.

Data and All-NBA probabilities

The metric we’re modeling with LEBRON is All-NBA probabilities. We won’t go too in-depth on the All-NBA models here. We’ve done some previous work on predicting All-NBA teams which turned out pretty accurate.

First, we collected data on every player whose career started on or after the 1979-1980 season (introduction of the 3-point line). We excluded players who played before the 3-point line because, when training LEBRON, we look at a player’s entire career arc. This makes it unreasonable to consider players before 1979-1980, as parts of their careers were played with no 3-point line. Also, we do not have data from the 2019-20 season, because it’s not done yet. Altogether, we had 15,355 player seasons in our data set.

We predicted whether or not a player would make an All-NBA team in a given year. We did not separate 1st, 2nd, and 3rd teams – we predicted the binary outcome of making an All-NBA team (1) or not (0). To predict the selections, we used 7 inputs. They were: games played, minutes played, PPG, RPG, AST, VORP, and WS. Several arguments can be made about the features we used here. For example, it may be more reasonable to use RAPTOR instead of VORP and WS. Maybe we should consider defensive stats, too. However, the models using these inputs performed very well. Changing the inputs a bit would likely result in minor changes in a player’s All-NBA probabilities. Given that the main task of LEBRON is predicting the sequence of future All-NBA probabilities, we did not focus on fine-tuning the All-NBA models too much.

We used 3 tree-based models (random forest, gradient boost, and extreme gradient boost) to predict All-NBA selections. First, we evaluated them like typical machine learning models, where we split the full data into training and testing sets, then calculate each model’s performance. We used 25% for training. The performance metrics (along with the results of a random model – the dummy classifier) are in the table below.

We won’t go too much into the model details here. The table shows that the models are very good at predicting All-NBA players. Accuracy doesn’t matter so much here, because the data set is imbalanced; in any given year, at most 15 players make an All-NBA team. So, a model predicting all 0s will get super high accuracy. However, our models have strong metrics all around, indicating they predict the All-NBA teams well.

Now that we see the models are good, we need to generate an All-NBA probability for every player in every season. To do this, we performed a type of leave-one-out cross-validation on each year. For example, say we wanted to predict All-NBA probabilities for every player in the 2008 season. To do this, we used all the historical data except for the 2008 season to train our models. Then, we averaged the predictions of our 3 models to assign each player an All-NBA probability. We repeated this process for each year. Then, we evaluated the predictions. The performance metrics are below.

This shows that our models are strong predictors of All-NBA teams. Furthermore, the prediction probabilities from the models are good, as seen by the low log loss and high AUC-ROC. Now that we’ve set up the All-NBA probabilities, we can proceed with the creation of LEBRON.

Creating LEBRON

We fit an LSTM (long-short term memory network) to each player’s All-NBA probability history. We then used this model to project each player’s future All-NBA selections. Here’s a general overview of the process and data:

• First, we dropped all players who had not played at least 4 years by the end of the 2018-19 season. So, there’s no Embiid, Doncic, etc. There are a few reasons for this. First of all, as hard as projecting a player’s longevity is in general, it becomes so much harder when you only have a few data points to use. So, we needed to have a minimum sequence length. Second, 4 years lessens the future variance of our predictions. Rookie contracts last 4 years, and 4 years gives us a decent sample size of a player’s performance.
• Then, we split the data. We used 60% to train, 20% to validate, and 20% to test. Each “sample” is a player’s entire career.
• We trained the model to predict a player’s All-NBA probability in year n+1 given their All-NBA probabilities from year 1 to n.
• After training the model, we used it to predict every player’s All-NBA probability next year.
• Then, we added this predicted All-NBA probability to their career arc. We then predicted the next All-NBA probability using the sequence that includes both the historical probability and the predicted one.
• We repeated this process for all players until their sequence length reached the maximum career length in our data set of 21 seasons.

Like any approach to this difficult problem, LEBRON has its flaws. However, our approach seems to minimize some of them. For example:

• One might ask why we use All-NBA probability as our sequence metric instead of a normal advanced stat like WS, RAPTOR, etc. Considering All-NBA probability lets us create a bigger separation between stars and non-stars. Also, it’s more interesting to project a star player’s career arc, given that they had to rise to be a star, then fall. Meanwhile, a role player may have progression and regression, but it will not be as dramatic and import to a team as a star player’s arc. Also, the main reason to use All-NBA probability is its interpretability. It’s much more meaningful to say “player x has 2.5 more All-NBA seasons left” than to say “player x has 10 more win shares left.”
• It will still be hard for the model to project career arcs for younger players. Even though we drop players who played fewer than 4 seasons, things still change after a player’s 4th season. From a modeling standpoint, players with fewer years under their belt are harder to project. They have fewer historical seasons, so there’s more uncertainty. We’re projecting to 21 seasons, so there’s more to project for younger players, meaning there’s more room for error. For this reason, LEBRON will be more accurate for someone like LeBron, with several years under his belt, than Giannis.
• The model tends to be pessimistic for young players. This goes back to the choice of All-NBA probability as a metric. In any given year, maybe 20 players have a real shot at making an All-NBA team. Indeed, in our 15,355 player data set, only 2.9% had an All-NBA probability above 50%, and 5.6% had a probability above 10%. This creates an imbalance towards lower values. So, the models tend to regress young stars towards these lower values before conventional knowledge would suggest they should regress. However, this doesn’t mean the model is wrong for young players.
• The model doesn’t adjust for the fact that in each year, 15 players will make an All-NBA team. This is impossible to account for; the 15 players will not always be in our current data set. Rookies and young players will grow and take over spots. If we somehow knew that x number of current players will make an All-NBA team in y years, we could scale their probabilities up or down. This would help with the pessimistic projection for young players, but is impossible to implement.
• Not everyone will reach the 21 seasons we’re projecting (in fact, very few will). However, this doesn’t affect the projections too much, because the model knows to regress long sequences (i.e. old players) to almost 0 by the end of their career. Also, some may play for longer than 21 seasons (unlikely but possible).

Now that we’ve discussed the approach and flaws of LEBRON, we can move on to the results.

Results

As mentioned earlier, we generated career arcs for each player who played at least 4 years as of the 2018-19 season. We project future years for them up until they reached a 21-year career.

With these projections, we can look at both a player’s year-by-year projections and their total projections. By summing all of the projected future All-NBA probabilities, we can say that “player x has y remaining All-NBA seasons.”

Below is an example of LeBron’s projected future, as predicted by LEBRON.

LEBRON projects a steady decline for LeBron, though he will still maintain his All-NBA level performance. It projects that in his 20th season, he will be a borderline All-NBA player. His All-NBA probability that year of about 50% would put him at the 18th highest All-NBA probability for the 2018-19 season, right below Blake Griffin and Russell Westbrook. So, this means that an All-NBA probability around 40-50% still implies strong, All-Star level performance. In his 21st year, LEBRON projects an All-NBA probability for LeBron just below 40%. This is way higher than any other player’s 21st year All-NBA probability. The high number also suggests that LeBron could keep playing at a high level past that season, perhaps raising his remaining All-NBA probability from 2.77 to above 3.

The table below shows the LEBRON projections for all players. Note that the current year is as of the 2018-19 season.

To view each player’s year-by-year LEBRON projection in a more digestible format, we created an R Shiny app. This allows you to view a plot of any player’s full LEBRON projection. It is available here:

https://dribbleanalytics.shinyapps.io/lebron-longevity-metric/

Conclusion

Hopefully, LEBRON sheds some light on how certain players will progress throughout their careers. Though it’s far from perfect, it seems much better than saying all players follow the typical model of reaching their prime at 28 and regressing after 30. The main issue with LEBRON is its difficulty in projecting young players. However, this is difficult for any model, as younger players have more variance. Maybe adding some type of similarity metric to other career arcs, like 538’s CARMELO used, to go along with the sequence modeling would help solve this problem.