Rewriting the GOAT Debate:
The NBA Through the ELO Lens

Traditional metrics have convinced us that greatness can be reduced to points, efficiency, or rings. But basketball is ultimately about winning. Winning means impacting the outcome of every game, not just stacking stats. Winning requires influencing your teammates and outmaneuvering your opponents, game after game regardless of which team is the favorite on paper. Winning is what separates legends from the rest — and that’s exactly what this new metric measures.

Inspired by the ELO system from chess — one of the most respected and widely used rating systems in the world — we introduce the ELO Rating system for NBA players. This metric applies principles proven reliable for decades in a very different competitive context. It measures a player’s impact with precision and consistency, and one of its most powerful advantages is that it allows us to compare players from completely different eras, even if they never faced each other.

Most traditional metrics fail here because they ignore the quality of the opposition, treating every point or win as equal. Wilt Chamberlain is often accused of playing against “plumbers”, while people mock LeBron James for playing in a soft era of “TikTokers”. This metric, however, accounts not only for the level of the opponent but also the strength of the player’s own team, providing a fair way to evaluate dominance across generations and finally answer the hardest of questions: who truly rises above the rest, no matter the era?

Another key feature is that it rewards overperformance against strong opponents and penalizes underperformance against weak ones. Unlike traditional box-score metrics, it recognizes that a 30-point blowout win against a weak team isn’t the same as leading your squad to victory against the league’s best. By capturing both successes and failures relative to the quality of competition, the metric emphasizes accountability, consistency, and real impact. Those who reliably overperform under pressure rise to the top, while players who occasionally shine but underperform in critical moments are exposed — mirroring how chess ratings balance wins and losses to measure true skill.

By adapting ELO to basketball, we can finally quantify greatness in a way that respects context, competition, and true influence on the court. It’s not just about points or rings — it’s about winning consistently against the best and avoiding costly losses against the worst. This metric provides a fresh lens for the GOAT debate, one grounded in logic, data, and competitive reality.

With this foundation in mind, the first challenge in adapting this system to basketball is that, unlike chess, basketball is a team sport, and we aim to measure the performance of an individual player rather than the team as a whole. In chess, each game has a single winner and loser, but in basketball, multiple players contribute simultaneously and diversely to a single outcome. Additionally, there is already extensive research and multiple examples that use ELO to rank teams in different competitions and sports: NBA, football, soccer... However, our goal is to rank players, not teams.

To address this, we start by defining a team’s rating based on the ratings of its individual players. A natural approach is to consider the team rating as the weighted average of the ratings of all players on the court, where weights reflect minutes played. This makes intuitive and mathematical sense: not all players contribute equally to the outcome of a game. A starter playing 36 minutes has far more influence than a bench player with 5 minutes on the court. Weighting by minutes ensures that the team rating truly reflects each player’s contribution, rather than treating all participants as equal, which would distort the expected outcome and undermine the reliability of the ELO updates for individual players. Formally,

$$ R_{team} = \frac{\sum_{i=1}^N R_i \cdot m_i}{\sum_{i=1}^N m_i} $$

Where:

• \(R_{team}\) is the rating of the team
• \(R_i\) is the current rating of player \(i\), before playing the game
• \(m_i\) is the number of minutes player \(i\) played in the game
• \(N\) represents the total number of players from the teams who participated in the game

One important aspect of this metric is that it incorporates the actual minutes each player spends on the court, which cannot be known before the match begins. This means that in-game events, such as injuries or unexpected substitutions, naturally affect the player’s contribution and rating adjustments. In other words, the metric captures a player’s true impact on the outcome rather than an estimate based on pre-game expectations. This makes the rating more accurate and reflective of real performance, but it also means that it cannot fully predict performance ahead of time—it measures impact ex post rather than forecasting it.

Before moving forward, let’s illustrate the calculation above using a historic game: Game 6 of the 1985 NBA Finals matchup between the Los Angeles Lakers and the Boston Celtics, featuring legends like Magic Johnson, Kareem Abdul-Jabbar, James Worthy, Larry Bird, Kevin McHale and Dennis Johnson, among others. In the following tables, the minutes played by each player and their ranking before the game are shown for the two teams.

Applying the formula above, the team ELO ranking for the Los Angeles Lakers was \(1,296.14\), while the Boston Celtics had a rating of \(1,267.75\).

Once we have defined the ratings of the two teams, we can calculate the expected outcome \(E\) for a matchup using the classic ELO formula, applied to team ratings:

$$ E_{team A} = \frac{1}{1+10^{(R_{team B}-R_{team A})/400}}$$ $$ E_{team B} = 1 - E_{team A}$$

Where \(R_{team A}\) and \(R_{team B}\) are the ratings of Team A and Team B, respectively.

Let’s give some intuition on the formula. The expected score \(E\) essentially represents the probability that a team will win based on its rating relative to the opponent. If two teams have identical ratings, then \(E=50\%\), meaning each team has an equal chance of winning. As the rating difference grows, \(E\) shifts closer to \(100\%\) for the stronger team and closer to \(0\%\) for the weaker team, reflecting an increasingly lopsided expected outcome.

In other words, \(E\) captures how surprising a result would be: a win against a much stronger team should count more, while a loss to a much weaker team should be judged more harshly. This is exactly why ELO naturally rewards overperformance and penalizes underperformance, making it a dynamic and context-sensitive measure of success. For every 400-point difference in rating, the higher-rated team’s win probability is exactly 10 times that of the lower-rated team, illustrating how strongly the formula weighs differences in skill.

Continuing with the previous example of the Finals game between the Los Angeles Lakers and the Boston Celtics, in which we had calculated Boston’s rating as \(1,267.75\) and Los Angeles’ rating as \(1,296.14\). Using the formula above, the probability of Boston winning was \(45.9\%\), which gives \(54.1\%\) chances of Los Angeles winning. As expected, a higher rating corresponds to a greater win expectancy.

Once the expected outcome \(E_{team}\) is calculated, we update each player’s individual rating using a slightly modified ELO formula:

$$ R'_i = R_i + K \cdot \frac{m_i}{36} \cdot (S_{team}-E_{team}) $$

Where:

• \(R_{i}\) is the current rating of player \(i\), before playing the game
• \(R'_i\) is the updated rating of player \(i\) after the game
• \(K\) is the scaling factor controlling sensitivity: 16 for regular season games and 32 for playoff games, reflecting the increased importance of postseason contests
• \(m_i\) is the number of minutes player \(i\) played in the game
• \(S_{team}\) is the actual result of the team (1 for win, 0 for loss)
• \(E_{team}\) is the expected outcome of the team based on team ratings

This formula captures a player’s true impact on the game in a dynamic, context-sensitive way. Here's how it works. The term \(S_{team} -E_{team}\) is always positive when the team wins (because the team’s expected result is always less than 1), which means the player’s rating increases. Conversely, if the team loses, the term is negative (because the expected result is always greater than 0), and the player’s rating decreases.

It’s fundamental to note that this metric is designed so that if you don’t win, your rating does not improve, regardless of how spectacular your individual performance might be. For example, Michael Jordan’s 63-point game against the Boston Celtics in the 1986 playoffs or LeBron James’ 51-point game against the Golden State Warriors in the 2018 Finals both resulted in ELO decreases. And that’s exactly how it should be: in basketball, winning is all that matters. Consequently, your rating improves if, and only if, your team wins.

That being said, observing the formula, the change in a player’s rating depends on three main components: the difference between the actual and expected outcome, the player’s minutes played, and the scaling factor \(K\).

1.- The difference between actual and expected outcome \(S_{team} -E_{team}\) measures performance relative to expectations. If a team wins against a stronger opponent, \(S_{team} -E_{team}\) is greater than if they beat a weaker one, leading to a greater rating increase. Conversely, if the team loses to a weaker opponent, the term is negative, causing a decrease. This is the core component that reflects whether a player’s team—and by extension, the player themselves—exceeded or fell short of what was expected.

2.- Minutes played \((m_i/36)\). Not all players have the same influence in a game. By scaling the rating change according to minutes played—normalized to a 36-minute standard—the formula ensures that players who spend more time on the court have a proportionally greater impact on their rating. A starter playing the bulk of the game will see larger rating adjustments than a bench player with limited minutes, even if both experienced the same team result. Consequently, a loss penalizes starters more than bench players, and a win rewards starters more heavily as well, reflecting their greater contribution to the game outcome.

3.- Scaling factor \(K\). The \(K\) factor adjusts the magnitude of rating changes based on game importance. In this system, regular season games use \(K=16\), while playoff games use \(K=32\), reflecting the higher stakes of postseason contests. A bigger \(K\) means that playoff performances move ratings more dramatically, ensuring that high-stakes games are weighed appropriately. The use of these values of \(K\) are a common practice in chess.

Together, these three components determine how much a player’s rating rises or falls after each game, combining team performance, player impact, and context into a single, interpretable metric.

To conclude the example that has accompanied us throughout the explanation, let’s calculate the updated ELO rankings for the players who participated in Game 6 of the 1985 NBA Finals, which ended with the Los Angeles Lakers winning \(100\)–\(111\). Let’s start by updating the ELO rankings of the Boston players. Since the Boston Celtics lost the game, their \(S\) value is 0. The percentage \(E\) had already been calculated and was \(45.9\%\). Since this was a playoff game, the \(K\) parameter is \(32\). Finally, the minutes played determine the adjustment for each player. For reference, for a player who played \(36\) minutes, the ELO point decrease is \(14.70\). In the following table, we show, for each Boston Celtics player, their minutes played, their ELO rating before the game, the ELO change, and finally their new ELO rating.

Now we repeat the calculations for the Los Angeles Lakers players. First, since Los Angeles won the game, the value of \(S\) is \(1\). On the other hand, the expected win percentage \(E\) had already been calculated and is \(54.1\%\), while the parameter \(K\) remains \(32\) because this was a playoff game. Finally, the minutes played depend on each individual player. As a reference point, for a Lakers player who played \(36\) minutes, their ELO increase would be \(14.70\) points. It’s important to note that this system guarantees a zero-sum structure: the total ELO lost by the players on one team is gained by the players on the other. The following table shows the ELO rating before and after the game, along with the ELO gain and the minutes played by each Lakers player.

As shown in the tables above, the change in ELO depends on court time. For example, James Worthy, who played \(45\) minutes, sees an ELO increase of \(18.37\) points, while Bob McAdoo, who played only \(10\) minutes, gains just \(4.08\) ELO points. This is consistent with the goal of rewarding real impact on the outcome of the game. Similarly, Dennis Johnson, who played \(43\) minutes, experiences a larger ELO decrease (\(-17.55\) ELO points) than Greg Kite, who played only \(11\) minutes and lost \(4.49\) ELO points.

Looking at this from another perspective, if this had been a regular season game instead of a playoff matchup, the ELO changes would not have been as significant. In fact, if the game had taken place during the regular season, then for every 36 minutes played, the Los Angeles players would have gained \(7.35\) ELO points—exactly half of what they earned in the playoff game.

Lastly, one might wonder how the ratings would have changed if Boston had won the game instead. Would the Lakers players have simply lost \(14.70\) points per 36 minutes played, just as the opposite occurred? The answer is no. Since in this case the probability of a Lakers win was slightly higher than that of Boston, the rating system would have rewarded this upset slightly more strongly (or penalized the Lakers slightly more heavily). For every 36 minutes played, Boston players would have increased their ELO by \(17.30\) points. As we’ve emphasized throughout the explanation, overperforming or underperforming relative to expectations has a greater impact on ELO ratings.

Now that we’ve explained how this metric is built, justified its validity, and highlighted its strengths for evaluating players fairly and with proper context, obtaining the historical evolution of each player’s ELO series becomes straightforward. It’s only worth noting that the chosen base rating is \(1000\), again inspired by chess. In other words, when a player enters the league, their initial rating is \(1000\), and as they win or lose games, this rating increases or decreases according to the dynamic system described above. All of this allows us to bring a rigorous and informed perspective to the never-ending debate about who is the true NBA GOAT. From now on, greatness isn’t just remembered or argued—it’s measured.

The biggest surprise may be seeing Chris Paul ranked third in peak ELO and sixth in average ELO, and Vlade Divac sixth in peak and fourteenth in average, but a closer look at the numbers explains their placements. Paul’s teams, across nearly twenty seasons, consistently improved wherever he went: he turned the Hornets into regular playoff contenders, the Clippers rose from irrelevance to a Western Conference powerhouse, the Rockets peaked with him alongside Harden, the young Thunder overperformed, laying the foundations for their bright future, and the Suns jumped from the lottery to the Finals. He is the definition of a floor general—dictating tempo, organizing offense, and making teammates better—while maintaining elite play over nearly two decades.

Vlade Divac’s influence was more subtle but equally meaningful. Over his career, he maintained a regular season win percentage above \(60\%\). He improved floor spacing, facilitated offense, and created opportunities for teammates such as Chris Webber, helping his teams overperform relative to expectations. Divac’s contributions often went unnoticed in traditional statistics, but an ELO-based system captures his consistent, context-adjusted impact on team success.

From an ELO perspective, the comparison is striking: in regular season losses, Chris Paul’s and Vlade Divac's teams were on average only \(18.40\) and \(21.31\) ELO points better than their opponents. As a reference, that's far lower than the average ELO advantage of \(133.15\), \(109.92\), and \(135.62\) points for Bill Russell, Larry Bird, or Magic Johnson. In regular season wins, Chris Paul’s teams were just \(94.00\) points better while this figure rises to \(103.67\) for Divac's teams. In comparison, that's less than Wilt Chamberlain (\(129.26\)) or Kareem Abdul-Jabbar (\(141.62\)). These numbers illustrate how both players consistently exceeded expectations with their teams. Together, these metrics justify why both Paul and Divac rank so highly.

It may be surprising not to see Kobe Bryant ranked near the top in these ELO metrics, especially since he is widely regarded as a top-10 player of all time and has a résumé that includes five NBA championships and multiple MVP-level seasons. Many fans even include him in the GOAT conversation due to his cultural impact and his legendary winning mentality.

However, throughout most of his career, Kobe played on extremely strong teams and was surrounded by other stars. His early titles came while playing alongside Shaquille O’Neal, one of the most dominant forces in NBA history, and later he benefited from talented supporting casts built around him in Los Angeles. Since ELO heavily values a player’s individual contribution on team performance, being part of stacked rosters can limit how high a player rises in these rankings. In fact, between 1998 and 2011 his team's were favored by \(119.88\) ELO points on average on regular season games and \(62.72\) in playoff games, so his expectations to win were high.

This context is reflected in Kobe’s ELO trajectory. His peak ELO sits outside the very top tier, and his average ELO rank drops even further. In the final phase of his career, prolonged injuries and less competitive Lakers teams pulled his numbers down significantly. Unexpected playoff losses also hurt his rating. For example, the 2004 NBA Finals defeat against the Detroit Pistons heavily penalized his ELO because the Lakers entered the series as clear favorites. Additionally, major disappointments in later seasons—such as the 2012–13 campaign, when he played alongside stars like Dwight Howard, Pau Gasol, and Steve Nash—further affected his numbers, as injuries and underperforming teams limited his impact.

Kobe’s legacy remains enormous, but ELO measurements offer a more analytical perspective that highlights how team context, late-career decline, and a few costly postseason setbacks can shape the statistical story of a player’s career.

Other notable absences include Wilt Chamberlain, Bill Russell, and Oscar Robertson, who rank only 28th, 38th, and fall outside the top 50 in peak ELO, and are also outside the top 50 in average ELO. This is largely because the competition faced by their teams was relatively weak, with average opponent ELOs of just \(1,055.47\), \(1,040.98\), and \(1,053.06\), compared to their own teams’ ELOs of \(1,144.67\), \(1,185.56\), and \(1,111.35\), respectively. As a reference, the ELO of opposing teams faced by Kevin Durant, David Robinson, and Scottie Pippen is generally around \(1,070\)-\(1,080\). While this may not seem like a huge gap, over the course of a long NBA career, it can definitely make a significant difference.

Finally, while there are many other surprising omissions and unexpected rankings in the ELO lists, one that stands out in particular is Allen Iverson. Despite his undeniable legacy and profound cultural impact, Iverson’s lack of significant team success—largely due to the absence of a strong supporting cast—has prevented him from climbing higher in both peak and average ELO ratings. His case highlights how ELO not only captures individual brilliance but also the critical influence of team context and competitive environment on a player’s statistical standing.

All things considered, when the question of the NBA’s GOAT comes up, the pool of realistic candidates narrows quickly once we apply a consistent, impact-based standard like ELO. The candidacies of legends such as Kareem Abdul-Jabbar, Wilt Chamberlain, Kobe Bryant, and Larry Bird begin to fade not because they weren’t individually dominant, but because their impact in team success comes short compared to that of our four final candidates. These four players manage to appear in the top five in both average career ELO and peak ELO simultaneously. That level of true, sustained superiority is reserved for LeBron James, Michael Jordan, Tim Duncan, and Shaquille O’Neal. These are the only legends who consistently lifted their teams to top-tier performance over long stretches and reached historically dominant peaks according to this context-adjusted metric.

From there, LeBron James takes the lead, as he ranks #1 in both average ELO and peak ELO. He has achieved this while maintaining exceptional performance throughout the longest meaningful prime the sport has ever seen. But let's take a closer look at how James builds his case for the NBA GOAT compared to the other three candidates. To do so, the following tables show the average ELO difference between the player's team and their opponents in wins and losses, both in regular season and playoffs.

As can be seen, Tim Duncan holds the strongest regular season win percentage, surpassing an impressive \(70\%\) win percentage. He is followed by Shaq with just over \(67\%\), Jordan with nearly \(66\%\), and James with almost \(64\%\). It is worth noting that in losses, Jordan’s teams were favored by only \(38.62\) ELO points on average, while the other three players were favored by more than \(60\) ELO points—and Duncan’s teams even exceeded a \(100\)-point advantage in those games. However, in wins, LeBron’s teams had the smallest advantage compared to their opponents, with roughly \(20\) fewer ELO points than Jordan and Duncan and \(10\) fewer than Shaq. In other words: although the teams of all four superstars were typically favored in losses, Jordan’s were the least favored—and while they were usually favored in wins as well, LeBron’s were the least favored among the group. In the next table, we present the same statistics but now focused exclusively on playoff performance.

As can be seen, the situation changes quite a bit in the playoffs. The win percentages of O'Neal and Duncan drop considerably, reflecting the higher level of competition in the postseason. This is also reflected in the average ELO difference between these players’ teams and their opponents: although all of them remain favorites in both wins and losses (on average), the margins have decreased significantly. Specifically, LeBron James now has the smallest ELO difference in both losses and wins. This means that, in the playoffs, he has faced comparatively tougher opponents than Jordan, Shaq, or Duncan. Furthermore, in the next table, it can be observed in detail his advantage (at the beginning of the series) in each of the playoff series that he has played along with the result of the series.

In the table above, it can be observed that LeBron James has played a total of \(55\) playoff series to date, of which he has won \(41\) and lost \(14\), yielding a \(74.55\%\) winning rate in playoff series. Of the \(14\) series he lost, he was the favorite according to the ELO rating in only \(4\) of them: the 2009 ECF against Orlando, the 2010 2nd Round against Boston, the 2021 1st Round against Phoenix, and the 2025 1st Round against Minnesota. In these series, his advantage averaged a significant \(62.55\) ELO points, capturing the big upsets in the Phoenix, Minnesota and Orlando series. It is worth noting that in the six Finals he lost, in every case the opposing team had a higher ELO than his team—on average by \(84.5\) points. The 2007, 2017, and 2018 Finals are especially striking, as his team faced an ELO disadvantage of around \(100\) points.

On the other hand, of the \(41\) series he won, in \(7\) of them his team was not the favorite. Moreover, of the 4 championships he won, he was the favorite only in the 2020 Finals, i.e., according to ELO his wins against OKC, San Antonio, and Golden State were all upsets.

Now, let’s compare this with Shaquille O'Neal, Tim Duncan and Michael Jordan, whose series results are shown in the tables below. The reader should keep in mind that first-round playoff series prior to 2003 were best-of-five. Let's start with Shaquille O'Neal.

In the table above, it can be observed that Shaquille O'Neal played a total of \(45\) playoff series, of which he won \(32\) and lost \(13\), representing a \(71.11\%\) winning rate in playoff series. Of the \(13\) series he lost, he was the favorite according to the ELO rating in \(6\) of them, generally with close margins around \(30\) ELO points, though the 2004 NBA Finals loss against the Detroit Pistons stands out with a ELO advantage of \(116.56\) points.

On the other hand, of the \(32\) series he won, in only \(4\) of them his team was not the favorite. Additionally, the average ELO advantage in his playoff series wins was \(90.31\) ELO points. In fact, his team was the favorite in all of his playoff series from 2000 until the Second Round of the 2006 Playoffs.

Regarding his 6 Finals appearances, he was the favorite in 4 of them (winning 3 championships) and not the favorite in 2 (although he managed to win one of those championships). Nevertheless, this spectacular résumé of the most dominant player in history still doesn’t reach LeBron’s rating. Both his slightly lower winning percentage in playoff series and playoff games, and the fact that, on average, his teams had a higher ELO advantage, place him behind LeBron on the NBA ELO ranking.

Now, let's address Tim Duncan's case.

Tim Duncan played a total of \(48\) playoff series, winning \(35\) and losing \(13\), yielding a \(72.92\%\) series win rate. Nevertheless, of the \(13\) series he lost, he was the favorite according to the ELO rating in most of them, 9 out of 13 precisely. Moreover, his average ELO advantage in these upsets was \(48\), and all of them occurred after 2006.

On the other hand, of the \(35\) series he won, in only \(3\) of them his team was not the favorite. However, the average ELO difference was only around \(30\) points. Additionally, the average ELO advantage in his playoff series wins was \(89.59\) ELO points. In fact, his team was the favorite in all of his playoff series from 1991 onwards. Consequently, in all of his 6 Finals he was the favorite to win it all.

To sum up, of his six Finals appearances, he was the favorite in all of them and won 5 rings, although the Miami Heat secured the victory with a spectacular comeback in 2013. Nevertheless, Tim Duncan’s legacy is extraordinary: he embodied the culture of San Antonio, was one of the most underrated big men in NBA history, and had a tremendous impact on the success of his teams. He earned numerous individual awards and accolades, demonstrating both consistency and excellence over his long and prolific career. Yet, he still does not surpass LeBron in ELO rating. The underlying reason is that the metric heavily values the ability to pull off upsets and penalizes heavily being the one who gets upset.

And finally, the comparison you’ve all been waiting for: Michael Jordan vs. LeBron James. Will we be able to answer the question of why Jordan falls short of LeBron in ELO rating?

Michael Jordan played a total of \(37\) playoff series, winning \(30\) and losing \(7\), representing a \(81.08\%\) winning rate in playoff series, the highest among all four. Of the \(7\) series he lost, he was the favorite according to the ELO rating in only \(1\) of them: the 1995 Second Round against Orlando, though his advantage was only \(35.44\) ELO points.

On the other hand, of the \(30\) series he won, in only \(2\) of them his team was not the favorite. Namely, these were the 1st and 2nd round of the 1989 playoffs. However, both matchups were fairly leveled since the average ELO difference was barely \(7.43\) points. Additionally, the average ELO advantage in his playoff series wins was \(125.31\) ELO points. In fact, his team was the favorite in all of his playoff series from 1991 onwards. Consequently, in all of his 6 Finals he was the favorite to win it all.

While Jordan’s competitive spirit and winning ability are unmatched, this helps explain his position below LeBron James in the rankings. Michael Jordan won throughout his career only and exclusively when he was expected to win. This is in no way meant to diminish his legacy. On the contrary, sustaining perfection and meeting sky-high expectations for six championship runs is an extraordinary accomplishment that deserves the highest admiration. Jordan’s greatness was so overwhelming that he often became the expectation itself — when he stepped on the court, the story felt already written, and the rest of the league was merely trying to rewrite fate. Moreover, it is important to acknowledge that in the early stages of his career, defeating powerhouse teams like the Celtics or the “Bad Boys” Pistons would have been nearly impossible when considering the massive ELO gaps between those teams and the Bulls.

However, this metric is defined on the grounds of rewarding winning relative to expectations. Therefore, given the results, we can say that in the eyes of this metric, LeBron’s victories against the odds carry more weight than Jordan’s wins when his team was superior to its opponent.

So, while the GOAT debate will always involve subjective elements like aesthetics, narrative, and cultural influence, an objective framework that rewards sustained excellence against the strength of competition points decisively in one direction: LeBron James stands alone as the true NBA GOAT.