The GOAT Ladder: Greatness is in the Eye of the Beholder

Putting Offense and Defense Together

With D_Score and two forms of O_Score in hand, we can combine offense and defense into a “one number” statistic. I have labeled the two variants of this stat differently to help the reader easily apprehend the difference: Total_Score per Possession adds O_Score per Possession to D_Score, while Total_Score adds O_Score by Volume to D_Score. So if you see “Total_Score” without any qualification, I am citing a player’s volume on both ends. When I cite “Total_Score per Possession”, I am referring to a player’s production rate.

There’s Levels to This

D_Score, and the other Scores outlined above, describe player defensive performance at the season level. There’s levels to this, though. Players play one game at a time. Being the GOAT is not a matter of a single game, though. Greatness has to do with career impact, so it is also necessary to calculate both a player’s total differential and their scores at the career level. O_Score, D_Score, and all the other component scores are weighted at the career level. A player’s score from seasons where he played a lot therefore counts more than his score in seasons where he rarely played. As an aside, this prevents some of the downward drag on career averages that we see for players with particularly long careers.

Aggregating a player’s season differentials over his entire career allows us to give proper credit to these players – the ones like Moses Malone and Kareem Abdul-Jabbar who play long after they have declined from the level of a star player. Weighted scores provide the counter-balance for this effect by valuing player performance on the level of most additional value relative to context on an individual season basis. Career total differentials tell us who had the greatest career. Career O_Score and D_Score tell us who would be a better choice if you had to win one championship.

You Only Get One Shot, Do Not Miss Your Chance to Blow

Which brings up another interesting level: the per-game level. In any discussion or debate about who the GOAT is, it’s common to evaluate a player’s per-game averages in addition to career totals and season averages. The scenario that pops up the most often is “one game for your life – who you got?”, but you may be more familiar with variants like “Which star’s team would be most likely to win make-it-take-it to 11?” or “Which star would win the most games in a YMCA-style run?”

In truth, it does all boil down to a game, doesn’t it? The regular season takes months to complete, and the playoffs feature series, but we know that it comes down to the ability to win one game. Regardless of how long the buildup is to that one elimination game, every team has to win the final, pivotal game in order to reach their ultimate goal. Our recognition of this fact is what draws us toward choosing the GOAT based on who could win one, single game. With all the chips down, who can win the game?

This instinct is so strong that I too feel the need to evaluate player per-game performance in my determination of the greatest players of all time. But I’m not out here citing points per game, rebounds per game, and assists per game. Counting stats offer an incomplete picture, and you can find them on bball-reference whenever you want to. I felt the need to develop a per-game statistic that would measure both offensive and defensive performance, and that would do so in a manner that would allow us to understand the differences between players.

What I wanted was to be able to express a player’s impact on a game, independent of opponent. I wanted to know how this player would fare against any opponent. We can go round and round dreaming up scenarios that create a matchup advantage or disadvantage for a certain player, but the greatest players of all time give their team an advantage every time they step on the floor. I wanted a result that would be absolutely trustworthy.

Put That On God

And that’s what I developed – a stat that you can put on God. Matter of fact, the stat is named ON_GOD:

Opponent

Normalized

Game

Offense plus

Defense

To determine a player’s ON_GOD value, I took his average Points Created relative to league average differential (actual – expected) and his Opponent Points Created relative to the players he was guarding ((actual – expected) * (-1)), and added them together.  

Although I’m bringing this up in the context of historical comparison of players, it also comes in quite handy for things like single season comparisons. Here’s the distribution of performance by game for the three leading MVP candidates in one of my favorite MVP races of all time – the 1993-94 race:

As you can see from the shape(s) on the red side, Hakeem Olajuwon was the most high-impact defender among the three. Although this was only Shaq’s second season and far from his peak, Shaq was still the best of the three on offense. David Robinson, the third candidate, was the most balanced of the three candidates between offensive and defense, and the most likely to have an above-average defensive game. It is evident that the differences between the three were very slight indeed. Olajuwon won both MVP and Defensive Player of the Year in this season, with Robinson placing second in the voting for both. (Olajuwon won DPOY by a single vote) Robinson and O’Neal would place 1-2 in the MVP voting the following season with very similar performances.

You can certainly use ON_GOD for things like MVP debates, and I tend to find visualizations (like the one above) that show a player’s consistency or inconsistency from game to game quite telling. It is also important, though, to analyze value on a per-game level in an historical evaluation.

Who is the GOAT, ON_GOD?

In my deliberation over the greatest players of all time, I used players’ rank in career ON_O (per-game offensive differential only), ON_D (per-game defensive differential only), and ON_GOD (per-game offensive and defensive differential) to capture per-game value. Although there is room for debate here, I believe that using offense and defense separately in addition to the one-number combined form strikes a delicate balance. The balance allows us to recognize that a) defense is important, and has as much impact as offense on team success, though b) individual star players typically have a much greater impact on the offensive end.

These two claims appear to contradict each other at first glance, but consider this fact: Kawhi Leonard’s offensive output has the same effect on the outcome of the game regardless of the opponent – he is always just as far above league average. His defensive output, on the contrary, may vary greatly depending on the opponent. If the opponent has a big wing as their primary scorer, Kawhi is likely to have a hug effect on the game by defending that player. If, on the other hand, all the opposing team’s offense comes through their guards, Kawhi may have less effect on the game. Defending a weaker player leaves the defender less room to make an impact. No wonder, then, that star players make a bigger difference on offense than on defense (on average).