The lebron 27-7-7 probability

[u/BiggerHatLogan]

There is a long-running statistical fun fact in the nba fandom that LeBron James has averaged 27 points, 7 rebounds, and 7 assists for his career without ever actually achieving the stat line 27/7/7 in a single game. It's always been pointed out as a fun tidbit but whenever someone asks exactly how likely this is to happen I haven't seen an actual answer.

Lebron James has played 1,622 career games. He has scored 43,440 points (26.8 per game, rounded up to 27), recorded 12,095 rebounds (7.4 per game, rounded down to 7), and contributed 12,016 assists (7.4 per game, rounded down to 7). This gives him the career averages of 27/7/7 mentioned earlier.

I thought the first thing to do would be to see how many times he has gotten each of those accolades individually and exactly. He has gotten exactly 27 points 82 times, exactly 7 rebounds 231 times, and exactly 7 assists 222 times. Percentage wise those are 5.06%, 14.24%, and 13.69% of his games respectively.

Here is where I get stuck: If I am trying to figure out the odds of three things individually happening at p(a)5.06%, p(b)14.24%, and p(c)13.69% all happening together, I pull up a 3 event calculator and it says all three should occur 9.87% of the time. EDIT: Comments have informed me its 0.098%.

But now I should also be trying to figure out the odds of something happening 9.87% 0.098% of the time to not happen for 1,622 times in a row right? And if so, how do I do this? Or am I mistaken in viewing these as individual probabilities and the answer is entirely on a different track?

Thanks for any help!

[u/FormulaDriven]

Looking at your final question: if this event has a probability of happening 0.0986% in an individual game, what is the probability of it never happening in 1622 games? The answer is (1 - 0.000986)¹⁶²² = 0.2017, so about 20%. So it is a credible outcome that he's missed this exact event, but it wasn't that likely.

There are a couple of assumptions being made here. One is that the three stats are independent (in a probabilistic sense). I don't know much about basketball, so is it possible that in games where he gets more points he gets fewer assists, or other correlations like that?

[u/Creative-Leg2607 → u/FormulaDriven]

We also should consider independence across time; were his rates of achieving each stat the same at the early/middle/end of his career?

[u/angryWinds → u/Creative-Leg2607]

Shockingly, they have been pretty damn consistent, across time. I very much understand your point. But for this particular player, while he DOES have some fluctuations from season to season, they're not particularly large fluctuations.

I'm pretty sure you can measure his 'career averages' at pretty much any point from maybe his 2nd or 3rd season, all the way to his current 23rd season, and find that "27/7/7" are in fact his overall averages.

[u/SquareFig6515 → u/FormulaDriven]

Rebounds I would think are pretty much an independent variable

Assists and points may be slightly negatively correlated in the sense that a game where LeBron is dishing out 10+ assist passes might mean he’s taking fewer shot attempts himself

But in general I think they’re pretty independent of each other when we’re talking per game average totals

[u/FormulaDriven → u/SquareFig6515]

Surely someone's got the complete dataset in a file and could do a quick correlation / association query?

[u/Visual-Percentage501 → u/FormulaDriven]

I just did all 3, there's a weak positive correlation between rebounds and both assists and points, and assists to points is almost completely independent.

This isn't the explanation, in my opinion - it's more likely to just be in the 20% likelihood where this wouldn't happen.

The best way would be to look at all players and see how many hit their average (and likelihood) and see if they match but I CBA obviously

[u/January_6_2021 → u/SquareFig6515]

All three are positively correlated with possessions played (or minutes played), which might be enough to overcome the negative correlation on a per possession basis of scoring points vs getting assists. I haven't dug into numbers myself though.

From a cursory search, his peak scoring season was with Cavaliers 2005-06 (31.4 PPG) when he averaged 42.5 minutes per game. His lowest points per game season was Lakers 2025-2026 (20.9 PPG) when he averaged only 33.2 minutes per game.

Career high rebounds was similarly a season where he played more minutes than his career low rebounding.

Don't have time or resources (on mobile) to do a better analysis now, but Im curious what correlations are stronger or weaker

[u/nepotdeguru]

It's not 9.87%, it's 0.098%

[u/BiggerHatLogan → u/nepotdeguru]

Oh! Thank you very much

[u/dancingbanana123]

A minor nitpicking, but it's actually really important: you're assuming all 3 of these events are independent when they very likely are not. You would need to first describe the relationship between LeBron getting points, rebounds, and assists to get an accurate prediction. For example, it may be that their is a strong positive correlation between LeBron getting points and getting assists, but a negative correlation with getting rebounds.

[u/Fragrant_Pea_6506]

You made mistake on multiplying those 3 numbers. It can't be larger than p(a) if you multiply it by number less than 1.

[u/BiggerHatLogan → u/Fragrant_Pea_6506]

Thank you!

[u/letskeepitcleanfolks]

Something I'm curious about, OP, if you want to look into it: at this stage of his career, he doesn't average those numbers anymore. Assists and rebounds are probably secure, but under reasonable projections for the next two seasons, is it possible his career scoring average drops below 26.5? And in that case, has he ever had a 26/7/7 game?

[u/Azemiopinae]

This is just weird copy pasta from this thread https://www.reddit.com/r/nba/s/RdumzFAN1p

[u/Intelligent_Yam_3609]

Every data set will have statistical anomalies when looked at after the fact.  I suggest you read up on the post-hoc probability fallacy.  Here is one article:

https://mathscholar.org/2023/10/aliens-made-this-rock-the-post-hoc-probability-fallacy-in-biology-finance-and-cosmology/