I just know that in the Big Five, athletes generally score above average in terms of extroversion, agreeableness, conscientiousness, below average in terms of openness to experience, and I think in neuroticism too. And that if they're more elite, their levels of conscientiousness are even more elevated. It requires a lot of persistence to be a pro athlete I guess.
Improving your happiness and changing your personality for the better
Jungian theory is not grounded in empirical data (pdf file)
The case against type dynamics (pdf file)
Cautionary comments regarding the MBTI (pdf file)
Reinterpreting the MBTI via the five-factor model (pdf file)
Do the Big Five personality traits interact to predict life outcomes? (pdf file)
The Big Five personality test outperformed the Jungian and Enneagram test in predicting life outcomes
Evidence of correlations between human partners based on systematic reviews and meta-analyses of traits
I expect more of P types in meaningful sport. As it looks as not reliable for long time activity.
Shaq, Iverson and Lebron can all be the same type. There's multiple variations to each type. They essentially seemed like Se leads and logical to me. I actually think Allen Iverson is SLI-Te sub now. I'm not entirely sure on Shaq. I can see Shaq being ethical over logical. Iverson has that assassins' mentality. He's not efficient but he will keep aggressively attacking all game. Has that pragmatic look and feel of the game where he just knows how to score with skill and technique on top of his athleticism. His Fe polr has gotten him into trouble by being "too real" with reffs, media etc. Such as his infamous practice interivew.
Lebron seems like a classic Se base to me too. I could see SEE but he also seems logical to me. He's egotistical and a bit emotional, but again, variation. I believe Enneagram plays a role in the sort of variation. Lebron being So/Sx makes him more people oriented. Remember he's almost 40 now and is a smart guy who has a shit ton of life experience now. He's learned what's important, and with Fe as a hidden agenda, I don't see why he wouldn't be focusing on relationships, family etc as he matures/ages.