Almost every Star Player, at least statistically, experiences a slight drop off in the playoffs.

I am not really concerned about whether they won the championship that year, although longer postseason runs are more impressive.

Avoid players that only played a single series since it is much easier to go nuclear over a smaller sample on a favorable matchup.

So 1986 Jordan / 1988 Hakeem / 2021 Luka are disqualified.

Some Candidates :

1970 Kareem - 29/15/4 on 55.2 TS% in RS to 35/17/4 on 60.8 TS% (10 games)

1977 Kareem - 26/13/4 on 60.8 TS% in RS to 35/18/4 on 64.6 TS% (11 games)

1984 Bernard - 26/5/2 on 61.9 TS% in RS to 35/6/3 on 62.0 TS% (12 games)

1987 Hakeem - 23/11/3 on 55.4 TS% in RS to 29/11/3 on 65.9 TS% (10 games)

1987 Worthy - 19/6/3 on 57.8 TS% in RS to 24/6/4 on 62.4 TS% (18 games)

2005 Ginobili - 16/4/4 on 60.9 TS% in RS to 21/6/4 on 65.2 TS% (23 games)

2006 Duncan - 19/11/3 on 52.3 TS% in RS to 26/11/3 on 62.5 TS% (13 games)

2009 LeBron - 28/8/7 on 59.1 TS% in RS to 35/9/7 on 61.8 TS% (14 games)

2016 Kyrie - 20/3/5 on 54.0 TS% in RS to 25/3/5 on 57.4 TS% (21 games)

2020 Murray - 19/4/5 on 55.9 TS% in RS to 27/5/7 on 62.6 TS% (19 games)

Observation - Quite interesting that none of the qualifying Jordan postseasons have vast improvements due to his insane regular seasons.