The Anomaly of Best Director

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Here's a list of directors who got three or more nominations:

Nominations Director
12 William Wyler
10 Martin Scorsese
9 Steven Spielberg
8 Billy Wilder
7 Woody Allen
David Lean
Fred Zinnemann
6 Frank Capra
5 Robert Altman
Clarence Brown[c]
George Cukor
John Ford
Alfred Hitchcock
John Huston
Elia Kazan
George Stevens
King Vidor
4 Francis Ford Coppola
Michael Curtiz[d]
Clint Eastwood
Federico Fellini
Stanley Kubrick
Frank Lloyd
Sidney Lumet
Joseph L. Mankiewicz
Mike Nichols
Peter Weir
3 Paul Thomas Anderson
Ingmar Bergman
Richard Brooks
Joel Coen[g]
Stephen Daldry
David Fincher
Miloš Forman
Bob Fosse
Alejandro González Iñárritu
James Ivory
Norman Jewison
Stanley Kramer
Ang Lee
Ernst Lubitsch
David Lynch
Leo McCarey
Lewis Milestone
Alexander Payne
Arthur Penn
Roman Polanski
Sydney Pollack
Carol Reed
David O. Russell
John Schlesinger
Ridley Scott
Oliver Stone
Quentin Tarantino
William A. Wellman
Robert Wise[f]
Sam Wood

And here are my choices:

Alfred Hitchcock 9
Ernst Lubitsch 9
Terrence Malick 9
Ingmar Bergman 8
Stanley Kubrick 8
Jean Renoir 7
Martin Scorsese 7
Robert Bresson 6
Francis Ford Coppola 6
Jean-Luc Godard 6
Michael Powell/Emeric Pressburger 6
Andrei Tarkovsky 6
Robert Altman 5
Paul Thomas Anderson 5
Carl Theodor Dreyer 5
Sergei Eisenstein 5
Terry Gilliam 5
Akira Kurosawa 5
Hayao Miyazaki 5
Roman Polanski 5
Satyajit Ray 5
Alexander Sokurov 5
Steven Spielberg 5
Orson Welles 5
Billy Wilder 5
Wes Anderson 4
Charles Chaplin 4
Terence Davies 4
Howard Hawks 4
Ben Sharpsteen 4
Preston Sturges 4
Quentin Tarantino 4
Francois Truffaut 4
Wong Kar-wai 4
Max Ophuls 3
Woody Allen 3
Theo Angelopoulos 3
Michelangelo Antonioni 3
Frank Capra 3
Henri Georges Clouzot 3
Constantin Costa-Gavras 3
George Cukor 3
Michael Curtiz 3
Jean and Luc Dardenne 3
Vittorio de Sica 3
Stanley Donen 3
Federico Fellini 3
David Fincher 3
Peter Jackson 3
Jean-Pierre Jeunet 3
Jim Jarmusch 3
Abbas Kiarostami 3
Sidney Lumet 3
David Lynch 3
Leo McCarey 3
Kenji Mizoguchi 3
Christian Petzold 3
Alain Resnais 3
Roberto Rossellini 3
Jacques Tati 3
Lars von Trier 3
Agnes Varda 3
Luchino Visconti 3