Tom Brady, Peyton Manning and Kurt Warner are tied for the most games with a passer rating of 158.3 or above and with 20+ passing attempts, with 3 games.

most games with a passer rating of 158.3 or above with a minimum 20 attempts
Interpreted as:
most regular-season games by a player with a passer rating of 158.3 or above with a minimum 20 passing attempts
BradyManningWarnerRoethlisbergerRodgersWatsonPrescottJacksonGoffCousinsSmithSmithFolesBreesMcNabbGreenCollinsFlutieBlakeChandlerKriegEricksonO'Brien33321111111111111111111
NAMEGPRATEATTCMPPCTYDSAVGYDS/GTDTD%INTINT%SCKSCKY
Tom BradyTom Brady3158.3796481.01,04313.2347.71417.700.0320
Peyton ManningPeyton Manning3158.3685479.490113.3300.31217.600.019
Kurt WarnerKurt Warner3158.3756080.01,06114.1353.71013.300.0637
Ben RoethlisbergerBen Roethlisberger2158.3453884.458913.1294.5817.800.0540
Aaron RodgersAaron Rodgers1158.3312580.642913.8429.0516.100.018
Deshaun WatsonDeshaun Watson1158.3332884.842612.9426.0515.200.000
Dak PrescottDak Prescott1158.3322578.140512.7405.0412.500.000
Lamar JacksonLamar Jackson1158.3201785.032416.2324.0525.000.011
Jared GoffJared Goff1158.3332678.846514.1465.0515.200.019
Kirk CousinsKirk Cousins1158.3252080.032413.0324.0416.000.0323
Geno SmithGeno Smith1158.3252080.035814.3358.0312.000.016
Alex SmithAlex Smith1158.3201785.028714.4287.0525.000.0212
Nick FolesNick Foles1158.3282278.640614.5406.0725.000.011
Drew BreesDrew Brees1158.3231878.337116.1371.0521.700.014
Donovan McNabbDonovan McNabb1158.3262180.838114.7381.0415.400.015
Trent GreenTrent Green1158.3252080.034113.6341.0312.000.000
Kerry CollinsKerry Collins1158.3292379.336612.6366.0413.800.000
Doug FlutieDoug Flutie1158.3252080.036614.6366.0312.000.000
Jeff BlakeJeff Blake1158.3221881.827512.5275.0313.600.000
Chris ChandlerChris Chandler1158.3262388.535213.5352.0415.400.012
Dave KriegDave Krieg1158.3252080.035114.0351.0312.000.0210
Craig EricksonCraig Erickson1158.3241979.231313.0313.0312.500.000
Ken O'BrienKen O'Brien1158.3322681.343113.5431.0412.500.0212
Vince EvansVince Evans1158.3221881.831614.4316.0313.600.0
Ken AndersonKen Anderson1158.3211781.029714.1297.0314.300.0
StatMuse has game-level data for passer rating and passing attempts going back to the 1950 season.

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