4 players are tied for the most games with a passer rating of 158.3 or above and with 15+ passing attempts, with 3 games. The first three are Ben Roethlisberger, Tom Brady and Peyton Manning.

most games with a passer rating of 158.3 or above with a minimum 15 attempts
Interpreted as:
most regular-season games by a player with a passer rating of 158.3 or above with a minimum 15 passing attempts
RoethlisbergerBradyManningWarnerJacksonMortonRodgersWatsonPrescottWilsonGoffCousinsTannehillMariotaSmithSmithFolesGriffinBreesMcNabbGreenCollinsFlutie33332211111111111111111
NAMEGPRATEATTCMPPCTYDSAVGYDS/GTDTD%INTINT%SCKSCKY
Ben RoethlisbergerBen Roethlisberger3158.3615183.679813.1266.01321.300.0862
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
Lamar JacksonLamar Jackson2158.3373286.554714.8273.5821.600.011
Craig MortonCraig Morton2158.3363186.156915.8284.5719.400.0
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
Russell WilsonRussell Wilson1158.3171482.424814.6248.0317.600.0211
Jared GoffJared Goff1158.3332678.846514.1465.0515.200.019
Kirk CousinsKirk Cousins1158.3252080.032413.0324.0416.000.0323
Ryan TannehillRyan Tannehill1158.3191894.728214.8282.0421.100.0441
Marcus MariotaMarcus Mariota1158.3151386.720913.9209.0426.700.0224
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
Robert Griffin IIIRobert Griffin III1158.3151493.320013.3200.0426.700.028
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
StatMuse has game-level data for passer rating and passing attempts going back to the 1950 season.

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