Tom Brady and Brett Favre are tied for the most games with 50+ passing yards, with 298 games.

who has the most games with 50 or more passing touchdownss
Interpreted as:
Who has the most regular-season games with 50 or more passing touchdownss?
BradyFavreBreesManningRiversMarinoTarkentonManningRoethlisbergerElwayTestaverdeRyanMoonBledsoeUnitasRodgersKriegCollinsHartPalmerHadlEsiasonFlacco298298284263241241235234233228218204202194190188188186184180179174173
NAMEGPYDSCMPATTPCTAVGYDS/GTDTD%INTINT%SCKSCKYRATE
Tom BradyTom Brady29879,1156,76910,57764.07.5265.55805.51901.85213,27297.4
Brett FavreBrett Favre29871,8066,29410,15462.07.1241.05085.03323.35233,46886.3
Drew BreesDrew Brees28480,2257,12810,52667.77.6282.55715.42412.34202,99198.8
Peyton ManningPeyton Manning26371,8946,1189,35665.47.7273.45395.82472.63001,94496.8
Philip RiversPhilip Rivers24163,4075,2728,12664.97.8263.14205.22092.64642,83295.2
Dan MarinoDan Marino24161,3534,9668,35559.47.3254.64205.02513.02701,93086.5
Fran TarkentonFran Tarkenton23546,7653,6536,37757.37.3199.03415.32644.181.0
Eli ManningEli Manning23456,9964,8918,10160.47.0243.63664.52423.04092,86184.3
Ben RoethlisbergerBen Roethlisberger23360,3485,0507,83864.47.7259.03965.12012.65163,43894.0
John ElwayJohn Elway22851,3094,1047,20557.07.1225.02994.12243.15043,70880.1
Vinny TestaverdeVinny Testaverde21845,9443,7546,62056.76.9210.82734.12634.04082,93375.4
Matt RyanMatt Ryan20455,7524,8657,44065.47.5273.33474.71582.14092,70394.5
Warren MoonWarren Moon20249,1893,9746,78558.67.2243.52914.32273.34523,35781.5
Drew BledsoeDrew Bledsoe19444,6113,8396,71757.26.6230.02513.72063.14673,13577.1
Johnny UnitasJohnny Unitas19040,0112,7955,07755.17.9210.62885.72414.779.9
Aaron RodgersAaron Rodgers18851,0654,2636,54765.17.8271.64126.3881.34613,099104.2
Dave KriegDave Krieg18838,0303,0885,26458.77.2202.32615.01973.74823,69882.0
Kerry CollinsKerry Collins18640,7073,4566,18055.96.6218.92063.31923.13292,19074.3
Jim HartJim Hart18434,3602,5564,99351.26.9186.72084.22404.867.3
Carson PalmerCarson Palmer18046,2163,9376,29362.67.3256.82944.71863.03402,36488.1
John HadlJohn Hadl17933,1892,3254,57750.87.3185.42425.32535.569.2
Boomer EsiasonBoomer Esiason17437,6762,9395,13657.27.3216.52474.81793.53112,36981.8
Joe FlaccoJoe Flacco17340,8533,7306,03861.86.8236.12243.71422.43632,60484.3
Ken AndersonKen Anderson17232,5272,6074,37659.67.4189.11974.51533.583.1
Dan FoutsDan Fouts17142,8363,2695,53559.17.7250.52544.62364.381.1
StatMuse has game-level data for passing yards going back to the 1950 season.

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