Drew Brees had the most games with 250+ passing yards, with 187 games.

who has the most games with 250 or more passing yards
Interpreted as:
Who has the most regular-season games with 250 or more passing yards?
BreesBradyManningFavreRiversRyanMarinoRoethlisbergerRodgersManningStaffordPalmerMoonFoutsRomoElwayWarnerFlaccoMontanaBledsoeTestaverdeCollinsCutler18717416814213313112612011310597969588818076747069676463
NAMEGPYDSCMPATTPCTAVGYDS/GTDTD%INTINT%SCKSCKYRATE
Drew BreesDrew Brees18761,5865,2687,57469.68.1329.34475.91662.22862,013104.5
Tom BradyTom Brady17455,4234,5286,79466.68.2318.54186.2981.42871,783106.1
Peyton ManningPeyton Manning16852,9774,3266,48066.88.2315.33996.21642.52051,370101.8
Brett FavreBrett Favre14242,9683,4955,49763.67.8302.63065.61653.02541,67593.7
Philip RiversPhilip Rivers13341,9773,3344,99866.78.4315.62705.41182.42571,519100.8
Matt RyanMatt Ryan13140,8263,4555,15667.07.9311.62454.8971.92931,90298.9
Dan MarinoDan Marino12639,4653,0424,93861.68.0313.22875.81543.11631,17593.1
Ben RoethlisbergerBen Roethlisberger12038,6153,1464,74766.38.1321.82475.21202.52471,62298.0
Aaron RodgersAaron Rodgers11335,8682,8364,29066.18.4317.42896.7551.32751,804109.1
Eli ManningEli Manning10532,8972,6784,18464.07.9313.32074.91273.01671,21092.0
Matthew StaffordMatthew Stafford9731,0772,5333,95464.17.9320.41995.0802.02241,49396.6
Carson PalmerCarson Palmer9630,1042,4293,74264.98.0313.61885.0962.61981,33895.8
Warren MoonWarren Moon9529,6992,2983,76461.17.9312.61624.31223.21891,40586.7
Dan FoutsDan Fouts8828,0112,0483,29862.18.5318.31785.41213.791.9
Tony RomoTony Romo8125,0992,0213,03166.78.3309.91705.6722.41611,090100.9
John ElwayJohn Elway8024,1011,7862,92961.08.2301.31505.1742.51721,32293.7
Kurt WarnerKurt Warner7624,5261,9572,89067.78.5322.71615.6863.01611,059100.0
Joe FlaccoJoe Flacco7422,2641,8822,96263.57.5300.91234.2561.91511,04192.3
Joe MontanaJoe Montana7022,2641,7422,61366.78.5318.11646.3702.7102.9
Drew BledsoeDrew Bledsoe6921,5301,7152,78661.67.7312.01364.9802.91431,02589.9
Vinny TestaverdeVinny Testaverde6720,6121,5682,66158.97.7307.61224.6943.513197784.0
Kerry CollinsKerry Collins6419,2581,5232,56459.47.5300.91084.2682.712783485.9
Jay CutlerJay Cutler6318,8071,5172,40263.27.8298.51134.7763.211467689.8
Donovan McNabbDonovan McNabb6319,5591,4832,36862.68.3310.51335.6451.914897399.5
Kirk CousinsKirk Cousins6219,5891,6092,33169.08.4316.01345.7472.0115862105.4
StatMuse has game-level data for passing yards going back to the 1950 season.

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