I looked at all the QBs drafted in the 1st round over the last 10 years and compared what number they were drafted in the 1st round with the most wins their team in a season while they were there.

NFL turnarounds are so common - especially with a top 5 draft pick at QB playing on a rookie contract - that there is little reason to worry about a bad team tanking a QB's career.

Here are a couple quick charts:



As you can see, the guys drafted with a top 3 pick usually actually win more (from a peak season standpoint) than those drafted later. Even guys who are seen as "busts" like Trubisky & Bortles can't really blame their teams when they each played made the playoffs after being drafted in the top 3. Newton, Luck, Goff, Wentz, RGIII, Baker, and Kyler were all drafted by terrible teams but eventually made the playoffs (I assumed 9 wins for Kyler this year). Even Mariota and Winston won 9 games after being drafted by teams who only won 2 the season before drafting them.

The one outlier is Joe Burrow whose success remains to be seen as they only have 2 wins this year.

The exception to the rule are the two guys drafted at #32 overall - Lamar Jackson and Teddy Bridgewater. They went to good teams and made them better. Here is what the chart looks like with them removed:



TLDR: bad NFL teams often become good so quickly that there's little reason to worry about a player (especially QBs) being drafted by a bad team. If the player has the talent, then the wins will follow. The success is dependent on the player more than the team that drafts them.