NFL- Emergency Quarterbacks

This season has been particularly rough for starting quarterbacks. Seems like every couple weeks, a high-profile QB gets injured- Tony Romo, Ben Roethlisberger, Joe Flacco... list goes on and on. 

These injuries, coupled with the new trend of only having 2 active QBs on gamedays got me thinking- What are the chances that all the active QBs on a team get injured in a game and a team is forced to play an out-of-position player at quarterback? 

To answer this question, I first looked at week 15 rosters and inactives to determine which teams actually only dress 2 QBs on gamedays. Out of the 32 teams, 13 have 2 quarterbacks on their roster and 19 have 3. Interestingly, every single team only had 2 active QBs week 15 except for the Carolina Panthers (Joe Webb, their 3rd string QB, is mostly used on special teams). 

I was surprisingly unable to find any sort of data on past NFL injuries, so I had to do some research myself and find out how many QBs have been knocked out of games.

According to my findings, through the first 16 weeks, the following QBs left during a game and didn't return due to injury:
Week 1- Derek Carr, Josh McCown
Week 2- Jay Cutler, Tony Romo
Week 3- Ben Roethlisberger
Week 6- Marcus Mariota, Michael Vick
Week 7- Josh McCown
Week 8- Ryan Fitzpatrick, Josh McCown
Week 9- Teddy Bridgewater, Ben Roethlisberger
Week 10- Sam Bradford, Brian Hoyer, Landry Jones
Week 12- Josh McCown, Ben Roethlisberger, Tony Romo
Week 13- Matt Hasselbeck
Week 14- Andy Dalton, Brian Hoyer
Week 15- Marcus Mariota, T.J. Yates
Week 16- Matt Hasselbeck

That's a total of 24 QB injuries. Although some QBs are more injury prone than others (Josh McCown has left a game injured 4 times), for the purpose of this exercise, I'll assume all QBs have equal probability of getting injured.

Since there has been 24 injuries in 240 games, there is a 5% chance that a team's starting QB gets injured each game. The back-up QB who replaces the starter would have a 2.5% chance of getting injured that same game assuming that the starter, on average, gets injured halfway through the game. 

Based on these numbers, the chances of a team having 2 QBs injured in a single game is only 0.125%, or 1 out of 800 games (5% * 2.5%). It is very unlikely to see an emergency QB play in any given game.

That being said, if the trend of having only 2 active QBs on gamedays continues, we will most certainly see an out-of-position player forced to finish a game at QB in the very near future.

At 0.125%, we are likely to witness an emergency QB finish a game every 400 NFL games (800 / 2), assuming every team only dresses 2 QBs on gamedays. There are 256 total games in a regular season, so each season, there is a 64% chance a team will be forced to play an out-of-position player at quarterback.

As much as I hate injuries in the NFL, I am looking forward to the day when an unprepared wide receiver or cornerback gets the midgame nod from the coach to play quarterback for the team.

Data Source:
www.ourlads.com
www.nfl.com
www.fftoday.com