It’s a tricky calculation to figure out how to value backups. During an auction, how much of your budget do you allocate to backups? When drafting, which is more important: a backup quarterback, or a fourth WR? First, let’s take a step back. We need backups for four scenarios:

- To fill in during bye weeks
- As replacement if a starter is injured
- As replacement if a starter underperforms
- As replacement if the backup’s performance exceeds the starters

The first scenario is straightforward to calculate: if the backup has the same bye week as your starter it has 0 value to you. If the backup has a different bye week, it’s value is about 1/16 of his projected value. The other three scenarios require some probabilistic work, because we do not know if our starter will be out-performed by the backup or injured during the season.

Above is a graph of expected points for Andrew Luck

Marcus Mariotta’s graph is similar. Luck is projected to score about half a point per game more. There’s a lot of uncertainty in the projection, and to see that a heap of ‘idunno’ is probably justified for future-looking predictions, try predicting the future yourself at quncertain.com.

In the system, Luck is projected as the 8th best QB and Mariota is projected as around 14th best, but it’s conceivable for either to be vastly better than this ranking at the end of the year. There is also injury concern with Luck. So, some teams will no doubt have Luck as a starter and Mariota as a backup with breakout potential. Also, both players have different bye weeks.

So how do you value Mariota? He could be your starter by the end of the season. Or, Luck could reel off an MVP year, with Mariota riding the bench and contributing very little to your score. It depends on who plays better. Because you are able to adjust your rosters week to week, you’re able to swap in the player with the better chance of a big game. Looking at the expected points for a weekly max-type function with Luck+Mariota gives a graph like this:

Expected points from a Luck, Mariota combination.

As you can see, backups are useful because they:

- Mitigate downside risk
- Increase the median of expected points

Adding a third backup is an improvement again, just not as dramatic. Adding Trevor Siemian as a third QB gives a graph like this:

Expected points for Luck, Mariota, Siemian combination, truncating the left tail, elongating the right tail, and shifting the median a little to the right.

With data like this we can calculate the value of backups, directly relating price to the amount they increase a team’s chance of winning a league. Calculations for positions with multiple starters, and flex options are more complicated because of the many combinations to consider, but the results are approximately the same. I hope to have my auction valuations on the site soon.