What is the Value of a Bench Player in Fantasy Football? Part III

What is the Value of a Bench Player in Fantasy Football? Part III

By Kevin Zatloukal (4for4 Contributor), last updated Sep 12, 2016

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Kevin is a Ph.D. computer scientist. His doctoral work at MIT was focused on quantum algorithms. During the fantasy offseason, he teaches computer science at the University of Washington, his alma mater.

Follow Kevin on Twitter: @kczat.

The value-based drafting (VBD) strategy focuses on drafting the starting players who will deliver the most points over the season. In order to win the championship, though, we also need to fill out our roster with high quality bench players who can step in when our starters are unavailable or have bad matchups. Since VBD becomes less useful as starting spots fill up, we need additional strategies to help us through the remainder of the draft.

The first step in developing such a strategy is estimating the value of potential bench players. In our first and second installments of this series, we looked at the value of backup players at QB, RB, WR, and TE to see how much value they are likely to add to our team. In the first half of this article, we will look at the final two positions, defenses and kickers.

Once we know the value of each potential bench player, the next step is to apply this knowledge to determine the optimal way to constitute our bench from these different positions. In the second half of this article, we will do just that.

For simplicity, we will focus on leagues using the best-ball format, where the best starting players are chosen automatically after all their scores are known. This format is used in draft-only leagues such as the popular MFL10 contests and the Scott Fish Bowl Draftmasters. For non-best-ball leagues, the value of backup players will almost always be less than described here. In both types of leagues, backups provide value when the usual starters are injured. However, in non-best-ball leagues, backups will only have the opportunity to contribute to our team when we explicitly choose to start them — usually only in their best matchups — while, in best-ball leagues, the backups can potentially contribute during any given week. These additional opportunities give backups a bit more value on average in best-ball leagues (which we'll use as the example below) than in non-best-ball leagues.

Defenses and Kickers

As in our first two installments, we determine the average value backups add to our team using Monte Carlo simulations. Since we don't know the exact number of points any particular player will score during a given week, we instead randomly chose a number of points that would be typical for a player at that position and draft rank over recent seasons. With their points in hand, we can see exactly how many more points we would get by having the backup compared to what we would get without them. By repeating this a large number of times, we get a good estimate of the average value added by each backup.

Rather than looking at the value of the specific players available at this moment in the later rounds of drafts, we instead look at the average value available in later rounds at each of the positions over recent seasons (see here for an example of what this looks like at the RB position). This allows us to learn some lessons that do not go out the window with changing ADPs.

The following table shows the value of backup defenses (DEF) and kickers (K) when we can start only one at each position. Each row shows the value the first and second backup at each position add to our team.


  Backup #1 Backup #2
DEF 75.20% 39.80%
K 28.50% 12.50%


Each value is listed as a percentage of the points that player would contribute as a starter. For example, if we take the 16th DEF off the board, we might expect them to score 5.3 points per game as a starter. However, as the first backup, we only get 75.2% of that value (or 4.0 points per game) more than we would score without them.

In each case, we only get a fraction of a player's points added to our score. This happens for two reasons. First, in many cases, the backup players end up on our bench instead of in a starter spot. In those cases, their points do not count toward our score. Second, even if they end up in a starter spot, the value they add to our score is only the amount they outscore the starter, who then drops to the bench. For example, if the first backup outscores a starter by 0.1 points, they've only added 0.1 points beyond what we would have had without them. For those reasons, the value added by backups is only a fraction (usually a small fraction) of the points they score.

(All of the estimates given here have an error of plus or minus 0.3 points per game. Regardless of whether you spend early picks on your starters or late ones, the estimate for the value of the backup given in the table will usually be within 0.3 points per game.)

From the table, we can see backup defenses retain more of their value. In fact, not only do they retain more value than backup kickers, but they actually retain more value than the first backup at any other position. Even in leagues where we start four RBs (each of which has a substantial possibility of being injured), the first backup defense retains more of its value than the first backup RB, provided we use best-ball scoring.

As we saw in our earlier installments, running backs keep a larger fraction of their starting points when used as backups than QBs, WRs, and TEs in part because RBs have a higher chance of being injured. An injury to a starter allows the backup to provide full value to the team. However, with defenses this is not due to injury risk. After all, other than bye weeks, team defenses will always play.

The reason backup defenses retain more of their value than any other position is the week-to-week variation in the points scored by defenses is much larger than the dropoff in average points scored between the starter and backup. For example, the difference in average points scored between the first defense off the board and the 16th is less than two points per game (using common scoring settings) while the week-to-week variation (as measured by the standard deviation) is over seven points per game. So the odds our backup defense will outscore the defense in our starter spot is actually quite large (if you'd like to learn more about this, check out John Paulsen's series on the most consistent players at each position, where he utilizes a closely related concept called the coefficient of variation).

Backup kickers, on the other hand, provide very little value. On the one hand, the dropoff from the first kicker off the board to the 16th is less than half a point, so as with defenses, it is quite possible  a backup will outscore the starter. However, the week-to-week variation in kicker points is only about 3.25 points, so even when our backup does outscore the starter, it won't usually be by very much. Not only does the backup kicker provide only a small fraction of its value as a starter, but also its value as a starter isn't very large. Put it all together and it makes backup kickers pretty worthless.

Building an Optimal Bench

Now that we have good estimates for the value added to our team by the backups at each position, we can determine how many backups we should draft at each position in order to add the most value to our team. In this section, we will discuss the allocation for various bench sizes.

We will consider a league which starts 1 QB, 2 RBs, 3 WRs, 1 TE, 1 DEF and 1 K. While drafters tend to broadly agree on the top picks at each position, my impression is larger differences appear later in the draft, so we will assume that once we start drafting backups, the other drafters are generally not sniping all of our top choices like they might in earlier rounds. In particular, we will assume we can draft backups with rank (on our board) of around 16 at QB, TE, DEF and K; 30 at RB; and 42 at WR. As a result, we will not need to worry about the exact order our picks are taken, and instead, can just focus on which positions to draft for our backups.

Per those assumptions, the following table shows the optimal number of backups to draft at each position for benches of size 5 through 10:


Bench Size QBs RBs WRs TE DEFs Ks
5 1 1 2 0 1 0
6 1 1 2 1 1 0
7 1 2 2 1 1 0
8 1 2 2 1 2 0
9 1 2 3 1 2 0
10 1 2 3 1 2 1


With a small bench containing only five spots, we get the most value added by taking 1 QB, 1 RB, 2 WRs and 1 DEF as backups. As we discussed, defenses have tremendous value in best-ball formats due to the week-to-week variation, so that is why we want one on our bench. We also want two WRs because, as we saw in our previous installments, backups have more value when there are more starters at a position, and the league setup we are considering has more WRs than anything else. A backup RB is also important since they get injured so frequently. Finally, we want a backup QB as well. While the backup QB provides a smaller fraction of its value as a starter than RB, WR or DEF, its starter value is so large that even a small fraction of it is worth more than a second backup RB, for example.

When we have six or seven spots on our bench, the next most important positions to draft are a backup tight end and a second backup RB. The second backup RB only provides value if two of the three RBs in front of him are injured or if he should outscore two of them (which will normally not be by very much). As we saw earlier, the second backup RB only provides 28.1% of its value as a starter, which is about the same as the first backup TE, which provides 29.0% of its value. The table says to take a backup TE with the sixth spot, but there is not much difference over taking a second backup RB, so go with whichever of those two positions have the most value on the table when you get to that part of your draft.

When we get to eight bench spots, we want to take a second backup defense. This is again due to the large value provided by backup tight ends in best-ball leagues. In a non-best-ball league, it would make more sense to skip this and take another wide receiver, as in the optimal bench for best-ball leagues with nine bench spots.

Finally, with ten bench spots, the most value is added by taking a backup kicker in our final bench spot. The backups at the other positions all have fairly minimal value at this point as evidenced by the fact that they have less value than a backup kicker. In non-best-ball leagues, it makes more sense to grab another RB or WR at this point. When we get to the bye week of our kicker, we can always grab any old kicker off the wire as they are pretty much all equally valuable.

One last thing to consider in non-best-ball leagues is what will be available on the waiver wire. It may be at one particular position there are enough good backup choices available that you think it is likely some of them will go undrafted. In such cases, it makes sense to not to draft that position as much as indicated in the table above and instead move on to the next best position according to the table. If you end up needing the skipped backup during the season, you can grab them off the waiver wire. In the meantime, you get a little extra value for your team by holding a backup for another position on your bench.

This wraps up our series on drafting backup players. After you have drafted your starters (using VBD, for example), the table above should be a good guide for which positions to draft on your bench. And as always, 4for4's projections (for standard and PPR leagues) will tell you exactly which players to draft at each of these positions so you have the best chance to dominate your league.

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Filed Under: Preseason, 2015

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