Why Hoarding Positions Doesn’t Work in Fantasy Football

“The top QBs in a fantasy league are super valuable. Why don’t I hoard this position, ‘corner the market’ and force my league-mates into making trades that help my team?”

This is a very common, and very alluring, line of thinking in single-QB leagues.

First, it’s feasible: the top four QBs in ADP are currently spread out across the first four rounds, which means you could nab at least two with your early picks.

Second, it’s generally intuitive: when you draft Justin Herbert and Patrick Mahomes and both put up awesome seasons, other managers are bound to take notice. They’ll be falling over themselves to trade with you, and you’ll be able to leverage this position to add fantasy assets that your team needs. It’s foolproof, right?

Wrong.

Hoarding the ‘onesie’ positions (we’ll be discussing QBs in this article, but this applies to TEs as well) is generally a terrible idea. Given correct play from your league-mates, your team will suffer massively from this strategy.

Hoarded Player Value

There are tons of ways to value players: with dynasty rookie picks, FAAB, or Wins Above Replacement. This article is more focused on the game theory of the hoarding strategy, and since we are less concerned with how to value players, we can just use FAAB (free agent budget, or how much you can bid on the waiver wire over the course of a season).

For example, consider Patrick Mahomes and Justin Herbert. Let’s say both can be valued independently at $100 FAAB; that is, it’s considered a ‘fair trade’ to trade $100 FAAB for Herbert or Mahomes. I’m using $100 as a round number here: the true value is probably even higher, but this is just an exercise to get the point across.

However, something happens when you roster both of these players: they are no longer worth $100 FAAB to you. Say that Patrick Mahomes has a slightly better year and is more often your starter. Justin Herbert is now – in a single-QB league – on your bench, scoring you zero points for your lineup each week! In this case, Herbert’s value added to your team drops tremendously, since his output doesn’t make it into your actual lineup. Let’s say that his value drops to $40 FAAB for your team; perhaps he starts 40% of the games because of Mahomes’ bye week and bad matchups (again, just picking a nice round number).

Now, this by itself isn’t necessarily a bad thing for the hoarding strategy. After all, you certainly didn’t anticipate starting all of your QBs at once! Of course, it makes less sense to keep Herbert on your roster, but that’s the whole point of the strategy: trade him away to other teams. That should work, right?

A Sequential Game

We’re going to dive into the game theory of fantasy trades here, hopefully at an understandable and accessible level. While some of these technical concepts might be foreign, I hope that the intuition makes sense. First, let’s imagine a trade as a ‘sequential game’, which just means two players – here, the fantasy managers – make moves sequentially (one after the other). In this example, “Manager 2” has Justin Herbert (no hoarding yet) and is looking to trade him. Manager 1 makes the first move, either by offering $100 FAAB or offering nothing. If Manager 1 offers $100 FAAB, Manager 2 can either accept (trade Herbert for $100 FAAB) or reject the offer. The boxes at the end of each ‘branch’ tell us the payoffs of the managers.

Now imagine the general case (non-hoarding) where Herbert’s fair value is $100 FAAB. We have the same structure, and the payoffs represent a ‘fair trade’: if the trade happens (Manager 1 offers $100 FAAB, Manager 2 accepts) then both managers net $0 in FAAB since Herbert was traded for his fair value.

Even better is when the trade can be mutually beneficial. Imagine that Manager 1 values Herbert at $100 FAAB, while Manager 2 values Herbert at $98 FAAB, perhaps because they have slightly different opinions on his future outlook, or their ‘team needs’ are slightly different. In this case, we have a ‘win-win’ situation. Manager 1 offers $99 FAAB, Manager 2 accepts and both get a ‘surplus’ of $1 FAAB. Manager 1 sends $99 FAAB for Herbert, who he values at $100 FAAB, and Manager 2 trades Herbert away, who he values at $98, but gets $99 in return. I’ve shaded out the branches that wouldn’t happen so we could see how this game would play out.

What happens, though, when we have the hoarding situation above, and Manager 2 has a much lower value for Herbert ($40 FAAB)? Well, Manager 1 now has a lot of moves he can make: he can offer $99 FAAB, or $98 FAAB, or $97, all the way down to ‘no offer’. At each offer branch, Manager 2 can either trade Herbert or reject the offer: I’ve only drawn the branches for a $99, $41, and $1 offer just to save space.

We can now think about what Manager 2 will do at each of these branches. In the extreme case – Manager 1 offers $99 FAAB – Manager 2 will happily accept. He values Herbert at $40, which means he’s getting a $99 – $40 = $59 surplus. Note that Manager 1 still has a $1 surplus for this trade, since he values Herbert at $100 and is sending $99 FAAB for him. On the other end of the spectrum, where Manager 1 offers $1, Manager 2 of course declines: even though Herbert is valued at a lower $40 FAAB, that’s still far too much to accept $1 FAAB for.

The ‘breakeven’ point happens at the $41 FAAB offer: Manager 2 has a positive surplus (receives $41 FAAB for a player he values at $40 FAAB) and thus would accept the trade.

So, what happens? The left-most case (Manager 1 offers $99) is certainly the ideal case for a hoarder: he gets a ton of value by trading Herbert away. However, the key point in this game is that Manager 1 can anticipate what Manager 2 will do. That is, Manager 1 knows (at least with some accuracy, perhaps not with as much precision as this toy example) which ‘branches’ Manager 2 will reject or accept the trade. Manager 1 can envision the tree above, and therefore will choose his branch as…

Voila! In the ‘equilibrium’ of the game, Manager 1 will offer $41 FAAB to Manager 2, who will accept because it still represents a surplus. Manager 1 won’t offer a higher FAAB, since he knows that he can still get the offer to go through by sending less FAAB, which is thus a better deal for him. The bedrock of this reasoning is that Manager 1 is aware that Manager 2 experiences much lower value by having Justin Herbert on his bench, and thus can lowball the offer. Manager 2 might huff and puff and demand a higher FAAB trade, and this might eventually work in some leagues. At the end of the day, though, if Manager 2 is acting purely in his best interest, he will take a trade that yields him a positive surplus.

Nash Equilibrium

If you aren’t interested in the technicals behind this idea, you can skip ahead to the conclusion. If you are, we’re going to discuss Nash Equilibrium, discovered by the famous mathematician John Nash.

In the above game, each player has a set of different strategies. Manager 1 can offer a variety of different FAAB amounts (or make no offer at all). Manager 2 can accept or reject the trade, all depending on what Manager 1 offers. A Nash Equilibrium occurs when two players are using strategies that are optimal given the other player’s strategy.

What does this mean? Well, think about our specific case. Given that Manager 1 is offering $41 (his strategy), Manager 2’s optimal strategy is to accept the offer and trade Herbert (since it represents a $1 surplus). The trickier case is in the other direction. Given that Manager 2 will reject any FAAB offer below $41 and accept any offer from $41 up, Manager 1’s best strategy is to offer $41, since it minimizes the amount he has to send.

Note that Manager 1 offering $99 and Manager 2 accepting is not a Nash Equilibrium. Manager 2 is quite happy – he gets a hefty surplus – but Manager 1 can do much better! He isn’t optimizing.

Conclusion

Hoarding is certainly a creative strategy, and it can be tempting. However, two crucial reasons make this a foolhardy strategy for your team. First, the ‘second’ QB that you roster will have much less value to your lineup, since he won’t be started often. Second, the rest of the league will recognize that you value this QB less and thus will be willing to trade him for less; the offer will end up being far lower than you expected.

I should reiterate that this is a simple example with easy, round numbers. There are a lot of complications and variances, but I think the broad strokes hold true. One counter-argument is that, by drafting two of the top QBs, you are pretty much guaranteeing having at least one elite QB on your team; you might argue that this is better than taking the chance on a player who could completely bust. I don’t buy this logic, though: even if the RB or WR that you draft in the third round isn’t incredible, it’s likely that he will still make important starts for your fantasy team. That is, he will add much more value than the second QB warming the fantasy bench!

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