Why GM's Don't Offersheet(But They Should)

Looking at how game theory influences GM decision making

I had a brief thread on our Instagram story regarding this topic a few weeks ago but never got around to finishing it. I figured it would be better suited as an article, especially since game theory is a very dense topic, and something people may prefer to look back on and refer to.

Game Theory is just a branch of mathematics that provides tools for analyzing situations where players are making decisions that are interdependent. Since decisions are interdependent and should influence the other player’s decision, each player must consider every other player's possible decisions to create a strategy.

The applications of game theory go way beyond mathematics. It applies to economics, all different fields in social science, computer science, and how sports teams are run. The latter is what we’ll be focusing on here, but mainly around the idea of offer sheets, and why they aren’t used, even though from a game theory perspective they should be.

Every decision made by a general manager revolves around game theory, whether they know it or not. The moves they make, whether it’s a trade, free-agent signing, or anything else, will get influenced by another GM’s decision making. Every decision is interdependent, and a good GM must understand this.

The stereotype around GM’s revolves around the idea that they don’t offer sheet players because they don’t want their own players to be offer sheeted, and they don’t want to ruin relationships with other teams. Is this true? And more importantly, is this the right decision? We’ll explore this using game theory.

The prisoner’s dilemma is one of the most popular applications of game theory. Imagine to prisoners are suspects for a crime. The cops put the two in different rooms and offer them deals. If neither of the criminals talk then they both get 1 year in jail, whereas if both admit to the crime they get 6 years each. If one prisoner talks and the other doesn’t, the one that talks gets sent home with no jail time, and the other gets 10 years.

The prisoner’s dilemma helps show us why two completely rational individuals might not cooperate, even if it appears that it is in their best interest. The “dilemma” faced by the prisoners here is that, whatever the other does, each is better off confessing than remaining silent. But the outcome obtained when both confess is worse for each than the outcome they would have obtained had both remained silent. This illustrates the conflict between individual and group rationality. If a player pursues rational self-interest, they may end up worse off had they gone in contrast to rational self-interest.

Every GM during offer sheet season may be choosing to not do it so as to act contrary to rational self-interest, which causes fewer problems for everyone overall. So the question becomes, are GMs all acting against rational self-interest, which benefits everyone more because of it? Well, not necessarily. While it would be nice to imagine that all the GMs in the league are playing game theory perfectly, they aren’t actually facing a normal prisoner’s dilemma.

GMs face what is called The Infinite Prisoners Dilemma. The prisoner’s dilemma we mentioned earlier only applies to decisions that would happen once. But this isn’t the case in management decisions. GMs face these prisoner dilemma situations constantly, every offseason, and during the regular season while trying to make trades/signings.

Since GMs face these decisions constantly, they really are closer to an Infinite Prisoner’s Dilemma situation. The prisoners in our previous example only had to make this decision once. What would happen if they had to make this decision repeatedly every day? Well, we’d see a change in their approach to the dilemma. Since the Infinite Prisoners Dilemma is infinite, the players can use their future decisions as bargaining chips for the present one.

For example, both can decide to not talk, and if one betrays the other, then the other can choose to talk for the rest of eternity, punishing the other player in perpetuity. So now that this is occurring, do the players agree to cooperate for the rest of history(like GMs supposedly do with offer sheets)? Not quite.

To know if the players will cooperate, we must understand the Delta of their decisions. Delta refers to how much a player cares about the present, vs how much they care about the future. They may discount the value of future wins for success now. If the Delta is 1/2, then on day one they care about their day two punishment half as much as day one. 1/3rd would indicate they care about it a third as much, as so on. If Delta is 0 then they don’t care about their future punishment at all, and if it is 1 then they care about their future punishment as much as a current one.

When Delta is 0 they are doomed to both be selfish and uncooperative for eternity, and if it is 1 they will mutually cooperate for eternity. Again, after looking at this we must ask ourself the question, are GMs being smart about their decisions to not offer sheet? We just went over the logic of the Infinite Prisoner’s Dilemma, and it seems like GMs are deciding to cooperate, isn’t this the smart move?

In a simple answer, no. This is because our example ignores a few variables. Firstly, while the Infinite Prisoner’s Dilemma goes on forever, a GM won’t have their job forever. GMs get fired, and most only last a few years at most. So while an NHL team will face an infinite amount of decisions because NHL teams don’t get fired, GMs don’t have this type of security.

When we discussed the Delta, we gave the example of how players will never cooperate if the Delta is 0 and they don’t care about the future consequences, well many GMs should inevitably be closer to a Delta of 0 than they are a Delta of 1. I’m not going to sit here and calculate the Delta for a GM, frankly because I’m not smart enough and a ton of the variables are going to be impossible to measure. But many GMs are on the hot seat every season, and many are a bad season away from being fired. At every moment a GM needs to be entirely hell-bent on making their team better, whether it’s for the future in a rebuild, or for now.

When figuring out whether a GM should offer sheet a player, you need to understand their specific team’s position. Do they have a bunch of RFA’s teams could offer sheet? Do they have the cap space to make a deal? Do they have the right draft picks to make a deal? All these factors need to be accounted for when trying to make this decision.

The beauty with offer sheets is they are both an excellent tool for improving your roster immediately, and in the future. RFA’s are typically younger players, and therefore will have an impact immediately, and into the future. This fact is what makes the lack of offer sheets so baffling, and irrational. Yes, I used the word irrational.

Many GMs need to urgently improve their team and should care far more about the current construction and record for their roster than the future. There are plenty of GMs who are on the hot seat that could desperately use one of the many available RFAs to improve their teams. Often times the lack of improvement from a roster due to not acquiring that player is what gets a GM fired. How many GMs could have saved their job if they acquired Aho last season? How many GMs could save their job and improve their team by acquiring Barzal, Pulock, Cirelli, Dunn, or the other elite RFA’s available.

It’s absolutely baffling from a game theory perspective why more GMs aren’t willing to sacrifice the future for the present, especially when GMs do this every year with the trades they make to win a cup. Isn’t that amazing? GMs are willing to sacrifice the future in almost every other circumstance, but with offer sheets, they won’t do it. They won’t risk angering another team or another team GM to improve their own team. It’s completely irrational.

If the reason GMs aren’t offer sheeting other teams isn’t because of mitigating future consequences for their team, then what is it? The only answer I can come up with is relationships. GMs know that they’ll eventually be fired, and their relationships with other GMs is the only thing that will allow them to get another job in NHL management.

They do not want to anger a person who may eventually become their boss, or be the person who gets to decide if they are hired or not. They also probably don’t want to screw over a GM who they may have to work with someday. This is the real reason in my opinion that it doesn’t happen. It has nothing to do with the success of a franchise, but career preservation for those GMs making the moves. This begs the question, is a GMs job to improve the team, or is it to improve their standing and employability across the league? I’d argue it’s the latter.

Thank you for everyone reading! If you liked this article please consider subscribing to the Newsletter. I plan on writing a new article every few days for you guys.- Eric