In economic theory (and game theory), there is a mathematical concept known as the zero-sum game. Essentially, in a zero-sum game, each participant’s gains (or losses) in utility are balanced out by another participant’s losses (or gains); if the total gains and total losses are added up, the sum should be zero, hence the term “zero-sum game”.

Poker is a great representation of a zero-sum game, as each player starts with a set number of chips, and for every gain that one player makes, there is an equal amount of loss incurred by another player (or several other players).

The opposite of a zero-sum game is a non-zero-sum game, where the total gains and total losses can be greater than or less than zero. A good example of a non-zero-sum game is the Prisoner’s Dilemma, as both parties involved can gain utility or lose utility based on the outcome of the game.

We can apply these theories to the NHL, at least to a limited extent.

For example, if we assume that each player has a number of goals above average that they can contribute to a team, then the total sum of goals above average in the entire league at the end of the year will equal zero; the best team will be well over average, and the worst team will be well below average, but in the end, the sum of all of the players who played at least one game would be equal to zero.

This essentially makes each NHL regular season a zero-sum game, with gains in utility by one team being offset by losses in utility by another team. This is, for the most part, how we view player trades within the NHL. Player 1 is worth X goals above average, while Player 2 is worth Y goals above average; if X is greater than Y, then whichever team acquired Player 1 in exchange for Player 2 “won” the trade.

This works best when we view each regular season as it’s own “game”, as trades for draft picks and prospects represent a gain of future utility for one team, and a loss of future utility for another, while trades for current players would be gains and losses of current utility.

The trade deadline is a great example of a zero-sum game in action, if we assume that each NHL regular season is in fact such a game. The sellers will lose utility as they send rental players to new teams, while the buyers will gain utility as they add new players to their roster.

When analyzing trades, we often look at them under the scope of all 30 teams being a part of the zero-sum game, which is perfectly logical. What we fail to take into account, however, is the fact that there are, for all intents and purposes, two different zero-sum games at play; one between all 30 NHL teams, and one between the 16 teams that make the playoffs.

The playoffs are their own zero-sum game, separate from the regular season, and it’s here that we can find the hidden value of a trade deadline acquisition. Playoff teams that add value to their roster are the trade deadline are making a positive sum transaction, but the loss within the playoff zero-sum game isn’t felt by the team making the trade; they aren’t one of the 16 teams that will be in the playoffs.

Instead, the loss is felt by the other 15 playoff teams that didn’t acquire this player. The player is no longer eligible to be added to their rosters, and the player will be actively helping one of their competitors.

Consider the following example, where each NHL team is “ranked” by goals above average. Each NHL team’s roster is worth a certain number of “goals above average”, going by intervals of 3 from the best to the worst. The 15th and 16th ranked teams are “average”, and therefore have a value of zero, while the best team has a value of 42 goals above average, and the worst team is 42 goals below average.

When we re-rank the teams and recalculate the goals above average values in order look at only playoff teams, the values are different; a good regular season team might end up being only an average playoff team. The numbers of goals that a team is above or below average changes, because the average playoff team is better than the average regular season team.

So, when a playoff team acquires a new player from a non-playoff team, they boost their own value. For the sake of this scenario, let’s assume that the second third, fourth, fifth, and sixth place teams all acquire new players from the 22nd-30th ranked teams. (each team ranked 22-30 lost 3 goals above average, while teams 2-5 gained enough goals above average to become equal with the top-ranked team).

When we look at the current playoff teams, then, we can see where the losses are accumulated for the teams that didn’t add players; the gains of one team have to be offset by the losses of another.

By improving their own team, these hypothetical general mangers essentially made their opposition worse. The other teams experience loss because they can no longer acquire certain players; these players are now on a different team, a team that they will be directly competing with.

To put this in a different way, the Chicago Blackhawks recently acquired Andrew Ladd. They gained value by adding the player that was considered by many to be the biggest name available at this year’s trade deadline. Other playoff teams around the league lost value because they no longer can acquire Ladd, and Ladd is now on a team that they may very well end up facing in the postseason.

The Chicago Blackhawks didn’t just pay the Winnipeg Jets a draft pick, a prospect, and a conditional pick in order to acquire Ladd; the Blackhawks paid that price to make sure that none of their competitors could secure Ladd’s services for the playoffs.

They improved, and the competition got worse. There’s the hidden value in trade deadline acquisitions, especially for teams that are going to be playing the playoffs; not only do you make your own team better, but you essentially make your opposition a little bit worse.

Teams that win the Stanley Cup often seem to do so with the help of trade deadline acquisitions. Last year, the Blackhawks added Antoine Vermette, Kimmo Timmonen, and Andrew Desjardins. The year before that, the Los Angeles Kings traded for Marian Gaborik. Two years before that, the Kings traded for Jeff Carter. Adding players at the deadline can not only make your team better, but also make your opponents just a little bit worse.

The game of hockey is a zero-sum game. Understanding this concept can help general managers out by providing just a little extra value at the trade deadline, and in a league where one or two goals can decide a playoff series, that extra little bit of value might not mean much to every team, but to the few teams with legitimate Cup aspirations, it could be the difference between winning the Cup and going home empty handed.