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Penalty Background

So, you think you know everything there is to know about penalties in USA Hockey®?

The USA Hockey® rulebook contains over a hundred penalty "situations". See, for example, pp. 102-115 and 123-126 of the printed 2021-2025 USA Hockey® Official Rules and Casebook of Ice Hockey. Each situation presents a hypothetical scenario whereby a series of penalties are assessed to the two teams over several stoppages. Each situation typically ends with a goal being scored by one of the teams. The bottom of each casebook situation presents the reader with an explanation of the proper handling for the situation upon the scoring of the goal. For simpler situations, the explanation is usually something simple, along the lines of "Player X returns" or "Nobody returns" from the penalty box.

Many of the situations in the rulebook have more complex handling. These situations oftentimes call for so-called "additional players" and "substitutes" and occasionally call for a "captain's choice". An additional player is an innocent player who is designated to serve a penalty for a teammate. The purpose of this player is to increase the team's on-ice strength when the teammate's penalty expires. A substitute is a player who must take the ice in place of a teammate who was penalized. Both additional players and substitutes may become necessary whenever coincidental penalties are involved. Coincidental penalties are penalties of the same type (e.g. minor) assessed to an equal number of players on both teams during the same stoppage. These penalties offset each other and result in no time on the penalty clock, but the players still must sit in the penalty box and serve the penalty. This concept alone has confused scorekeepers—particularly parent scorekeepers who are not certified officials—for generations.

Things get interesting when one player is serving multiple penalties where, some penalties were offset as coincidental and others not: in this situation, the additional player serves the clock penalty (or penalties) and leaves the penalty box when the clock penalty (penalties, resp.) expires, but the penalized player remains in the box to serve the remaining coincidental penalty time, which is not shown on the clock.

Another area of complexity arises when the penalties assessed to the teams are lopsided. For example, if a player from Team A is assessed a penalty and two different players from Team B are also assessed penalties during the same stoppage, there becomes a choice of which Team B player's penalty should be made coincidental and which one should serve the time on the clock. The choice is not simply a trivial bookkeeping exercise. Rather, the choice can determine which player leaves the penalty box first. Who gets to make the choice is another major area of confusion. Sometimes it is the official that must make the choice, and sometimes the team captain. More on that later.

Whenever there is a differential between the number of penalties assessed to both teams during the same stoppage, the official must decide which penalties from one team to offset from which other penalties from the other team. For example, if Player 1 from Team A receives a penalty and Players 2, 3, and 4 from Team B also receive a penalty during the same stoppage, Team A's player 1 penalty must be coincidental, but there is a choice of which Team B player's penalty to offset the Team A penalty with. In general, the choices available to the official are not simply a trivial bookkeeping matter, but may rather have a significant impact on the team and therefore the game. In the future, we expect to produce some videos illustrating how this is the case.

The use of additional players and substitutes is generally not desirable because it is disruptive: an additional player is an innocent player who is taken out of the game temporarily to serve someone else's penalty. A substitute is forced off the player bench to replace another player. The substitute may not be fully rested and is likely not playing with their usual line. Both of these situations are disruptive and although they are sadly a required part of the game, USA Hockey® seeks to minimize their use as much as possible. To this end, it turns out that when an official selects the penalties to offset, each potential offset choice may result in a different number of additionals and substitutes. Some offset choices result in more overall "disruption", while others result in less.

So, how are officials expected to minimize disruption? Each penalty offset choice will yield some total number of additionals and substitutes among the two teams. The official is expected to choose the offset choice with the lowest total. In situations where there are multiple offset choices yielding the same total, the official is then expected to defer to the captain of the team requiring penalty offset choices to be made. In other words, the captain is allowed to choose which penalties to offset for their own team, but only if the choice would not affect the total game "disruption". Stated differently, the official is expected to whittle down the total number of offset choices to only those having the lowest possible disruption total. If, after applying this filtering, there is more than one choice, then the captain gets involved.

Hopefully the above discussion makes perfect sense to the reader. Sadly, however, most of this very critical discussion appears anywhere in the USA Hockey® rulebook or casebook. However, the fact remains that one cannot properly handle all of the casebook penalty situations without a thorough understanding of this "least disruption" principle.

Can This be Automated?

All of the complexities noted above are enough to make anybody's head spin. How on earth is an ice hockey official supposed to process all of this in their head during a game?

Back in 2019, Cory Plock, a hockey official from Connecticut, was reviewing the situations listed in the casebook, trying to determine how USA Hockey® was arriving at each explanation. This led Plock to search for the step-by-step procedure used by USA Hockey® for arriving at the correct answer for each situation. He naively assumed that one must already exist and be published somewhere, since USA Hockey® provides over a hundred such penalty situations that it took the time to provide explanations for. He further assumed that, whatever the procedure was, it must be relatively simple and straightforward, since USA Hockey® tests its officials on their knowledge of how to handle these situations. Yet no such procedure is published anywhere. So, if hockey officials are expected to know how to deal with each casebook situation, how come they are not provided with the right tools for solving what we call the penalty assessment problem?

As a computer scientist, Plock had been developing software algorithms to solve real-world problems for decades. At first, he viewed this just another typical problem to be solved. However, as he became more engrossed in discovering what the penalty assessment procedure was, the more he came to realize that the procedure was anything but simple. Fortunately, the pandemic afforded Plock with the extra time he might otherwise not have had to work on the algorithm. Plock took an iterative approach, implementing what he thought the correct penalty assessment procedure would be, then using unit tests to determine if the software was able to reproduce the outcomes described in the casebook. At first, the procedure developed by Plock failed the majority of unit tests. Each time one failed, Plock set out to figure out why it was wrong and updated the procedure accordingly. Sometimes, fixing the procedure on one failed test case caused several other previously working test cases to fail. In many cases, the reason for the failure was straightforward once it became known. In other circumstances, it was necessary to approach USA Hockey® directly, to determine how they arrived at certain outcomes in their penalty situation explanations. In total, it took several years of research to arrive at the correct procedure.

Finally, in mid to late 2022, the procedure had been perfected so that it was finally able to pass all of the casebook unit tests. Now that the correct procedure was finally known—at least to one person—Plock realized that the correct procedure was not only extremely complicated for a human to understand, it moreover belonged to a class of problems known to be time-consuming for even computers to solve! There is no way that humans can solve all of the casebook situations in their mind during a hockey game. Only the simplest cases could be done in one's mind. Everything else would require the official to figure out the right outcomes with a pen and paper, provided they knew the correct procedure, and provided they were provided ample time to solve each situation. The latter approach is unacceptable during live gameplay, as hockey officials are expected to assess penalties quickly and get on with the game. So although the simpler penalty assessment cases may be useful in allowing a hockey official to "get the jist" of how to assess penalties, the truth of the matter is that the more complex cases are completely unmanageable for officials to solve in real life.

HockeyPenalty.com is Born

Notwithstanding the lack of simplicity, Plock believed that USA Hockey®'s motivation behind the penalty assessment procedure, such as to minimize additional players and substitutes for example, was nevertheless a worthy one despite all of the required effort. If only there was some way hockey officials could receive a little "help" in arriving at the proper way to handle any penalty situation imaginable. Thus, Plock set out to transform the procedure into an interactive web site that hockey officials could train on and learn from. In this way, officials could enter any penalty situation they can think of, and see how it should be properly handled in accordance with USA Hockey® rules. It would be no longer necessary for officials to limit themselves to the preselected situations in the USA Hockey® casebook. It would also no longer be necessary for officials to search through the casebook in search of the one case they are looking for. This web site feature now exists and is called the penalty Simulator. The web site front end and many aspects of the unit testing were carried out by Plock with the assistance of Samantha Stone.

The simulator is useful for training purposes, but is not designed for use during live games. Therefore, a secondary goal is to allow this algorithm to be used during live gameplay. One common issue Plock noticed is that scoreboard operators, often parents, go back and forth between a scoresheet and a scoreboard controller durng games. First they write the penalties down on paper as signaled by the referee, then they transfer the penalties over to the scoreboard. To eliminate this error-prone back-and-forth procedure, Plock and Stone further impelemnted a design whereby the scoreboard operator would simply record the details of each stoppage as it happens. For stoppages involving penalties, the scoreboard operator justs enters the list of penalties assessed by the referee. They do not need to be a certified official and they don't need to know anything about coincidental penalties or any of the minor nuances discussed above. The scoreboard operator need only read the instructions provided by the game feature.

The user interface for the game function borrows heavily from the penalty simulator, but they are not the same. The main feature of the game component is that it receives stoppage-by-stoppage input from the scorekeeper. In the case of penalty stopapges, the only thing that needs to be entered is a list of penalties. The primary outputs are the following:

Did you Know?

The published USA Hockey® casebook situations are only the tip of the iceberg. There exist infinitely many penalty situations. Software is particularly well-suited to identifying rare and unique situations that could arise. Here are some observations that were made while testing the software procedure on penalty situations other than those shown in the casebook. Plock further noted that many of these situations could realistically arise during a real game and are not far-fetched:

We intend to produce videos highlighting some of these unusual situations in the future. The hockey official training functionality noted above is the Simulator, and is fully accessible right now through this web site with a free account. The live gameplay function is in Beta testing currently, as of this writing.