Establishing a Theoretical Bound for Baseball Codebreaking - PowerPoint Presentation

1. Establishing a Theoretical Bound for Baseball Codebreaking Professor Anton Dahbura, Ethan Yang ‘23, Jack Pausic ‘22Johns Hopkins University | Whiting School of Engineering | Baltimore, MDDesign Day 2020Baseball is a sport rich in its tradition and notorious for its intricate strategy. One of the oldest practices in the sport is the utilization of hand signals to conceal one team’s strategy from its opponent. If a team is able to “steal,” or decrypt, its opponents’ signs without their knowledge, they can anticipate everything from upcoming pitches to baserunning strategy, gaining a significant competitive advantage. There have been multiple documented instances of technologically-aided attempts to steal signs in professional baseball, but our project solely focuses on the method of observing the signs being transmitted from coach to player, a widely-accepted practice occasionally employed by even the casual Little League coach. This type of observation can often reveal informative patterns and is not considered cheating in the baseball community at large.The goal of our research was to draw conclusions about how quickly this aforementioned observation could, in fact, obtain meaningful information about plays the opposing team was planning for the next pitch. Given the number of assumptions made and the situational constraints baseball coaches face (plays being required at certain points in the game), the goal of establishing the bound is to generate discussion surrounding how sign systems are designed and effective strategies for keeping signs encrypted.ObjectivesIntroductionMaterials and MethodsOur team developed a systematized method for the aforementioned observation. Using it were able to construct a theoretical bound for the maximum number of sequences a coach could give to his players before the observer was guaranteed to be able to obtain meaningful information about the upcoming play. This required rigorous definition of the problem, each scenario, and the algorithm itself, most of which can be found in an ongoing paper due to poster space constraints. In addition to writing a paper discussing the bound in more detail, we have more recently begun to run simulations in order to verify our findings and explore trends in multiple situational variables. ResultsDiscussion & ConclusionFigure 3: Sequence Length, Frequency, and “Robustness” DurationFigure 1: Key Frequency vs. Average “Robustness” Duration Robustness Duration: average number of sequences for which the key was successfully obfuscated from observer.Results obtained from averaging the outcomes of 1000 simulations per data point.While the construction of the bound cannot be fully explained on the poster, the result hinges for the most part on the fact that the first sequence is the most taxing to the list of possible keys (all m are eliminated), and subsequent sequences have a minimum cost of 1. Therefore, we concluded that for a system in which signs cannot be repeated more than once per sequence, whose alphabet is of length n and sequences are of length m, the maximum number of sequences that can be given before the observer is guaranteed to obtain meaningful information is equal to n – m + 1. Perhaps the most practically applicable result of the research thus far is not the bound itself, but rather the illustration of just how detrimental suboptimal implementation of a sign system can be to a team. For example, if a coach using the previously defined system gives a sequence containing the key (action sequence), the observer’s suspect list is reduced to length n, the length of the sequence containing the key. The coach should now change signs within the next handful of pitches to avoid having his signs stolen. It is these intuitions and self-awareness that we hope will benefit the average coach and team.TerminologySign System: a methodology for conveying plays (also called events) from the Sender to the Receiver (see below). The system is fixed, i.e. it is assumed that its rules do not change, and defines the interpretation process for the Receiver. Sign: a single indication made by the sender during the transmission of the orders; while signs are typically the touching of facial features or body parts, they can be anything previously agreed upon by the Sender and Receiver.Alphabet: the complete set of signs a sign system employs. Sequence: a list of signs given transmitted by the Sender to the Receiver. One sequence is given per pitch. For the purpose of this study sequences are assumed to be of fixed length m, but the results are extensible to variable-length sequences.Key: a particular sign that has a one-to-one mapping to a particular event. The observer wishes to determine which sign is the key. Their process can be modeled by creating a list of possible keys and whittling it down using process of elimination. The coach/sender then wants to act in a way that minimizes the number of signs the observer can remove from their list after each sequence. We show using casework that the usual minimum is 1 sign removed per sequence, with some special cases.Key Definitions & Intermediate Results