Originally written in 2021. There may be some outdated information.
Abstract:
Rematch Win Expectancy (RWE) is a predictive metric, estimating the probability that Team X would defeat Team Y in a rematch based on the sustainable aspects of their original football game. RWE draws inspiration from Bill Connelly’s “Postgame Win Expectancy” but seeks to shift from an explanatory to a predictive framework. While Postgame Win Expectancy predominantly focuses on past game events, RWE aims to provide insights into future match outcomes, positioning itself as a power ranking system for football teams.
1. Introduction:
1.1 Background and Motivation
The introduction of RWE arises from the personal desire of more forward-looking metrics in football analytics. While Postgame Win Expectancy offers valuable insights into the outcomes of past matches, the transition to a predictive model becomes crucial for enhancing its utility in ranking football teams.
1.2 Previous Win Expectancy Work
Bill Connelly’s Postgame Win Expectancy serves as a foundational metric for RWE, with its emphasis on explosiveness, efficiency, field position, red zone success, and turnovers. However, RWE aims to overcome the inherently explanatory nature of Postgame Win Expectancy by neutralizing elements such as explosiveness and turnovers. Success Rate was also an inspiration for RWE. In RWE I planned to improve the pass/fail binary aspect of Success Rate into a more complex, in depth statistic.
2. Conceptual Framework:
2.1 Definition of RWE
Rematch Win Expectancy (RWE) is defined as the probability that Team X would defeat Team Y in a rematch modeled around the sustainable aspects of their original football game.
2.2 Goals of RWE
Rematch Win Expectancy (RWE) is designed to serve as a power ranking system, aiming to elucidate the comparative strength of football teams and their anticipated success when pitted against one another on a neutral field. It is imperative to underscore that the application of RWE should be strictly prospective in nature, refraining from assessments of past games to determine who “should have won.” In this regard, Postgame Win Expectancy proves to be a more apt tool.
The fundamental premise underpinning RWE revolves around the recognition that relying solely on averages can yield deceptive insights, as outliers possess the capacity to exert disproportionate influence on the overall average. While assessing teams based on average yards per play is conventionally insightful, instances of outlier plays, such as two 80-yard gains, can distort the perceived offensive efficiency on a play-by-play basis. To mitigate this, RWE employs a formula to regress values toward the mean, thereby mitigating the impact of outliers, albeit not entirely eliminating them.
Contrary to a simplistic reliance on the mean, RWE places emphasis on statistical measures within the quartiles and median. This focus allows for a nuanced evaluation of team performance, recognizing the significance of extreme values while simultaneously acknowledging the stabilizing influence of more central tendencies. Consequently, RWE offers a more robust and comprehensive assessment of a team’s potential, beyond the potentially misleading implications derived solely from average statistics.
3. Methodology:
3.1 Data Collection
RWE is derived through play-by-play yardage gained or lost, incorporating exceptions and rules for specific plays.
3.2 The “Rectangle Root Formula”
Upon the collection of play-by-play data, the next phase in the RWE methodology involves the application of the Rectangle Root Formula to each individual play, generating a value subsequently utilized in Section 3.4. Termed as such due to its resemblance to a Square Root Formula, the Rectangle Root Formula is expressed as follows:
(IFS(Yardage>0, (Yardage-0.95)^0.5, Yardage<0, (-1*((Yardage+0.95)*-1)^0.5), Yardage=0, 0)+IF(Yardage>1, -0.3, 0)+IF(Yardage<-1, 0.3, 0))*IF(Yardage<0, 0.875, 1)
Breaking down the Rectangle Root Formula elucidates its fundamental components. In cases where yardage gained is positive, 0.95 is subtracted from the gained yards, and the square root of this value is calculated. Conversely, if yardage gained is negative, a multiplication by -1 precedes the addition of 0.95 to the lost yards, followed by the computation of the square root, and a subsequent multiplication by -1 to revert the yardage back to a negative scale. The addition and subtraction of 0.95 are integral to counteract the inverse effects of square rooting numbers less than 1. Furthermore, when yardage gained is precisely 0, the formula outputs 0. If the yardage gained exceeds 1, 0.3 is subtracted from the previously calculated positive value. This adjustment is also due to square roots, addressing nuances associated with numbers falling within the range of 0 to 1. Lastly, for negative yardage, the value is multiplied by 0.875. This addition serves to marginally attenuate the impact of negative yardage. The rationale underlying this approach is twofold: firstly, negative plays are often less sustainable than their positive counterparts, and secondly, an initial over-penalization of negative plays in Section 3.4 necessitated the incorporation of this corrective measure.
3.3 Penalties
Penalties within the context of RWE merit careful consideration. Certain penalties have been designated as unsustainable and are consequently excluded from contributing to the RWE metric. Conversely, penalties classified as sustainable receive a dedicated entry, as expounded in Section 3.7.
In the initial iteration of RWE, all penalties were incorporated as plays, yielding suboptimal outcomes that favored the team with fewer penalties. In response to this limitation, a modification was introduced, introducing a distinct data entry point denoted as the “Penalty Box.” This space is reserved for aggregating values associated exclusively with sustainable penalties. The cumulative sum within the Penalty Box always assumes a negative value if non-zero, reflecting the penalizing nature of these events.
Upon completion of the data input process, the cumulative value within the Penalty Box is multiplied by 0.325. The resultant value assumes the role of an individual play within the subsequent RWE calculation (Section 3.4). This adaptation serves to address the problematic influence of penalties on the overall RWE outcome.
3.4 Expected Yards Per Play Calculation
Upon the collection of all requisite data and the application of their respective formulas, the subsequent step in the RWE process involves the computation of expected yards per play in a rematch. This entails determining the average value derived from the previously applied formulas, typically yielding a value proximate to 1.35. However, due to the earlier utilization of the Rectangle Root Formula involving a square root, a correction involves squaring the average value to restore the yardage to its original scale. Furthermore, a final adjustment entails the multiplication of this squared value by a factor of 3. This factor of 3 serves a critical purpose in aligning the computed value with the conventional scale of yards per play, thereby facilitating an interpretable comparison. The resulting figure represents the estimated expected yards per play attainable by each team in a rematch scenario. This metric is denoted as Rematch Win Expectancy yards per play (RWEypp).
3.5 Expected Points Calculation
Upon ascertaining the RWEypp for both participating teams, the following step in RWE involves a transformation by multiplication. Specifically, the RWEypp values for each team are subjected to multiplication by a predetermined factor of 4.5. The selection of this coefficient results from a process of fitting past data to approximate realistic point totals, ensuring an alignment with recent historical football scoring patterns. This multiplied value assumes the role of the estimated Expected Points for each respective team in the hypothetical rematch scenario.
3.6 Rematch Win Expectancy Calculation
The derivation of RWE culminates in the calculation of the probability for a team to be victorious in a hypothetical rematch scenario. This process begins with the computation of the difference in Expected Points between the two teams, representing the average margin of victory for a team in a potential rematch. Subsequently, this difference is normalized by dividing it by a factor of 6.25. The resultant value, denoted as x, is then introduced into the Normal Probability Density Function, a fundamental statistical framework. This serves to generate a probability distribution, thereby encapsulating the likelihood of a team securing a victory in the theoretical rematch. The resultant probability value stands as the definitive RWE metric, representing an assessment of a team’s prospective success in a rematch scenario.
3.7 Rules
a. Interceptions = -2
Interceptions are regarded as negative plays warranting penalties. However, it is acknowledged that the distinction between potential interceptions and actual interceptions involves inherent uncertainties, considering instances where interceptions may be dropped or result from unfortunate bounces for the offense.
b. Successful First Downs on 2nd or 3rd down with between 1-3 yards to go that result in 3 or less yards gained are voided.
The significance of a 2nd & 3 play gaining precisely 3 yards as a successful offensive play is acknowledged. However, recognizing the potential limitation of the Rectangle Root Formula to capture such nuances, these particular plays are excluded from consideration, with a deliberate focus on including plays with 4 or more yards gained for analytical purposes.
c. 3rd & 15+ = Yardage Gained / 2 (if unsuccessful)
On long third downs defenses may concede 5-10 yards without concern for a first down. To address the potential oversight by the Rectangle Root Formula, which solely perceives the yardage gained, a corrective measure is implemented—dividing the yardage by 2, thereby moderating the impact of these plays deemed unsuccessful.
d. Defensive Pass Interference Yards / 2, limited between 5 and 7.5
Recognizing the subjectivity inherent in DPI penalties, often prone to inaccurate calls or oversights, a nuanced approach is adopted. To mitigate the potential exaggeration of impact, yardage gains attributed to DPI are halved, with an additional constraint ensuring a minimum of 5 yards and a maximum of 7.5 yards.
e. Defensive Offsides Plays Accepted = Void
Defensive Offside penalties that are declined retain inclusion in the analysis, while those accepted are exempted from consideration.
f. Roughing the Passer = Void
RWE recognizes its subjective nature, frequently prone to miscalls and deemed unsustainable.
g. Unsportsmanlike Conduct = Void
Instances involving flags thrown for Unsportsmanlike conduct are identified within RWE as singular, one-off mistakes deemed inherently unsustainable in nature.
h. Garbage Time = Void
The integration of Garbage Time, characterized by the utilization of backups and introducing random noise into football games, poses a methodological challenge requiring delineation. Within the RWE framework, the initiation of Garbage Time is contingent upon observable shifts in playstyle, such as offensive teams introducing backups or defensive units permitting strategically unimpeded gains, signaling a departure from the norm in a concerted effort to manage game time efficiently.
i. All Fumbles = Yardage where ball was fumbled
Fumbles are recognized within RWE as high-impact plays characterized by limited to no repeatability, with marginal distinctions observed between the fumbling tendencies of the best and worst players.
j. All Special Teams = Void
Little consideration is given to the relatively low impact of punting and returning plays, as even elite returners may not secure a touchdown in a full season. While acknowledging the high impact of kicking, the marginal distinctions between proficient and less proficient kickers are recognized as generally negligible within the analytical scope of RWE.
k. Safety = Yards Lost – 2
The inherent strategic intention of offenses is to avoid safeties when positioned near their own end zone.
l. All Touchdowns = + 4 yards on the yardage gained
Touchdowns with a minimal yardage gain of 1 yard are considered successful plays, albeit perceived otherwise by the Rectangle Root Formula. To rectify this, a uniform adjustment is implemented, whereby 4 yards are added to all touchdown plays, establishing a minimum yardage of 5 for assessment within RWE.
m. All Successful 4th Downs receive a minimum of 4 yards
In alignment with Rule I, this methodological framework extends recognition to a 4th & 1 play where precisely 1 yard is gained, deeming it a success in accordance with its demonstrated importance.
n. Hail Mary’s = Void
Hail Mary attempts, commonly characterized as random jump ball scenarios, are deemed inherently non-repeatable within RWE.
o. Defensive Holding = 5 yards
This condition is exclusively applicable when a penalty is accepted; in the event of a declined penalty, the actual yardage gained is added.
p. Offensive Holding = -5 added to penalty box
q. Offensive Pass Interference = -5 added to penalty box
r. Intention Grounding = -5 added to penalty box
s. False Start = -2.5 added to penalty box
t. Delay of Game = -2.5 added to penalty box
Listed above the penalties deemed sustainable within RWE. The majority of penalties delineated in rules p through t are subject to a reduction, with half of the yardage penalty allocated to the penalty box.
4. Limitations:
RWE is not immune to limitations. Teams with exceptionally proficient or deficient special teams units may consistently surpass or fall short of their RWE expectations by a marginal point differential.
The intrinsic variability of interceptions, as noted in rule a, introduces an element of unpredictability, especially in cases where quarterbacks like Jameis Winston exhibit a consistent propensity for placing the ball in dangerous situations, potentially causing teams with such quarterbacks to outperform RWE projections.
RWE’s design to neutralize outlier plays encounters challenges when facing offenses that strategically exploit this feature, manipulating the secondary to facilitate deep pass options and generate significant gains.
Finally, the impact of coaching, encompassing elements such as clock management and play calling, emerges as a critical variable, as adept play callers may consistently outperform RWE by leveraging their abilities to accrue incremental advantages.
5. Future Direction:
Prospective research endeavors could focus on mitigating the recognized limitations of RWE, particularly through the integration of special teams dynamics and a more nuanced consideration of coaching decisions.
The current manual data entry process for RWE, predominantly executed via a Google Sheet, offers a preliminary framework, yet future developments aim to automate this process. The envisioned automation anticipates a monumental reduction in the time required for each game analysis, which currently stands at 5-7 minutes.
Continuous validation of parameters within the Methodology, such as cross-referencing RWE total points against actual points scored in games, remains an essential practice to ensure the ongoing reliability and accuracy of the metric.
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