Applying analytical techniques to quantitative sports data allow users to rank and evaluate player and team performances. A rank refers to ordinal placement of ratings, while “ratings come from a continuous scale such that the relative strength of team individual is directly reflected in the value of its rating” (Massey, 1999, p. 2). Early sports modelling work was based on ratings methodologies (Stefani, 2011).

In general, sport rating systems provide an objective evaluation of a team or individual based on prior performances and are implemented for player comparisons and improving player and team selection process. Generally, such systems are used by coaches, players, team managers and other key stakeholders.

Formally, a sport rating system assigns each team or individual a single numerical value representing a team or individual’s strength relative to the rest of the league on some predetermined scale (Massey, 1999). These ratings are beneficial to numerous parties, especially athletes, coaches and managers who utilise such systems to track and predict form, progress and applied as a motivational and benchmarking tool.  According to Leitner et al. (2010) sport ratings are typically derived by suitably aggregating a competitor’s previous performances and provide predictive power in forecasting future performances. Many American sporting franchises, such as The Oakland A’s (Baseball) and Dallas Mavericks (Basketball), adopt such an ideology.

Using a common framework, Stefani (1997) presented a survey of major world sport rating systems. The study stipulated that sport rating systems have 3 key steps: 1) weigh the observed results – this is the most important factor in determining points for a competitor, in any given competition , 2) combine the competitive points to produce season value, and 3) Aggregate the seasonal value to produce a rating.

The most well-known sport rating methodologies are the Bradley-Terry (1952), Elo (1978) and Glicko (1999) models (please see section Chapter Two for more details).

1.7.2.1 Type of sport ranking systems

Sorensen (2000) claimed that sport ranking systems, in general, fall into one of the two following categories: 1) Earned ranking systems utilise past performances to provide a suitable method for selecting either a winner or a set of teams that should participate in a play-off (Sorensen, 2000). Earned ratings are assigned an ordinal rank to produce team rankings. Majority of international sports such as tennis, basketball and football adopt an earned ranking system to produce [conference] seedings to establish play-off matchups. 2) Predictive ranking systems utilise past performances to build a forecasting model to predict future match outcomes between two teams. No internationally recognised sport adopts this ranking approach to determine seedings, as in practise this would not make sense and be problematic to implement. However, betting agencies, sport networks and analyst use such systems to set odds, predict margin of victory and establish winning probabilities.

Stefani (1997) stated sport rating systems can be separated into three further distinct types depending on how new ratings are calculated for each rating system: (1) Adjustive systems (2) Accumulative systems and (3) Subjective systems.

1.7.2.2 Adjustive Systems

Adjustive systems, also known as adaptive systems, “provide the best predictors for future performance because each adjustment follows from a predictor correction action in which a rating for team , can increase, decrease or stay the same, as each new result is compared to each prediction based on information available prior to the competition” (Stefani, 2011, p.8). Such systems cause ratings to fluctuate, depending on performances, and account for leapfrogging. This is a situation in which a player who cannot participate due to injury, is exposed to being overtaken by teammates who can play more games, and therefore can earn more points. Adaptive rating systems are adopted by sports such as golf, cricket, chess, football, and rugby. According to Stefani (2011) an adaptive system for competitor,  has the following form:

Here,  represents the rating for competitor after competition (i.e. match or game)  derived by adjusting the previous rating,  for competition  by a multiple . As mentioned previously weighing the observed result is the most important factor in determining points, as a large value would make ratings respond aggressively to the error term in the square brackets, while a small  would make ratings unresponsive. The adjustment  depends on,  which represents the difference between the actual performance of competitor  in competition  (i.e. , and the predicted performance  which is based on competitor  previous ratings. Competitor  and opponent  previous rating is affected by and , defined as weightings and other factors (i.e. money won, quality of entrants, number of skills used etc.) present in competition , respectively. The weighting procedure,  converts performances to points and varies across sports. For example, FIBA basketball provides weightings ranging from 0.1-5 for various championships (i.e. Olympic and Worlds) over an eight-year window. The ATP [men’s professional] and WTP [women’s professional] tennis publishes a matrix where each row represents final placement points for a given championship and columns represent the placement for each championship (Stefani, 2011).

1.7.2.3 Accumulative Systems

Accumulative systems are ‘running sums’ rating methods that are non-decreasing over a defined time-frame. These systems are predominately adopted by athletic sports such as gymnastics, power lifting and cycling. According to Stefani (2011) an accumulative system for competitor  has the following form:

Here,  represents competitor  rating after competition , based on past performances. “The function, , for competition  operates on  which is the performance of  in competition , using , which is a weighting procedure used to convert performance to points” (Stefani, 1997, p.7). The performance points are adjusted by an ‘ageing’ factor , and other factors , for competition . The factors ,    and are sport dependent on the sport.

1.7.2.4 Subjective Systems

Subjective systems consist of a panel of experts (i.e. judges) who rank the competitors and then combine the individual ratings to produce the overall ratings. Subjective systems are formally adopted by sports such as kickboxing, mixed martial arts and boxing.

Although statistical models are utilised to evaluate many problems in the sporting industry, the focus of this study will purely centre on team and individual rating systems.

1.3     RATING SYSTEMS

There are two overarching characteristics across the three ratings methodologies: 1) resultant outcome and 2) overall objective. The systems produce a single real number [0,1] representing a human’s ability to perform either athletically, financially, or technically in their respective environment. Moreover, each system aims to evaluate the performance of the same entity, i.e. a human. Here, system definitions, common methods, and modelling practices across the three industries are provided.

1.8.1 Sport Rating Systems

Formally, a sports rating system assigns each team a single numerical value to represent team or player strength relative to the rest of the league on some predetermined scale (Massey, 1997).  Stefani (1997) stated that sport rating systems have three steps: 1) Weigh the observed results to provide competition points - this is the most important factor in determining points for competition i for a given competition, 2) Combine the competition points to produce seasonal values, and 3) Aggregate the seasonal value to produce a rating.  Generally, sport rating systems fall into two categories: 1) Earned ranking – These systems utilise past performance to provide a suitable method for selecting either a winner or a set if teams that should participate in a play-off, and 2) Predictive ranking – These systems utilises past performance to provide the best prediction of the outcome of future games between two teams. Additionally, Stefani (2011) stated that sport rating systems can be separated into three distinctive types depending on how new ratings are calculated for each rating system: 1) Adjustive, 2) Accumulative and 3) Subjective.  A potential drawback of sport rating systems are small sample sizes due to a limited number of contested sporting events.  To derive a deeper understanding of the requirements for a meaningful sports rating system, this research builds on work from: Patel, Bracewell & Rooney (2017); Patel, Bracewell & Wells (2017); McIvor, Patel, Hilder & Bracewell (2018); Campbell, Patel & Bracewell (2018). References