An understanding of our unique polo player rating system

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The objective of this development of a new player  rating system for determining the individual players strength as part of team at all levels was born out out of years of debates on many club and NGB handicap committees where getting a consensus on a players handicap was incomplete due to consistency of observation by the panels and the importance of delivering a competitive playing environment. To increase player/team participation in sports leagues requires improving the competitiveness of matches which intern  increases the engagement of individuals in the sport due to the chance of success is perceived to be higher.  

A player’s performance does not only depend on physical, technical and tactical skills, but also on psychological and mental components (Beswick 2010). The assessment of a player’s strength based on subjective impressions or cumulative statistics therefore turns out to be difficult to be impossible. 

The overriding objective, with which a  team or  player starts with in  a match, is on the other hand conceivably simple and can be sufficiently described in one word: Winning. 

Taking into account the results of a player, i.e., 

· how often he or she reaches the goal of winning, and the level at which the player acts,

· the strengths of his / her teammates,

· the strength of his/her opponents,

one can calculate and objective rating, which describes the strength of the individual player and which is comparable with the ratings of other players.

We calculation is derived from  an Elo-based rating system but unlike Elo which is based on 1 v 1 match ups we adapted it to perform a multi-team player and multi- team scenario.

What is Elo ?

Its actual who is Elo, the American statistician Arpad Emrick Elo (1903 – 1992) developed the Elo algorithm in 1960, which serves since 1970 the world chess federation FIDE for the calculation of FIDE ratings—objective scores, which indicate the playing strength of chess players. Each chess player has an Elo rating (= FIDE rating) R, whose value correlates positively with his playing strength. The best players in the world have a rating of over 2 800. Elo based ratings underpin the majority of all sports rating systems. E.g. 

· The EA Sports Players Performance Index (Actim Index) is the official player rating system of the English Premier League and awards points for good stats as well as for positive team results (McHale et al. 2014).

· BHA’s Racehorse Official Rating (OR) - Designed specifically to help handicappers assess the weight a horse must carry for each race – handicapping is used to ensure horses with lower ratings can a competitive. Weighting/ ‘K’ factors are used i.e the course, distance, ground, relative weights, previous results and the OR is a plus minus model to create a rating for each race start . 

· Equirating - Eventings new Elo rating system 

· NBA - FivethirtyEight Elo rating 

· Baseball – Oaklands ‘A’-  Bill Beans introduced this analytical approach to selecting players rather than on subjective scouting - dramatised in the film MoneyBall and now adopted as part of all teams process for selecting players. 

As mentioned earlier, Elo is originally designed for 1 v 1 match ups i.e. Team vs Team or Player v Player. In our development of the Elo equation we look at the contribution of the individual towards a team’s final match result. And based on the premises that a  team is only as good as; 

1. its individual players 

2. the strength of the opposition. 

It’s not just who scores all the goals but how well you defend , and who you are playing against !   

A further advantage of our approach compared to Elo ratings of whole teams is that our model performs across seasons and levels. 

The input of the system is solely the information found in the official match reports. After each match played, the rating of each player involved is adjusted. Its a +/-  rating system and the algorithm determines how much a players rating increase or decrease based on the expectation factor on that player.  If the player has exceeded the expectations placed on them before the game, their rating will be increased by more than if this was just proving the expected outcome —if they could not meet the expectations, the player  will be devalued. If a player is not yet registered in the system, their Elo rating is initialised based on their profile weightings or the average at the time. After each played game, the rating of the player will be updated according to his result and taking into account the relative playing strength of the opponent.

The algorithm that has been adapted for polo studied matches from 16 different European domestic leagues, the UEFA Champions and Europa Leagues have been recorded, with more than 17 000 matches played in recent years, and 12 400 different players.

Figure 1 illustrates the basic structure of the algorithm. 

The developed system is able to:

(a) rank the playing strengths of polo players, 

(b) rank the playing strength of polo teams combinations, 

(c) predict the outcomes of future matches, and 

(d) identify new talents in polo.

K Weightings (Age, Frequency,Level)

For the algorithm to respond properly to a player’s individual situation, the individual k and q weights are important. If a player is newly registered in the system, his ability to perform can initially only be estimated and under certain circumstances may differ significantly from that of his teammates. For this reason, a high value is chosen for both kAi and qAi, which means that the rating is adjusted more rapidly than and established player.  The algorithm  considers the age of the players during the initialisation and introduces different rating and younger players have a steeper improvement curve. This can either speed up the rate of a players rating change or slow it down according to the requirements for the best outcome of player development. 

With each completed game, the player’s rating becomes more accurate and the comparability with the ratings of his teammates better—therefore, k and q are decremented after each game in which the player has played. If the player does not play for a long time due to injury or other reasons, the accuracy of his rating will decrease, which is why kAi and qAi are increased in each match without Ai.

Player initialisation

The players have to be initialised according to their traditional handicap, so all uninitialised players on the same handicap start on a predefined rating. In a model without initialisation, the system would take to long, or respectively, a large number of games to adapt the expectation values for everyone to achieve a realistic range. If all players start with the same rating, those who are in good teams and play lots of games have an advantage—however, it is not the quantity of the games that should be judged, but the quality of the results on the pitch. The following example shows that more games do not necessarily lead to a higher rating: If player A plays all games, he is always on the field when the team loses. If player B, who belongs to the same team, is absent during one of these defeats and plays all the other games, he has a better rating than player A.

Summary 

The modified polo  algorithm was adapted from a rating system for  football players which  takes into account the strengths of the two opposing teams and the result of the game as well as for each individual players personal rating and the individual result. This algorithm can be applied at all levels of polo and would rate players from different counties at the same level. E.g a 4 goaler in Peru would be the same as a 4 goaler in Australia. It is derived from actual match data which is objective. Its also very difficult to manipulate. In order to do so , a player would have to manipulate his own performance, his team mates performance, his opposition players performance over a period of time. It also helps to explain if a player should go down rather than the opposition players going up and creating inflation and under-competition of players being moved up e.g. 

If two 8 goal sides (Team A and Team B) play each other 10 times in a row and Team A always wins. Does that suggest that Team A players should go up in handicap? or should it be that Team B should be lowered in handicap? In a subjective handicap design the likely outcome is that Team A would go up but in this objective approach it takes into account results from the individual players other games and determines the correct expectation on that player and the likely results outcome. 

Therefore, the beneficial effect is that players will be confident to play to their full potential not in fear of being unjustly handicapped due to;

1. Being watched a few time and achieving good results 

2. Being penalised with an unjustified raise in handicap playing against bad teams 

3. Young talent, therefor being hidden in fear of being quickly promoted. 

4. Consistency across seasons

5. Accurate and up-to-date handicaps rather than being 6 months old when the player was last assessed