Hybrid player props modelling for the modern sportsbook
This post was authored by Theofanis Cheras
Player prop markets continue to grow rapidly and are extremely popular selections for our Unibet sportsbook customers here at Kindred Group, both as stand-alone bets and as part of same-game parlay bets via existing Bet Builder products. For a sport like association football, player props include a wide range of markets such as anytime goalscorer, player shots on target, player assists, player to receive a card and player tackles.
The Kindred Quant Team is working on in-house hybrid player props pricing as part of the multi-year Kindred Sportsbook Platform (KSP) project. Put simply, these hybrid models will allow us to combine market prices with features engineered from event-level data to provide differentiated pricing. This should lead to greater control of our offering in the player props space for key sports, markets and products.
Motivation
Let’s start by assuming we have a parametric model which predicts the number of goals scored by each team. Many popular football markets, such as win-draw-win (1x2) or total goals, are highly efficient, with most bookmakers offering similar prices, shaped by flows and action in the broader marketplace. By taking odds input from a few of these efficient markets, we can reverse-engineer model parameters, such that the predictions and pricing coming out of the model most closely match the input being fed in. These inferred parameters can, in turn, be fed back into the model and broader pricing system to price a range of additional team- and match-based markets. We term this market-implied pricing.
By contrast, many player prop markets are more niche and may not always be so efficient due to lower turnover and liquidity, lower limits, customer biases (e.g. preference for betting overs) as well as other factors. Following R&D work within the Quant Team, we have found that we can sharpen some of our player props pricing using market odds inputs combined with engineered features. We anticipate this will allow us to have greater flexibility to differentiate on some of our existing player props pricing, whilst also diversifying the risk of tying our player prop pricing tightly to any particular market odds source.
Enabled via Opta Data
The contract Kindred Group signed with Stats Perform at the start of the year has helped accelerate our work on player props by providing us with access to extensive high-quality player-level Opta events data, which is crucial for fuelling the feature engineering underpinning our hybrid models. You can read more about our partnership with Stats Perform here.
Player Assists Hybrid Model
The toy example below is intended to give further intuition behind hybrid player props modelling without getting into too much detail.
Let’s assume that we want to predict the probability that Cole Palmer, one of Premier League’s top assist providers in the most recent 23/24 season, will provide an assist in the Euro 2024 Quarter-Final game between England and Switzerland. To come up with this probability, we assume the number of assists provided by Palmer follows a Poisson distribution. This becomes a task of forecasting Palmer’s expected assists (i.e. the single intensity rate parameter of the Poisson distribution) for the upcoming game using both market and historical event data.
Let’s take the market data first. We can infer Palmer’s market-implied expected assists using market odds data from one or more external feeds suppliers. Now let’s turn our attention to historical event data. We can use feature engineering to transform player and/or team statistics to construct ‘fundamental’ features that may enhance a model’s ability to predict assists over and above information inferred from market prices.
Examples of such ‘fundamental’ features could include but are not limited to
· Past average assists/corners/free-kicks taken: An average of the player’s past number of assists/corners/free-kicks taken achieved per match.
· Past average pitch position: An average of the player’s past pitch coordinates per match, calculated over relevant events (such as passes, shots etc) and fixtures.
In practice, these predictive features are chosen through extensive model evaluation performed over a large number of datapoints.
Figure 1 shows how we can combine this information using a simple linear hybrid model to obtain our final prediction for Palmer’s expected assists. In this example, our final prediction is a weighted linear combination of the market-implied and ‘fundamental’ features, with the more predictive features given more weight.
Putting everything together, Figure 2 provides a sense of how price differentiation can be achieved through hybrid modelling. Hybrid model-derived expected assists and market-implied expected assists are, in this example, subtly different. When expected assists are converted into odds space, this leads to higher fair prices for Palmer and Rice, and lower fair prices for Kane using hybrid models.
Hybrid Modelling Pipeline
Hybrid modelling pipelines share similarities with standard machine learning pipelines, including:
· Architecture: hybrid models can include many features and, therefore, require robust and scalable feature stores to allow features to be added, modified and updated over time upon new flow of data.
· Tech stack: various big data technologies, including Apache Spark, can be leveraged on the data engineering side to create efficient data pipelines for facilitating model research, training and evaluation.
· Data management: data validations can be added straight-forwardly to existing feature store pipelines to ensure the integrity of the data being used to fit hybrid models.
· Modelling: Regularisation techniques, cross-validation and hyper-parameter tuning can be used on the research side to produce parsimonious and generalisable models.
· Model evaluation: Models can be rigorously evaluated using historical data by comparing model predictions to observed outcomes based on out-of-sample test set performance.
Conclusions
In conclusion, hybrid models combine the benefits of pure market-implied pricing with data-driven fundamental models. While our work is still under development for now, we anticipate that it will allow us to generate opinionated pricing in various niche player props markets. This has the potential to pass on benefits to our customers in terms of improved offering, broader coverage and differentiated pricing.
Whilst we have initially focussed our efforts on football player props, we will look to refine our hybrid models further and extend out these modelling techniques and architectures more broadly.
If you’ve enjoyed this post, watch this space for upcoming posts, including one on our Bet Builder product, which will highlight the value of accurate player props pricing in the context of same-game parlays.
Are you interested in finding out more about the Quant Team at Kindred, or even joining us? Read our other blog posts here or browse our current vacancies page.
Thanks for reading!
