Accounting For Player Strength - Alternative Methods

G’day lads! In the best sports models, the lineup of a team is considered. How you factor in changes to a lineup within a model is very important, and in this article I’ll give you some strategies!

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Player-Based Model

In the best and most accurate sports models, the strength of a team is calculated by considering the strength of each of its players. While in a defensive context the overall strength of a team might be considered (as the quality of a player’s defence is very hard to quantify), Player-Based Models are able to effectively account for squad ins & outs.

For example, consider the Excel LADZ NBA Model. A team’s simulated score is the sum of each player’s simulated points. There’s also a defensive adjustment applied to each player by calculating the overall opposition defence strength (multiple = opposition average points conceded during season/points conceded average throughout league).

In the above simulation, the New York Knicks had a score of 118. Running 1,000 of these games yields an average (or expected) score of 110 for the Knicks, giving them a Win Probability of 44.7% (winning 447 out of 1,000 trials against the Warriors).

However, you may notice the injured players excluded from the Knicks lineup:

• Julius Randle
• Mitchell Robinson
• OG Anunoby

When included in the lineup, they improve the Knicks’ Expected Score and consequently their Win Probability.

A Player-Based NBA Model is possible due to the statistics available. The split and accuracy of every player’s shots is recorded, and is able to be simulated to project points scored.

Furthermore, there is reliability to these stats. NBA players take hundreds of shots every season. Due to the Law of Large Numbers, a player’s shot percentages will converge to the true value because of the huge amount of data generated each season.

However, when there is less frequent data, the output of the model can become more volatile.

Download the Excel LADZ NBA Model here: https://www.patreon.com/posts/2023-24-excel-93076132

Player-Based Model - Volatile Data

In the process of building an NHL Model, I decided to use a player’s Goals Created to calculate their value to the team. While this model worked well for two teams close in ability, the model overestimated the difference between a relatively good and bad team.

In the above example, the Canadiens are playing the Panthers. The Panthers are overwhelming favourites according to this model, with an 86.22% chance of winning. This is significantly higher than the bookmaker’s projection of 75%.

The reason for this discrepancy is the ‘Goals Created’ stat. While NBA players shoot and make hundreds of shots throughout the season, good NHL players only create about 0.2 goals per game. As a result, a sudden flurry of GCs for a player drastically increases his value even if the Goals Created can be attributed to pure luck (and vice versa).

Consider an NHL player who has contributed 2 Goals Created over 10 games. His contribution towards his team can be valued at 0.2 goals. However, in Game 11 suppose he scores 2 GC’s. Now that he has 4 Goals Created over 11 games, his contribution rises to 0.36 goals, nearly doubling his worth from one good game. On the other hand, a dry spell could undervalue a player.

In conclusion, the Goals Created stat by itself is not powerful enough to be the sole input into a model. This was proved by backtesting the model.

Now, if I switch to a team-based model, the output of the model becomes more accurate and realistic (as proven & evident through backtesting).

Here, the team’s Goals Scored and Goals Conceded stats are considered and used to come up with the Expected Goals Figure. While the results are more accurate, this model can’t quantify the change in a team’s strength when a player is injured (like in the NBA Model).

Team-Based Models with a Player Adjustment

Good news lads, there is a compromise! It is possible to build a model that takes into account a team’s overall strength, but make adjustments to those figures when considering the quality of a team’s lineup.

In this example, I’ll use a model to predict the winner of an Australian Football League (AFL) match. In AFL, a team can either score a Goal (worth 6 points) or a Behind (worth 1 point). Building a model using team-based statistics, I get the following Attack (ATT) and Defence (DEF) Ratings for each team in each scoring method (Goals & Behinds).

***If you don’t recognise/understand ATT & DEF Ratings, have a read of this lads: https://www.patreon.com/posts/excel-ladz-7-88895696 ***

Let’s consider the Goal ATT for the Lions in our example. Let’s pretend the Lions have their starting forward injured, and need to replace them. Obviously, this should reduce the Goal ATT Rating for the Lions. However, we still have two questions we need to answer: how, and by how much?

To assess the individual strength of each player in the Lions’ lineup, I can grab their Average Fantasy Score (called SuperCoach in Australia) throughout the season. The sum of all attacking players’ Fantasy Scores will equal the Team Attacking Fantasy Score. In this way, I’m using individual stats to come up with a total team score. The results are below:

There is a noticeable pattern here; the higher the SuperCoach ATT, the higher the Goal ATT. I can plot this with Excel and then find an equation (with an intercept of 0).

In the equation produced above, I can input the team’s ATT SuperCoach Sum going into a game and output an expected Goal ATT. This allows me to proportionally scale a player’s absence/appearance in a lineup.

For example, the Lions have a Goal ATT of 1.14 and a SuperCoach ATT of 831. Suppose a good player with a score of 80 is not playing and is replaced with a weaker player that has an expected score of 30. This would reduce the Lions’ SuperCoach ATT from 831 to 781.

With a SuperCoach ATT of 831, the Lions have an Expected Goal ATT of 1.08 (831 * 0.0013).

With a SuperCoach ATT of 781, the Lions have an Expected Goal ATT of 1.01 (781 * 0.0013).

Taking 1.01 / 1.08, the Lions have experienced an Expected Reduction of 0.93. This can be applied as a multiple to the Lions current Goal ATT Rating. 1.14 * 0.93 = 1.06. Therefore, the Lions new Goal ATT Rating going into the match has been reduced from 1.14 to 1.06.

Thanks for reading lads, if you have any questions let me know here on Patreon or on Discord.