UCL Match Quality Score

Creation of two metrics to analyze the performances in the UEFA Champions League from the 2020-21 to the 2024-25 season using Football Reference's data.

There are four steps to create these two metrics, as follows:

1 - Selection of match statistics

We select the match statistics that are relevant to compute the quality of the performance of a team in a football match. We decided to select the following statistics that comes from the Football Reference website:

npxG E (Non Penalty Expected Goals), SoT (Number of Shots on Target), xAG E (Expected Assisted Goals), SCA (Number of Shot-Creating Actions), GCA (Number of Goal-Creating Actions), PrgP (Number of Progressive Passes), PrgC (Number of Progressive Carries), STO(Number of Successful Takes-Ons), Tkl (Number of Tackles), Int (Number of Interceptions), Blocks (Number of Blocks).

2 - Compute the Empirical Cumulative Distribution for each statistic of a team $t$ in match $m$

For each statistic, we compute the Empirical Cumulative Distribution based on the values of the same statistic from all the UEFA Champions League performances between the 2020-21 and 2024-25 season. We multiply the value obtained by 100 to have a more understandable score between 0 and 100.

Here is the formula that we use for each statistic:

$$ M(v_{s, t, m}) = \frac{1}{n} \sum_{i=1}^n \mathbf{1}_{{x_{s, i} \leq v_{s, t, m}}} \times 100 $$

Where:

• $v_{s, t, m}$ is the value of the statistic $s$ for team $t$ in match $m$.
• $x_{s, i}$ is the value of the statistic $s$ for the team performance $i$.
• $n$ is the number of team performances from the 2020-21 to 2024-25 Champions Leagues seasons.
• $\mathbf{1}{x_{s, i} \leq v_{s, t, m}}$ is an indicator function that equals 1 if $x_{s, i} \leq v_{s, t, m}$ else 0

3 - Compute the Team Match Quality Score ($TMQS$) for a team $t$ and a match $m$

For all the statistics presented in the first step, we apply the $M$ function from step 2 and we compute the mean of all those values. This mean corresponds to the $TMQS$ metric. Here is the formula of it for a team $t$ and a match $m$:

$$ TMQS_{t, m} = \frac{M(v_{\text{npxG E}, t, m}) + M(v_{\text{SoT}, t, m}) + M(v_{\text{xAG E}, t, m}) + M(v_{\text{SCA}, t, m}) + M(v_{\text{GCA}, t, m}) + M(v_{\text{PrgP}, t, m}) + M(v_{\text{PrgC}, t, m}) + M(v_{\text{STO}, t, m}) + M(v_{\text{Tkl}, t, m}) + M(v_{\text{Int}, t, m}) + M(v_{\text{Blocks}, t, m})}{11} $$

4 - Compute the Match Quality Score ($MQS$) for a match $m$:

When the $TMQS$ metric is computed for the two teams of a match, we can compute the Match Quality Score ($MQS$) by computing the mean of the two team's $TMQS$. Here is the formula of this new metric:

$$ MQS_m = \frac{TMQS_{\text{Home team}, m} + TMQS_{\text{Away team}, m}}{2} $$