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FIVB ranking: Misstep in the right direction

Salma Tenni, Daniel Gomes de Pinho Zanco, Leszek Szczecinski

TL;DR

The paper scrutinizes the FIVB ranking algorithm that employs an explicit probabilistic model for six-level ordinal volleyball outcomes to infer team skills $\boldsymbol{\theta}$ from match results. It casts ranking as statistical inference, examines the thresholds $\boldsymbol{c}$, home-field effect $\eta$, and numerical scores $\boldsymbol{r}$, and studies parameter identification via cross-validation and numerical optimization. The authors show that while the modeling framework is a positive step, several approximations (notably the fixed $\boldsymbol{c}$, the poorly tuned $\boldsymbol{r}$, and the use of match weights) hinder optimality, and they demonstrate practical improvements by deriving better numerical scores $\tilde{\boldsymbol{r}}$, incorporating a modest home-field boost, and evaluating real-time updates with unit weights. The findings provide a principled evaluation methodology for multi-level sport rankings and offer concrete, low-cost adjustments to enhance online ranking performance, with a public repository for reproducibility.

Abstract

This work presents and evaluates the ranking algorithm that has been used by Federation Internationale de Volleyball (FIVB) since 2020. The prominent feature of the FIVB ranking is the use of the probabilistic model, which explicitly calculates the probabilities of the future matches results using the estimated teams' strengths. Such explicit modeling is new in the context of official sport rankings, especially for multi-level outcomes, and we study the optimality of its parameters using both analytical and numerical methods. We conclude that from the modeling perspective, the current thresholds fit well the data but adding the home-field advantage (HFA) would be beneficial. Regarding the algorithm itself, we explain the rationale behind the approximations currently used and show a simple method to find new parameters (numerical score) which improve the performance. We also show that the weighting of the match results is counterproductive.

FIVB ranking: Misstep in the right direction

TL;DR

The paper scrutinizes the FIVB ranking algorithm that employs an explicit probabilistic model for six-level ordinal volleyball outcomes to infer team skills from match results. It casts ranking as statistical inference, examines the thresholds , home-field effect , and numerical scores , and studies parameter identification via cross-validation and numerical optimization. The authors show that while the modeling framework is a positive step, several approximations (notably the fixed , the poorly tuned , and the use of match weights) hinder optimality, and they demonstrate practical improvements by deriving better numerical scores , incorporating a modest home-field boost, and evaluating real-time updates with unit weights. The findings provide a principled evaluation methodology for multi-level sport rankings and offer concrete, low-cost adjustments to enhance online ranking performance, with a public repository for reproducibility.

Abstract

This work presents and evaluates the ranking algorithm that has been used by Federation Internationale de Volleyball (FIVB) since 2020. The prominent feature of the FIVB ranking is the use of the probabilistic model, which explicitly calculates the probabilities of the future matches results using the estimated teams' strengths. Such explicit modeling is new in the context of official sport rankings, especially for multi-level outcomes, and we study the optimality of its parameters using both analytical and numerical methods. We conclude that from the modeling perspective, the current thresholds fit well the data but adding the home-field advantage (HFA) would be beneficial. Regarding the algorithm itself, we explain the rationale behind the approximations currently used and show a simple method to find new parameters (numerical score) which improve the performance. We also show that the weighting of the match results is counterproductive.
Paper Structure (18 sections, 1 theorem, 45 equations, 7 figures, 6 tables)

This paper contains 18 sections, 1 theorem, 45 equations, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Model and ranking
  3. Ranking as statistical inference
  4. Integrating exogenous variables
  5. Current FIVB ranking algorithm
  6. Data
  7. Implicit loss function
  8. Model identification
  9. Model identification via cross-validation
  10. Finding thresholds $c$ and parameter $\eta$
  11. Finding numerical score $r$
  12. From thresholds to numerical scores
  13. Numerical optimization
  14. Weights
  15. Real-time ranking
  16. ...and 3 more sections

Key Result

Lemma 1

The implicit loss function, $\ell^{{\textnormal{FIVB}}}_y(z)$ is convex in $z$. Proof: The second derivative of implicit loss $\ell^{{\textnormal{FIVB}}}_y(z)$ is positive if the first derivative $g^{{\textnormal{FIVB}}}_y(z)=\check{r}(z)-r^{\textnormal{FIVB}}_y$ increases monotonically in $z$. The

Figures (7)

  • Figure 1: Functions $\mathsf{P}^{{\textnormal{FIVB}}}_y(z)$ in the ranking algorithm, where $y=0$ corresponds to the result "3-0", $y=1$ to "3-1", etc.
  • Figure 2: Results of optimization in \ref{['hat.bc.eta.logloss']}: thresholds $\hat{c}_0$, $\hat{c}_1$ and the $\hat{\eta}$. The horizontal dotted lines are drawn for the values $c^{{\textnormal{FIVB}}}_0=-1.06$ and $c^{{\textnormal{FIVB}}}_1=-0.394$ used by the ranking, see \ref{['bc.FIVB']}. All thresholds satisfy \ref{['c.l.are.symmetric']} so $c_2\equiv 0$ need not be shown.
  • Figure 3: Validation metrics $U^{{\textnormal{ntr}}}$ (hollow markers) and $U^{{\textnormal{hfa}}}$ (colored markers) given by \ref{['U.ntr']}-\ref{['U.hfa']} shown as a function of $\gamma$ using the loss function $\ell_y(z)$ defined in \ref{['log.score']}.
  • Figure 4: Loss functions: log-score $\ell_y(z)$ (solid line) and rescaled/shifted implicit loss function $a\ell^{{\textnormal{FIVB}}}_y(z;\boldsymbol{r})+b_y$ (dashed line) for $y=0,1,2$ corresponding, respectively, to the outcomes "3-0", "3-1", and "3-2".
  • Figure 5: Validation metrics $U^{{\textnormal{ntr}}}$ (hollow markers) and $U^{{\textnormal{hfa}}}$ (colored markers) given by \ref{['U.ntr']}-\ref{['U.hfa']} shown as a function of $\gamma$ for the loss function $\ell^{{\textnormal{loss}}}_y(z)=\ell^{{\textnormal{FIVB}}}_y(z)$ defined in \ref{['implicit.loss.FIVB']} using parameters which may be: predefined ($\boldsymbol{r}^{{\textnormal{FIVB}}}$), analyticaly calculated ($\tilde{\boldsymbol{r}}(\boldsymbol{c}^{{\textnormal{FIVB}}})$), or, numerically optimized ($\hat{\boldsymbol{r}}$).
  • ...and 2 more figures

Theorems & Definitions (1)

  • Lemma 1