View source for FIVB Senior World Rankings

{{Short description|Ranking system for men's and women's national teams in volleyball}}
The '''FIVB Senior World Rankings''' is a ranking system for men's and women's national teams in [[volleyball]]. The teams of the member nations of [[Fédération Internationale de Volleyball]] (FIVB), volleyball's world governing body, are ranked based on their game results with the most successful teams being ranked highest. A points system is used, with points being awarded based on the results of all FIVB-recognised full international matches. The rankings are used in international competitions to define the seeded teams and arrange them in pools. Specific procedures for seeding and pooling are established by the FIVB in each competition's formula, but the method usually employed is the [[serpentine system]].

The ranking system has been revamped in 2020, responding to criticism that the preceding calculation method did not effectively reflect the relative strengths of the national teams. The old version of the ranking system was finally used on 31 January 2020. 

As of 23 July 2023, the highest ranked team in the men's category is [[Poland men's national volleyball team|Poland]], while in the women's category is [[Turkey women's national volleyball team|Turkey]].

==Previous calculation method==
{{main|FIVB Senior World Ranking system (until 2020)}}

The system of point attribution for the selected FIVB World and Official Competitions below is as follows:<ref name="FIVBPR">{{cite web|title=FIVB World Ranking system |url=http://www.fivb.com/en/volleyball/rankings |publisher=FIVB  |access-date=21 December 2019}}</ref>
*Olympic Games and qualifying tournaments: included for 4 years and points are also granted for the qualification matches, to the best non-qualified teams.
*World Championship and qualifying tournaments: included for 4 years and points are also granted for the qualification matches, to the best non-qualified teams.
*World Cup: included for 4 years 
*World Grand Prix: included for 1 year
*World League: included for 1 year

==Current calculation method==
In 2019, FIVB collaborated with Hypercube Business Innovation of the Netherlands to design a new world ranking platform. The previous calculation method had a problem of circularity in the international volleyball calendar: only countries who participate in the major volleyball events can earn ranking points, whilst the number of ranking points of countries also determines seeding and access of teams for major events. This unfair principle does not contribute to the sporting and commercial quality of volleyball.<ref name="FIVBNR">{{cite web|title=Ranking FIVB (2019) |url=https://www.hypercube.nl/en/ranking-fivb-2019/ |publisher=Hypercube |access-date=1 February 2020}}</ref>

On 1 February 2020, the new ranking system will be implemented and will take into account all results from 1 January 2019.<ref>{{cite web|title=FIVB to introduce new World Ranking system for 2020 |url=http://www.fivb.com/en/about/news/fivb-to-introduce-new-world-ranking-system?id=89970 |publisher=FIVB  |access-date=21 December 2019}}</ref> The system will be consistently updated to reflect the latest results and performances. The new World Ranking considers the match results from all official competitions:
*[[Volleyball at the Summer Olympics|Olympic Games]] and qualifying tournaments
*[[FIVB Volleyball World Championship (disambiguation)|FIVB World Championship]]
*[[FIVB Volleyball World Cup (disambiguation)|FIVB World Cup]] 
*FIVB Nations League and Challenger Cup
*Confederations' Championship and qualifying tournaments
*Other annual official events organized by Continental Confederations.

The rankings outcome of each match depends on two main factors:
*The playing strength of the teams competing
*The actual match performance or final result of the match

===Ranking Procedure===
It is based on the zero-sum system, like [[CONCACAF#Men's CONCACAF Ranking Index|CONCACAF Ranking Index]] or [[FIFA Men's World Ranking|FIFA World ranking]], where, after each game, points will be added to or subtracted from a team's rating according to the formula:<ref>{{cite web|title=HOW IT WORKS |url=https://www.fivb.com/-/media/2020/fivb%20corporate/volleyball/world%20ranking/fivb%20world%20ranking%20-%20how%20it%20works.pdf?la=en |publisher=FIVB |access-date=14 January 2021}}</ref>
:<math>S_\text{after} = S_\text{before} + {K(R-E) \over 8} </math>
where:
*<math>S_\text{after}</math> – the team's number of ''World Ranking scores''  after the game
*<math>S_\text{before}</math> – the team's number of ''World Ranking scores''  before the game
*<math>K</math> – the match importance:
** 10.0 – Other annual official events organized by Continental Confederations
** 17.5 – Confederations' Championship qualifying
** 20.0 – FIVB Challenger Cup
** 35.0 – Olympic Games qualifying, FIVB World Cup and Confederations' Championship
** 40.0 – FIVB Nations League
** 45.0 – FIVB World Championship 
** 50.0 – Olympic Games
*<math>R</math> – the result of the game depended on match and sets won (3-0, 3-1, 3-2, 2-3, 1-3 or 0-3); see below
*<math>E</math> – the expected result of the game has the value between -2 and +2.  If the match is completely balanced, the expected result is 0. The bigger the surprise, the more points are transferred; see below for calculation details.

====Match result====
{{col-begin}}
{{col-1-of-2}}
We set the result <math> R=R_n</math>, where <math>n</math> is the index of the actual result (set score)
*<math>n=1</math> – A win ''3–0''
*<math>n=2</math> – A win ''3–1''
*<math>n=3</math> – A win ''3–2''
*<math>n=4</math> – A lose ''2–3''
*<math>n=5</math> – A lose ''1–3''
*<math>n=6</math> – A lose ''0–3''

{{col-2-of-2}}
{| class="wikitable" style="font-size: 100%; text-align: center;"
!Match Result ||<math> R_n</math> ||<math> P_n</math>
|-
|style="text-align: left;"|''A win'' 3–0  ||+2   ||<math> P\text{1}</math>
|-
|style="text-align: left;"|''A win'' 3–1  ||+1.5 ||<math> P\text{2}</math>
|-
|style="text-align: left;"|''A win'' 3–2  ||+1   ||<math> P\text{3}</math>
|-
|style="text-align: left;"|''A lose'' 2–3 ||-1   ||<math> P\text{4}</math>
|-
|style="text-align: left;"|''A lose'' 1–3 ||-1.5 ||<math> P\text{5}</math>
|-
|style="text-align: left;"|''A lose'' 0–3 ||-2   ||<math> P\text{6}</math>
|}
{{col-end}}

====Expected match result====
The expected results is then calculated as 
<math> E = R_1 P_1 + R_2 P_2 + R_3 P_3 + R_4 P_4 + R_5 P_5 + R_6 P_6</math>
where <math>P_n</math> is the probability of the outcome <math>R_n</math> obtained using the following model (known as [[Ordered probit]]):

;Team A win 3–0
:<math> P_\text{1} = \Phi(C_\text{1}+\Delta) </math>
;Team A win 3–1
:<math> P_\text{2} = \Phi(C_\text{2}+\Delta) - \Phi(C_\text{1}+\Delta) </math>
;Team A win 3–2
:<math> P_\text{3} = \Phi(C_\text{3}+\Delta) - \Phi(C_\text{2}+\Delta) </math>
;Team A lose 2–3
:<math> P_\text{4} = \Phi(C_\text{4}+\Delta) - \Phi(C_\text{3}+\Delta)</math>
;Team A lose 1–3
:<math> P_\text{5} = \Phi(C_\text{5}+\Delta) - \Phi(C_\text{4}+\Delta) </math>
;Team A lose 0–3
:<math> P_\text{6} = 1- \Phi(C_\text{5}+\Delta) </math>
where <math>\Phi(z)</math> is the Cumulative distribution function of the [[Normal distribution]], and 
<math> C_1,\ldots, C_5 </math> are the cut-points
*<math>C_1=-1.06</math>
*<math>C_2=-0.394</math>
*<math>C_3=0</math>
*<math>C_4=0.394</math>
*<math>C_5=1.06</math>
set so that <math>P_n</math> is the probability of the outcome <math>n</math> between two equal strength opponents (that is when <math>\Delta=0</math>), which is derived from the actual match results of the past decade.

{{Col-begin}}
{{Col-1-of-2}}
[[File:Cut-ponts of Brazil and Japan H2H in the normal distribution.png|thumb|left|500px|The cut-points in the normal distribution based on head-to-head between two equal strength teams, i.e <math>\Delta=0</math>.]]
{{-}}

{{Col-2-of-2}}

[[File:Brazil and Japan result probabilities in the normal distribution.png|thumb|left|500px|The cut-points in the normal distribution based on head-to-head between two teams after considering a strength difference, i.e <math>\Delta>0</math>.]]
{{-}}
{{Col-end}}

The parameter <math>\Delta</math> represents the scaled difference of the teams rankings 
:<math> \Delta = {8(S_\text{teamA}-S_\text{teamB}) \over 1000} </math>
where:
*<math>S_\text{teamA}</math> – the team A's number of ''World Ranking scores'' before the game
*<math>S_\text{teamB}</math> – the team B's number of ''World Ranking scores'' before the game

===Examples===
Before the match at the ''FIVB Volleyball World Championship (K = 45)'', Brazil ''(Team A)'' is ranked number 1 with a ''415 WR score'' and Japan ''(Team B)'' is ranked number 11 with a ''192 WR score''. 

;Strength difference between Brazil and Japan
:<math> \Delta = {8(415-192) \over 1000} = 1.784 </math>

;Expected match result


*<math>P_1 = \Phi(-1.060+1.784)</math>
*<math>P_2 = \Phi(-0.364+1.784) - \Phi(-1.060+1.784)</math>
*<math>P_3 = \Phi(0.000+1.784) - \Phi(-0.364+1.784)</math>
*<math>P_4 = \Phi(0.364+1.784) - \Phi(0.000+1.784)</math> 
*<math>P_5 = \Phi(1.060+1.784) - \Phi(0.364+1.784)</math>
*<math>P_6 = 1 - \Phi(1.060+1.784)</math>


Expected match result for Brazil:
:<math> E = 76.5%(+2) + 15.2%(+1.5) + 4.5%(+1) + 2.2%(-1) + 1.2%(-1.5) + 0.2%(-2) = +1.76</math>

Expected match result for Japan:
:<math> E = 0.2%(+2) + 1.2%(+1.5) + 2.2%(+1) + 4.5%(-1) + 15.2%(-1.5) + 76.5%(-2) = -1.76</math>

{{Col-begin}}
{{Col-1-of-2}}
;World Ranking scores after Brazil win 3–0
World Ranking scores for Brazil:
:<math>S_\text{after} = \text{415} + {45(2-1.76) \over 8} = 416.35 </math>
World Ranking scores for Japan: 
:<math>S_\text{after} = \text{192} + {45(-2+1.76) \over 8} = 190.65 </math>

;World Ranking scores after Brazil win 3–1
World Ranking scores for Brazil:
:<math>S_\text{after} = \text{415} + {45(1.5-1.76) \over 8} = 413.54 </math>
World Ranking scores for Japan: 
:<math>S_\text{after} = \text{192} + {45(-1.5+1.76) \over 8} = 193.46 </math>

;World Ranking scores after Brazil win 3–2
World Ranking scores for Brazil:
:<math>S_\text{after} = \text{415} + {45(1-1.76) \over 8} = 410.73 </math>
World Ranking scores for Japan: 
:<math>S_\text{after} = \text{192} + {45(-1+1.76) \over 8} = 196.27 </math>
{{Col-2-of-2}}
;World Ranking scores after Brazil lose 0–3
World Ranking scores for Brazil:
:<math>S_\text{after} = \text{415} + {45(-2-1.76) \over 8} = 393.85 </math>
World Ranking scores for Japan: 
:<math>S_\text{after} = \text{192} + {45(2+1.76) \over 8} = 213.15 </math>

;World Ranking scores after Brazil lose 1–3
World Ranking scores for Brazil:
:<math>S_\text{after} = \text{415} + {45(-1.5-1.76) \over 8} = 396.66 </math>
World Ranking scores for Japan: 
:<math>S_\text{after} = \text{192} + {45(1.5+1.76) \over 8} = 210.34 </math>

;World Ranking scores after Brazil lose 2–3
World Ranking scores for Brazil:
:<math>S_\text{after} = \text{415} + {45(-1-1.76) \over 8} = 399.48 </math>
World Ranking scores for Japan: 
:<math>S_\text{after} = \text{192} + {45(1+1.76) \over 8} = 207.52 </math>
{{Col-end}}

==World and Continental Rankings==
{{further|FIVB Senior Continental Rankings}}
The five Continental Rankings filter the World Ranking points won and lost in matches played between teams from the same Continental Confederation.
*Intercontinental Tournaments – ''calculated in '''World Rankings''', but some matches can be calculated in '''Continental Rankings''' ''
**[[Volleyball at the Summer Olympics|Olympic Games]] final and intercontinental qualification tournaments 
**[[FIVB Volleyball World Championship (disambiguation)|FIVB World Championship]] final and intercontinental qualification tournaments 
**[[FIVB Volleyball World Cup (disambiguation)|FIVB World Cup]] 
**FIVB Volleyball Nations League and Challenger Cup
**some Continental Cups: Pan-America
**some FIVB recognised international events, e.g. [[Pan American Games]], [[Montreux Volley Masters]]

*Continental Tournaments – ''calculated in '''World''' and '''Continental Rankings''' ''
**[[Volleyball at the Summer Olympics|Olympic Games]] continental qualification tournaments 
**[[FIVB Volleyball World Championship (disambiguation)|FIVB World Championship]] continental qualification tournaments 
**FIVB Challenger Cup qualification tournaments 
**Continental Championships: [[Asian Volleyball Championship (disambiguation)|Asia]] (AVC), [[African Volleyball Championship (disambiguation)|Africa]] (CAVB), [[European Volleyball Championship (disambiguation)|Europe]] (CEV), [[NORCECA Volleyball Championship (disambiguation)|North America]] (NORCECA), and [[South American Volleyball Championship (disambiguation)|South America]] (CSV)
**some Continental Cups: [[Asian Volleyball Cup (disambiguation)|Asia]] (both AVC Cup and Challenge Cup) 
**Zonal Championships, e.g. Eastern Asia, [[ASEAN Grand Prix|ASEAN]], Central America
**some FIVB recognised international events, e.g. [[African Games]], [[Asian Games]], [[European Games]]

;Examples
Japan (Asian Volleyball Confederation) vs Italy (Confédération Européenne de Volleyball)<Br>
''The points calculated in FIVB World Rankings.''

Japan (Asian Volleyball Confederation) vs South Korea (Asian Volleyball Confederation)<Br>
''The points calculated in FIVB World Rankings, and AVC Continental Rankings.''

==FIVB World Rankings==
{{Col-float}}
===Current men's top teams===
{{Sports rankings table|FIVB World Rankings|1|30<!--RANKINGS ARE UPDATED AT: Module:SportsRankings/data/FIVB World Rankings-->
|style=margin-left:1em;
|caption=
|header1=
|header2='''Top 30 rankings as of INSERT_UPDATE_DATE'''INSERT_REFERENCE
|footer1=<small>*Change from INSERT_LAST_DATE</small>
|footer2=<small>[https://en.volleyballworld.com/volleyball/world-ranking/men Complete rankings at volleyballworld.com]</small>
}}
{{col-float-break}}

===Current women's top teams===
{{Sports rankings table|FIVB Women's World Rankings|1|30<!--RANKINGS ARE UPDATED AT: Module:SportsRankings/data/FIVB Women's World Rankings-->
|style=margin-left:1em;
|caption=
|header1=
|header2='''Top 30 rankings as of INSERT_UPDATE_DATE'''INSERT_REFERENCE
|footer1=<small>*Change from INSERT_LAST_DATE</small>
|footer2=<small>[https://en.volleyballworld.com/volleyball/world-ranking/women Complete rankings at volleyballworld.com]</small>
}}
{{col-float-end}}

{{Col-float}}

===Historic men's leaders===
For historical men's FIVB rankings from October 2005 to present.<ref>{{cite web|url=https://public.tableau.com/views/2005-2017-fivb-mens-ranking/Sheet1?:embed=y&:display_count=yes|title=Tableau Public|website=public.tableau.com}}</ref>
{{FIVB Men's World Ranking leaders}}
{{col-float-break}}
===Historic women's leaders===
For historical women's FIVB rankings from September 2005 to present.<ref>{{cite web|url=https://public.tableau.com/profile/brahmin#!/vizhome/shared/YTXTJ8HD5|title=Tableau Public|website=public.tableau.com}}</ref>
{{FIVB Women's World Ranking leaders}}
{{col-float-end}}

==See also==
{{Portal|Volleyball}}
*[[FIVB Senior Continental Rankings]]
*[[FIVB Youth and Junior World Rankings]]

==Notes and references==
{{Reflist}}
* {{cite web | url = https://www.fivb.com/en/volleyball/rankings | title = FIVB World Rankings | access-date = 2022-12-18 | author = Fédération Internationale de Volleyball (FIVB) }}

{{Volleyball}}
{{Sport world rankings}}

[[Category:Fédération Internationale de Volleyball|World Rankings]]
[[Category:Volleyball-related lists]]
[[Category:Sports world rankings]]