Noisy-channel coding theorem: Difference between revisions

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30 year-old Entertainer or Range Artist Wesley from Drumheller, really loves vehicle, property developers properties for sale in singapore singapore and horse racing. Finds inspiration by traveling to Works of Antoni Gaudí. The World Football Elo Ratings is a ranking system for men's national teams in association football. The method used to rank teams is based upon the Elo rating system method but modified to take various football-specific variables into account. These ratings should not be confused with the FIFA World Rankings, which is more prevalent because it is the official rating system used by the international governing body of football to rank national teams.

The ratings consider all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches.^[1] Ratings for teams with fewer than 30 matches should be considered provisional.

The FIFA Women's World Rankings system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula.

Top 100 ranking

Current table, as of 24 January 2014, of the World Football Elo Ratings, compiled by the World Football Elo Ratings web site.

Each national team's FIFA World Rankings as of 19 December 2013.^[2] Cell color indicates confederation.

Template:Col-begin Template:Col-2

Elo Rank	Team	Points	Confederation	FIFA Rank
1	Template:Fb	2110	CONMEBOL	10
2	Template:Fb	2082	UEFA	1
3	Template:Fb	2060	UEFA	2
4	Template:Fb	1994	CONMEBOL	3
5	Template:Fb	1979	UEFA	9
6	Template:Fb	1912	CONMEBOL	4
7	Template:Fb	1906	UEFA	13
8	Template:Fb	1905	UEFA	5
9	Template:Fb	1898	CONMEBOL	6
10	Template:Fb	1896	CONMEBOL	15
11	Template:Fb	1887	UEFA	7
12	Template:Fb	1855	UEFA	20
13	Template:Fb	1841	CONCACAF	14
14	Template:Fb	1822	UEFA	8
15	Template:Fb	1819	UEFA	22
16	Template:Fb	1816	CONMEBOL	23
17	Template:Fb	1813	UEFA	12
18	Template:Fb	1807	UEFA	11
19	Template:Fb	1806	UEFA	27
20	Template:Fb	1796	UEFA	18
21	Template:Fb	1786	CAF	17
22	Template:Fb	1784	CONCACAF	21
23	Template:Fb	1779	UEFA	16
24	Template:Fb	1758	UEFA	19
25	Template:Fb	1747	AFC	47
26	Template:Fb	1733	UEFA	28
27	Template:Fb	1729	UEFA	25
28	Template:Fb	1727	UEFA	30
29	Template:Fb	1719	AFC	33
30	Template:Fb	1718	CAF	37
31	Template:Fb	1711	CONCACAF	31
31	Template:Fb	1711	AFC	58
33	Template:Fb	1700	CAF	24
34	Template:Fb	1696	CONMEBOL	39
35	Template:Fb	1695	CAF	41
36	Template:Fb	1686	UEFA	43
36	Template:Fb	1686	UEFA	67
38	Template:Fb	1685	CONMEBOL	36
39	Template:Fb	1683	CONCACAF	38
40	Template:Fb	1681	CONMEBOL	51
41	Template:Fb	1680	UEFA	32
42	Template:Fb	1672	AFC	54
43	Template:Fb	1671	UEFA	34
44	Template:Fb	1664	CONCACAF	42
45	Template:Fb	1650	UEFA	44
46	Template:Fb	1646	UEFA	64
47	Template:Fb	1643	AFC	71
48	Template:Fb	1639	AFC	68
49	Template:Fb	1638	UEFA	46
50	Template:Fb	1633	UEFA	29

Template:Col-2

Elo Rank	Team	Points	Confederation	FIFA Rank
51	Template:Fb	1624	UEFA	76
52	Template:Fb	1618	UEFA	63
53	Template:Fb	1613	UEFA	74
54	Template:Fb	1603	CONMEBOL	70
55	Template:Fb	1593	CAF	50
56	Template:Fb	1603	UEFA	54
57	Template:Fb	1585	CAF	62
58	Template:Fb	1583	AFC	92
59	Template:Fb	1582	CAF	26
60	Template:Fb	1580	UEFA	60
61	Template:Fb	1577	AFC	138
62	Template:Fb	1570	CAF	65
63	Template:Fb	1566	UEFA	52
64	Template:Fb	1562	AFC	85
65	Template:Fb	1560	UEFA	81
65	Template:Fb	1560	OFC	90
67	Template:Fb	1558	CAF	45
67	Template:Fb	1558	UEFA	56
69	Template:Fb	1555	UEFA	35
70	Template:Fb	1552	CAF	59
71	Template:Fb	1551	CAF	53
72	Template:Fb	1549	AFC	105
73	Template:Fb	1544	AFC	65
74	Template:Fb	1529	CAF	73
75	Template:Fb	1519	AFC	87
76	Template:Fb	1518	CAF	61
77	Template:Fb	1516	CAF	86
78	Template:Fb	1508	CAF	39
78	Template:Fb	1508	CONCACAF	90
80	Template:Fb	1507	UEFA	49
81	Template:Fb	1506	AFC	110
82	Template:Fb	1504	CAF	48
83	Template:Fb	1501	CONCACAF	80
84	Template:Fb	1499	CONCACAF	78
85	Template:Fb	1494	AFC	103
86	Template:Fb	1488	UEFA	83
87	Template:Fb	1484	UEFA	57
88	Template:Fb	1480	CAF	77
89	Template:Fb	1477	CAF	69
90	Template:Fb	1473	CAF	72
91	Template:Fb	1465	UEFA	101
92	Template:Fb	1464	CONCACAF	112
93	Template:Fb	1460	CONCACAF	113
94	Template:Fb	1459	AFC	129
95	Template:Fb	1450	CAF	109
96	Template:Fb	1448	CAF	82
97	Template:Fb	1442	CAF	88
97	Template:Fb	1442	UEFA	94
99	Template:Fb	1437	AFC	110
100	Template:Fb	1433	UEFA	116

Template:Col-end

Strongest teams since the mid to late 1960s

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.^[3]^[4]^[5] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 January 2014. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score. Since Elo scores reflect past accomplishments, the table represents the relative strength of national teams since the mid to late 1960s.

Rank	Country	Avg Elo
1	Template:Fb	2012.1
2	Template:Fb^[6]	1975.3
3	Template:Fb	1924.3
4	Template:Fb	1923.6
5	Template:Fb	1923.0
6	Template:Fb	1908.7
7	Template:Fb	1902.0
8	Template:Fb	1881.5
9	Template:Fb^[7]	1852.8
10	Template:Fb^[8]	1833.0
11	Template:Fb^[9]	1817.5
12	Template:Fb	1816.9
13	Template:Fb	1798.9
14	Template:Fb	1781.9
15	Template:Fb	1774.5
16	Template:Fb	1773.4
17	Template:Fb	1771.3
18	Template:Fb	1761.1

Rank	Country	Avg Elo
19	Template:Fb	1757.1
20	Template:Fb	1739.3
21	Template:Fb	1727.3
22	Template:Fb	1721.1
23	Template:Fb	1716.0
24	Template:Fb	1709.4
25	Template:Fb	1696.4
26	Template:Fb	1689.1
27	Template:Fb	1686.0
28	Template:Fb	1685.4
29	Template:Fb	1681.2
30	Template:Fb	1676.0
31	Template:Fb	1666.3
32	Template:Fb	1654.8
33	Template:Fb	1654.4
34	Template:Fb	1654.2
35	Template:Fb	1653.8

Rank	Country	Avg Elo
36	Template:Fb	1645.6
37	Template:Fb	1644.5
38	Template:Fb	1643.8
39	Template:Fb	1638.3
40	Template:Fb	1637.5
41	Template:Fb	1637.3
42	Template:Fb	1633.8
43	Template:Fb	1611.3
44	Template:Fb	1609.6
45	Template:Fb	1603.5
46	Template:Fb	1602.2
47	Template:Fb	1595.9
48	Template:Fb	1595.8
49	Template:Fb	1589.5
50	Template:Fb	1580.8
51	Template:Fb	1569.6
52	Template:Fb	1561.3

List of number one teams

The following is the list of nations who have achieved the number one position on the World Football Elo Ratings since 2000: Template:Col-begin Template:Col-3

Start Date	Nation	# of days
5 Jun 1999	Template:Fb	389
28 Jun 2000	Template:Fb	708
6 Jun 2002	Template:Fb	1
7 Jun 2002	Template:Fb	4
11 Jun 2002	Template:Fb	1
12 Jun 2002	Template:Fb	4
16 Jun 2002	Template:Fb	5
21 Jun 2002	Template:Fb	351
7 Jun 2003	Template:Fb	4
11 Jun 2003	Template:Fb	8
19 Jun 2003	Template:Fb	83
10 Sep 2003	Template:Fb	291
27 Jun 2004	Template:Fb	4
1 Jul 2004	Template:Fb	10

Template:Col-3

Start Date	Nation	# of days
11 Jul 2004	Template:Fb	3
14 Jul 2004	Template:Fb	35
18 Aug 2004	Template:Fb	290
4 Jun 2005	Template:Fb	4
8 Jun 2005	Template:Fb	21
29 Jun 2005	Template:Fb	102
9 Oct 2005	Template:Fb	3
12 Oct 2005	Template:Fb	265
4 Jul 2006	Template:Fb	43
16 Aug 2006	Template:Fb	52
7 Oct 2006	Template:Fb	122
6 Feb 2007	Template:Fb	1
7 Feb 2007	Template:Fb	140

Template:Col-3

Start Date	Nation	# of days
27 Jun 2007	Template:Fb	14
11 Jul 2007	Template:Fb	4
15 Jul 2007	Template:Fb	334
13 Jun 2008	Template:Fb / Template:Fb	2
15 Jun 2008	Template:Fb	6
21 Jun 2008	Template:Fb	368
24 Jun 2009	Template:Fb	373
2 Jul 2010	Template:Fb	1
3 Jul 2010	Template:Fb / Template:Fb	3
6 Jul 2010	Template:Fb	1
7 Jul 2010	Template:Fb	1089
30 Jun 2013	Template:Fb	45
14 Aug 2013	Template:Fb	59
12 Oct 2013	Template:Fb	Template:Age in days

Template:Col-end

Ranking by days as leader since 1 January 2000

Nation	# of days	Last Date as Leader
Template:Fb	2204	Current
Template:Fb	1523	12 October 2013
Template:Fb	1115	10 July 2007
Template:Fb	316	14 July 2007
Template:Fb	109	6 July 2010
Template:Fb	43	15 August 2006
Template:Fb	8	7 June 2005

All-time highest ratings

The following is a list of national football teams ranked by their highest Elo score ever reached. Template:Col-begin Template:Col-2

Rank	Nation	Points	Date
1	Template:Fb	2166	30 June 1954
2	Template:Fb	2153	17 June 1962
3	Template:Fb	2142	23 June 2013
4	Template:Fb	2117	3 April 1957
5	Template:Fb	2106	15 August 2001
6	Template:Fb	2101	6 July 2010
7	Template:Fb	2099	4 September 1974 (as West Germany)
8	Template:Fb	2079	20 July 1939
9	Template:Fb	2047	1 September 1974
10	Template:Fb	2041	22 October 1966
11	Template:Fb	2035	13 June 1928
12	Template:Fb	2023	9 October 1983 (as Soviet Union)
13	Template:Fb	1999	27 June 2004
14	Template:Fb	1998	31 May 1934
15	Template:Fb	1983	15 November 2000
16	Template:Fb	1967	11 July 1998
17	Template:Fb	1961	25 June 1998 (as FR Yugoslavia)
18	Template:Fb	1960	13 June 1986
19	Template:Fb	1953	10 March 1888
20	Template:Fb	1950	25 June 1950
20	Template:Fb	1950	22 June 1974
22	Template:Fb	1936	19 June 2005
23	Template:Fb	1932	21 February 1954
24	Template:Fb	1919	12 July 2011
25	Template:Fb	1916	9 September 1981

Template:Col-2

Rank	Nation	Points	Date
26	Template:Fb	1913	13 June 2000
27	Template:Fb	1912	5 June 1994
28	Template:Fb	1909	9 June 1990
29	Template:Fb	1896	18 August 2004
30	Template:Fb	1889	21 August 2002
31	Template:Fb	1881	26 January 2013
32	Template:Fb	1876	22 June 1994
33	Template:Fb	1871	8 July 2009
34	Template:Fb	1867	14 December 1997
	Template:Fb	1867	15 August 2001
	Template:Fb	1867	19 June 2003
37	Template:Fb	1862	26 March 2013
38	Template:Fb	1859	20 May 1981
39	Template:Fb	1856	15 June 1969
39	Template:Fb	1856	11 June 1978
41	Template:Fb	1849	26 June 2003
42	Template:Fb	1835	31 January 2010
43	Template:Fb	1824	8 June 2005
44	Template:Fb	1820	15 November 2013
45	Template:Fb	1818	22 June 2002
46	Template:Fb	1816	5 June 2004
47	Template:Fb	1809	23 April 1986
48	Template:Fb	1803	16 June 2002
49	Template:Fb	1800	10 March 1960
50	Template:Fb	1799	3 February 2008

Template:Col-end

Averages by decade

The table below shows the teams with the best average Elo score per decade (Jan 1 19X0 - Dec 31 19X9). Because the Elö scores take into account past achievements with an inercy of months, the averaging over a decade is more representative of the teams' strengths for a decade starting a few years earlier and ending with the latest results of the decade relatively underweighted. For instance, this partially explains England claiming #3 spot despite missing two WCs in the 70s, boosted by results legacy from the late 60s. Or conversely the surging of France in the late 90s and Spain in the late 00s not being fully reflected in that decade but rather on the subsequent one.

Rank	1920s		1930s		1940s		1950s		1960s
1	1911	Template:Fb	1976	Template:Fb	2036	Template:Fb	2025	Template:Fb	1962	Template:Fb
2	1873	Template:Fb	1970	Template:Fb	2018	Template:Fb	1997	Template:Fb	1928	Template:Fb
3	1859	Template:Fb	1899	Template:Fb	1892	Template:Fb	1996	Template:Fb	1924	Template:Fb
4	1843	Template:Fb	1868	Template:Fb	1876	Template:Fb	1917	Template:Fb	1923	Template:Fb
5	1820	Template:Fb	1866	Template:Fb	1858	Template:Fb	1870	Template:Fb	1917	Template:Fb
6	1795	Template:Fb	1859	Template:Fb	1852	Template:Fb	1856	Template:Fb	1887	Template:Fb
7	1771	Template:Fb	1841	Template:Fb	1841	Template:Fb	1853	Template:Fb	1867	Template:Fb
8	1768	Template:Fb	1814	Template:Fb	1832	Template:Fb	1850	Template:Fb	1852	Template:Fb
9	1761	Template:Fb	1810	Template:Fb	1814	Template:Fb	1817	Template:Fb	1843	Template:Fb
10	1760	Template:Fb	1785	Template:Fb	1768	Template:Fb	1815	Template:Fb	1840	Template:Fb
11	1739	Template:Fb	1759	Template:Fb	1766	Template:Fb	1799	Template:Fb	1810	Template:Fb
12	1712	Template:Fb	1685	Template:Fb	1746	Template:Fb	1796	Template:Fb	1800	Template:Fb
13					1734	Template:Fb	1790	Template:Fb	1796	Template:Fb
14							1753	Template:Fb	1783	Template:Fb
15							1728	Template:Fb	1741	Template:Fb

Rank	1970s		1980s		1990s		2000s		2010s ^[10]
1	2060	Template:Fb	1975	Template:Fb	1998	Template:Fb	1998	Template:Fb	2104	Template:Fb
2	2040	Template:Fb	1964	Template:Fb	1988	Template:Fb	1984	Template:Fb	2057	Template:Fb
3	1948	Template:Fb	1951	Template:Fb	1952	Template:Fb	1966	Template:Fb	2023	Template:Fb
4	1933	Template:Fb	1927	Template:Fb	1928	Template:Fb	1964	Template:Fb	2023	Template:Fb
5	1888	Template:Fb	1897	Template:Fb	1920	Template:Fb	1955	Template:Fb	1946	Template:Fb
6	1883	Template:Fb	1890	Template:Fb	1904	Template:Fb	1941	Template:Fb	1924	Template:Fb
7	1877	Template:Fb	1884	Template:Fb	1901	Template:Fb^[11]	1916	Template:Fb	1876	Template:Fb
8	1869	Template:Fb	1884	Template:Fb	1901	Template:Fb	1891	Template:Fb	1871	Template:Fb
9	1861	Template:Fb	1847	Template:Fb	1869	Template:Fb	1887	Template:Fb	1869	Template:Fb
10	1851	Template:Fb	1839	Template:Fb	1869	Template:Fb	1872	Template:Fb	1858	Template:Fb
11	1838	Template:Fb	1820	Template:Fb	1842	Template:Fb^[12]	1838	Template:Fb	1852	Template:Fb
12	1831	Template:Fb	1819	Template:Fb	1834	Template:Fb	1825	Template:Fb	1846	Template:Fb
13	1830	Template:Fb	1818	Template:Fb	1828	Template:Fb	1821	Template:Fb	1822	Template:Fb
14	1809	Template:Fb	1803	Template:Fb	1825	Template:Fb^[13]	1807	Template:Fb	1820	Template:Fb
15	1803	Template:Fb	1785	Template:Fb	1825	Template:Fb	1799	Template:Fb	1816	Template:Fb
16	1793	Template:Fb	1784	Template:Fb	1813	Template:Fb	1790	Template:Fb	1794	Template:Fb
17	1771	Template:Fb	1784	Template:Fb	1810	Template:Fb	1786	Template:Fb	1793	Template:Fb
18	1766	Template:Fb	1776	Template:Fb	1784	Template:Fb	1785	Template:Fb	1775	Template:Fb
19	1766	Template:Fb	1775	Template:Fb	1776	Template:Fb	1782	Template:Fb	1769	Template:Fb
20	1755	Template:Fb	1773	Template:Fb	1773	Template:Fb	1774	Template:Fb	1758	Template:Fb

Highest rated matches

A list of the 10 matches between teams with the highest combined Elo ratings (the nation's points before the matches are given).

Rank	Combined points	Nation 1	Elo 1	Nation 2	Elo 2	Score	Date	Occasion	Location
1	4212	Template:Fb	2101	Template:Fb	2111	0 : 1 ^aet	2010-07-10	World Cup F	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Johannesburg
2	4190	Template:Fb	2063	Template:Fb	2127	3 : 0	2013-06-30	Confederations Cup F	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Rio de Janeiro
3	4161	Template:Fb	1995	Template:Fb	2166	3 : 2	1954-07-04	World Cup F	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Bern
4	4159	Template:Fb	2051	Template:Fb	2108	2 : 1	2010-07-02	World Cup QF	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Port Elizabeth
5	4151	Template:Fb	2061	Template:Fb	2090	0 : 0	2011-06-04	Friendly	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Goiânia
6	4149	Template:Fb	2068	Template:Fb	2081	0 : 1	1973-06-16	Friendly	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Berlin
7	4129	Template:Fb	2085	Template:Fb	2044	1 : 0	2010-07-07	World Cup SF	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Durban
8	4120	Template:Fb	2051	Template:Fb	2069	1 : 0	1982-03-21	Friendly	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Rio de Janeiro
9	4118	Template:Fb	2108	Template:Fb	2010	4 : 2	1954-06-27	World Cup QF	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Bern
10	4116	Template:Fb	2141	Template:Fb	1975	4 : 2	1954-06-30	World Cup SF	41 yr old Film, Tv, Radio and Stage Owners Anton Lester from Lively, has many hobbies which include guitar, property developers in singapore apartment for sale and rowing. Recalls what an attractive place it had been having gone to San Marino Historic Centre and Mount Titano. Lausanne

History

This system, developed by Hungarian-American mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess players, and by the European Go Federation, to rate Go players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site, now maintained by Kirill Bulygin.

Overview

The Elo system was adapted for football by adding a weighting for the kind of match, an adjustment for the home team advantage, and an adjustment for goal difference in the match result.

The factors taken into consideration when calculating a team's new rating are:

The team's old rating
The considered weight of the tournament
The goal difference of the match
The result of the match
The expected result of the match

The different weights of competitions in descending order are:

World Cup Finals
Continental championships finals and Intercontinental tournaments
World Cup and Continental championship qualifiers
All other tournaments
Friendly matches

The single difference is Elo giving a special treatment for minor tournaments, while FIFA consider them as friendly matches.

These ratings take into account all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional. Match data are primarily from International Football 1872 – present web site.

Basic calculation principles

The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables who effectively run their table as a normal league table, but with weightings to take into account the other factors, the Elo system has its one formula which takes into account the factors mentioned above. There is no first step as in the FIFA system where a team immediately receives points for the result, there is just one calculation in the Elo system.

The ratings are based on the following formulae:

$R_{n}=R_{o}+KG(W-W_{e})$

or

$P=KG(W-W_{e})$

Where;


$R_{n}$	= The new team rating
$R_{o}$	= The old team rating
$K$	= Weight index regarding the tournament of the match
$G$	= A number from the index of goal differences
$W$	= The result of the match
$W_{e}$	= The expected result
$P$	= Points Change

Status of match

The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;

Tournament or Match type	Index (K)
World Cup Finals	60
Continental Championship and Intercontinental Tournaments	50
World Cup and Continental qualifiers and major tournaments	40
All other tournaments	30
Friendly Matches	20

Number of goals

The number of goals is taken into account by use of a goal difference index. G is increased by half if a game is won by two goals, and if the game is won by three or more goals by a number decided through the appropriate calculation shown below;

If the game is a draw or is won by one goal

G=1

If the game is won by two goals

G={\frac {3}{2}}

If the game is won by three or more goals

Where N is the goal difference

G={\frac {11+N}{8}}

Table of examples:

Goal Difference	Coefficient of K (G)
0	1
+1	1
+2	1.5
+3	1.75
+4	1.875
+5	2
+6	2.125
+7	2.25
+8	2.375
+9	2.5
+10	2.625

Result of match

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss).

Expected result of match

W_e is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

W_{e}={\frac {1}{10^{-dr/400}+1}}

where dr equals the difference in ratings plus 100 points for a team playing at home. So dr of 0 gives 0.5, of 120 gives 0.666 to the higher-ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher-ranked team and 0.01 to the lower.

Examples

The same examples have been used on the FIFA World Rankings for a fair comparison. Some actual examples should help to make the methods of calculation clear. In this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.

Before the tournament the three teams have the following point totals.

Team	Points
A	630
B	500
C	480

Thus, team A is by some distance the highest ranked of the three: The following table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:

Example 1

Team A versus Team B (Team A stronger than Team B)

	Team A	Team B	Team A	Team B	Team A	Team B
Score	3 : 1		1 : 3		2 : 2
$K$	20	20	20	20	20	20
$G$	1.5	1.5	1.5	1.5	1	1
$W$	1	0	0	1	0.5	0.5
$W_{e}$	0.679	0.321	0.679	0.321	0.679	0.321
Total (P)	+9.63	-9.63	-20.37	+20.37	-3.58	+3.58

Example 2

Team B versus Team C (both teams approximately the same strength)

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following table illustrates how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:

	Team B	Team C	Team B	Team C	Team B	Team C
Score	3 : 1		1 : 3		2 : 2
$K$	20	20	20	20	20	20
$G$	1.5	1.5	1.5	1.5	1	1
$W$	1	0	0	1	0.5	0.5
$W_{e}$	0.529	0.471	0.529	0.471	0.529	0.471
Total (P)	+14.13	-14.13	-15.87	+15.87	-0.58	+0.58

Note that Team B loses more ranking points by losing to Team C than by losing to Team A.

Notes

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↑ Template:Cite web
↑ Template:Cite press release
↑ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
↑ Arpad Elo, Chess Life, 1962.
↑ About the Chessmetrics Rating System, by Jeff Sonas
↑ Representing West Germany from 1949 to 1990
↑ Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
↑ Combined record of Czechoslovakia (1970-1992) and Czech national football teams (1993-present)
↑ Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
↑ (up to January 1st, 2014)
↑ Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)
↑ Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)
↑ Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)

[1] Template:Cite web

[2] Template:Cite press release

[3] Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.

[4] Arpad Elo, Chess Life, 1962.

[5] About the Chessmetrics Rating System, by Jeff Sonas

[6] Representing West Germany from 1949 to 1990

[7] Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)

[8] Combined record of Czechoslovakia (1970-1992) and Czech national football teams (1993-present)

[9] Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)

[10] (up to January 1st, 2014)

[11] Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)

[12] Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)

[13] Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

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Noisy-channel coding theorem: Difference between revisions

Revision as of 13:01, 7 December 2013

Contents

Top 100 ranking

Strongest teams since the mid to late 1960s

List of number one teams

Ranking by days as leader since 1 January 2000

All-time highest ratings

Averages by decade

Highest rated matches

History

Overview