Threeandtwentyism Decides

Quick recap: I have invented threeandtwentyism to decide which one of 23 ties in the Second Qualifying Round of the FA Cup next Saturday to go to next weekend.  I have associated each match with a letter of the alphabet by choosing the 23 most common letters in the English language (both in words in general and for the initial letters of words).  Therefore Q, X and Z are omitted.  This means I can associate each match with the surname of people that can share or exhibit 23ness in their lives this week, up to 2323 (11.23pm) on Sunday.

Here are the final results, combining the themes of football, travel and groundhopping with friends' suggestions and personal links.  The numbers on the right are the total number of links I have been able make with the number 23  for each letter.  I have 120 links with the number 23 altogether.  There are more for the letter S than any other - but S is a very common initial letter in the English language.

1	Ashton United	v	Marine	A – 8
Shola Ameobl wears 23 at Newcastle (thanks @PayasodeMierda), as does Andrey Arshavin at Arsenal and Armand (Accrington).  On 23/04/11 in the Faroe Islands I saw AB lose 2-3 at home to FC Suðuroy.  Australia beat Argentina 23-19 in rugby union yesterday.  BA Flight 23 will take you to Atlanta.  Yasser A was in block Z3, which looks like 23, for QPR v Chelsea on Saturday.
2	Bamber Bridge	v	Guiseley AFC	B – 14
William Burroughs believed in the enigma of 23.  Peter B likes the fact that 23 is sending me mad!  Bolton Wanderers won the first match at Wembley Stadium, the 1923 “White Horse” FA Cup final (thanks @HoundofMeath).  I hopped to Bury Town on 23/11/10.  Berkley (Colwyn Bay) scored in the 23rd min yesterday.  Bristol Rovers are 23rd in League One this morning.  Blackstock (Nottm Forest), Bennett (Doncaster), Bradley (Aldershot), Bell (Burton), Burgess (Port Vale), Barker (Southend), Boyle (Dundee), Barron (St Mirren) all wear 23.
3	Bishop Auckland	v	AFC Fylde	C – 14
Clark is the name of the two captains in Borroughs' tale of the 23 enigma.  Jim Carrey is the star of the film "The Number 23".  Sol Campbell wore 23 at Arsenal (thanks @cordelan) as does Seamus Coleman (Everton), Jamie Carragher (Liverpool), Tom Cleverley (Man U) and Carlo Cudicini (Spurs).  Also Craney (Rochdale).  Charlton is the 23rd team on my chronological groundhopping list.  I saw Crawley draw at York on 23/11/08, and Crawley is reached via the M23 motorway.  On 23/10/11 I was at Celtic Park.  Coventry are 23rd in League One.  Cambridge City are the home side in tie number 23 in this round of the FA Cup.
4	Buckland	v	Bath City	D – 1
Alou Diarra (West Ham) wears 23.
5	Carlton Town	v	New Mills	E – 1
Etuhu (Barnsley) wears 23.
6	Chorley	v	Frickley Athletic	F – 7
On 23/01/10 I saw Farsley v Northwich Victoria and the score was 2-3.  My Grandma F’s birthday.  I was teaching at Fearnhill School in Letchworth when I was 23.  Frecklington (Peterboro), Freeman (Derby) and Faye (Hull) all wear 23.
7	Dereham Town	v	Chasetown	G – 1
On 23/08/11 I hopped to an FA Cup game at Greenwood Meadows.
8	Fareham Town	v	Blackfield & Langley	H – 11
Kathy H’s parents were both born in 1923.  Huddo Hudson pointed out to me that 23 is the number of players in a World Cup squad.  David Hoilett (QPR) and Ian Harte (Reading) wear 23.  Also Hector (Shrewsbury).  I hopped to Histon on 23/08/08.  It took 23 years for a report on the Hillsborough incident to be accepted as the truth.  Hyde are 23rd in the Conference this morning.  You’d need M6 J23 to go to the races at Haydock Park.  Hayes & Yeading have moved their FA Cup tie to the 23rd.
9	Frome Town	v	Weston Super Mare	I – 1
Ipswich Town are 23rd in the Championship.
10	Gillingham Town	v	Sholing	J – 1
23 was Michael Jordan’s shirt number for Chicago Bulls in the NBA.
11	Gosport Borough	v	Bideford Town	K – 3
I hopped to Kentish Town on 23/09/09.  Kabamba (Uxbridge) scored in the 23rd min yesterday.  Keegan (Southend) wears 23.
12	Grays Athletic	v	Maidstone United	L – 6
On 23/03/10 I hopped to Leverstock Green.  Lopez (Stevenage) and Lustig (Celtic) wear 23. On 11/09/01 (now known as "9/11") United Airlines' Flight 23 to Los Angeles is believed by many to have averted a hijacking because of the captain's actions on the runway.  Virgin Atlantic Flight 23 also flies to Los Angeles.  Notts County's Joss Labadie was the only substitute deployed in the 23rd minute in the weekend's games.
13	Merthyr	v	Hungerford Town	M – 13
Virgina Madsen is the co-star in the film "The Number 23".  Elaine M’s wedding anniversary.  Broadcaster Aasmah Mir just tweeted a link to a video of her at age 23 (thanks @putajumperon).  James McClean (Sunderland) and Gareth McAuley (WBA) wear 23.  Also McArdle (Bradford C) and Mohamed (Cheltenham).  My visit to Eastlands to see Man City 0-0 Portsmouth was on 23/08/06.  There is an enormous Morrisons depot next to J23 on the M5.  Nathaniel Mendez-Laing (Peterborough) scored in the 23rd minute today.  Maynard (Cardiff) and McKeown (Kilmarnock) wear 23.  M is the 23rd letter of Numbers chapter 23 verse 23 in the King James version of Old Testment, ("Surely there is no enchantment ...)
14	Newport (IoW)	v	Salisbury City	N – 1
Nantwich lost a match 23-0 to Manchester United in 1952 (thanks @richard242).
15	Nuneaton Griff	v	Hednesford Town	O – 2
O'Shea (MK) and O'Brien (Oxford U) wear 23.
16	Salford City	v	FC United Of Manchester	P – 1
23 is a Prime number.
17	Shildon	v	Altrincham	R – 3
Gerda R likes the number 23 because it is her son’s birthday.  Rochina (Blackburn) wears 23, also Randall (Chesterfield).
18	South Park	v	Harefield United	S – 16
Joel Schumacher directed "The Number 23" and the central character is Walter Sparrow.  @putajumperon was 23 when he saw an Aussie Rules game, won by St Kilda.  Daniel Sturridge (Chelsea), Luke Shaw (Southampton), Darnel Situ (Swansea) and Ronnie Stam (Wigan) wear 23.  Also Spector (B'ham), Speiss (Notts Co), Simonsen (PNE).  My visit to Sunderland’s old ground (Roker Park) was on 23/10/93.  On 23/10/10 I saw Sheffield v Tipton Town and wrote my first piece for @therealfacup.  Shepshed Dynamo are located near M1 J23 and the South Mimms Services are located at J23 of the M25.  Rifca Stanescu of Romania appears to have become the world's youngest grandmother, at age 23.  Slough Town have moved their FA Cup tie to the 23rd.
19	Tadcaster Albion	v	Skelmersdale United	T – 6
@TravellingFan is 23 and the last time I saw him was at Three Bridges.  Marc Tierney (Norwich) and Michael Tonge (Stoke) wear 23.  Toomey (St Albans) scored in the 23rd min yesterday.  Thompson (Wycombe) wears 23.  Throbbing Gristle sang a song (in the loose sense of the term) about Flight 23.
20	Trafford	v	Spennymoor Town	U – 1
“Trafford v Spennymoor Town” has 23 characters not including the spaces.
21	West Auckland Town	v	Harrogate Town	V – 3
Rowan Vine of St Johnstone wore the 23 shirt AND scored the winning goal against Celtic.  There are 23 protons in the nucleus of every atom of the element Vanadium.
22	Whitby Town	v	Droylsden	W – 4
Wabara (Oldham), Woodall (Dag & Red) wear 23.  "Whitby Town v Droylsden" has 23 characters if spaces are included.  "23 Minutes in Hell" is the title of an utterly loopy book written by a religious fanatic by the name of Bill Weise about which I will say no more.
23	Yate Town	v	Oxford City	Y – 2
Yussuff (AFC Wimbledon) wears 23.  "Yate Town v Oxford City" has 23 characters if spaces are included.

However, since most of the links are surnames, we need a significance test otherwise the decision is made by the distribution of first letters and not by 23ness at all.  To find out what the "expected" distribution is, I took a telephone directory and counted the number of pages devoted to each initial letter, to the nearest column (or 0.25 of a page).

For example, there were 11.25 pages of Ks out of 398, which would be 2.83%  ( 11.25 x 100 / 398 ).  We found 3 out of 120 links of 23ness for K, which is 2.50% of them  ( 3 x 100 / 120 ) which shows that we found a very slightly smaller % than we might expect.  We can calculate a simple significance factor by simply working out the ratio of the actual percentage to the expected percentage.  The bigger the number, the greater the significance - we found more 23ness examples than we would have expected to find if it were just due to the initial letter.  All of this is moderately reasonable and plausible so far.  There are other more sophisticated significance tests, but the simple one will give me an answer that is good enough for this pointless purpose.

So ...

Letter	Directory No. of Pages	Expected % (E)	23ness Score	Actual % (A)	SIGNIFICANCE = A / E
A	13.00	3.27%	8	6.67%	2.04
B	40.50	10.18%	14	11.67%	1.15
C	34.00	8.54%	14	11.67%	1.37
D	18.50	4.65%	1	0.83%	0.18
E	8.25	2.07%	1	0.83%	0.40
F	14.25	3.58%	7	5.83%	1.63
G	20.50	5.15%	1	0.83%	0.16
H	32.75	8.23%	11	9.17%	1.11
I	1.75	0.44%	1	0.83%	1.90
J	10.25	2.58%	1	0.83%	0.32
K	11.25	2.83%	3	2.50%	0.88
L	17.00	4.27%	6	5.00%	1.17
M	33.50	8.42%	13	10.83%	1.29
N	7.25	1.82%	1	0.83%	0.46
O	6.00	1.51%	2	1.67%	1.11
P	22.25	5.59%	1	0.83%	0.15
R	19.00	4.77%	3	2.50%	0.52
S	37.25	9.36%	16	13.33%	1.42
T	16.25	4.08%	6	5.00%	1.22
U	0.75	0.19%	1	0.83%	4.42
V	3.00	0.75%	3	2.50%	3.32
W	29.00	7.29%	4	3.33%	0.46
Y	1.75	0.44%	2	1.67%	3.79
Total	398.00	100.00	120	100.00

There are more initial Bs in the directory than anything else, so the number of 23ness links to B were about what would be expected.  We found more links to S than any other letter, but the significance factor is not that high.  The clear winner by this spurious methodology, with a result of 4.42, is the letter U, which was linked to Trafford v Spennymoor Town.  On the face of it, this is a fluke result caused by the fact that the expected % was so low that it is surprising that we found any 23ness for this game at all ... but it is delicious and wonderful that the one that I did find is that it has 23 letters.  You just can't argue with logic.

Trafford v Spennymoor Town will be my randomish FA Cup hop for next Saturday.

Small print for real and partially real mathematicians:
The way that the games were linked to letters was as fair as anything can be with alphabetical order.  I have been consistent about searching for and recording examples of so-called "23ness".  The telephone directory listing used was the residential section of the St Albans Phone Book, and there is no reason to believe that it is unrepresentative.  Page counts were done to the nearest column, or quarter of a page.  The significance test is fair up to a point - it is true that it shows the letters that showed up more or less than "expected".  However, the variations are large and the true statistical significance is dubious, especially for those letters which appear the least.  Another significance test involving differences from expected rather than ratios (i.e. subtraction rather than division) would have kept S at the top.  I could probably have devised plausible sounding tests that would have put Y or A at the top had I wished to be devious.  I didn't know that this method would favour the low frequency letters until I completed it.  But I don't care - I'm going to Trafford v Spennymoor - it has 23 letters, I have spent the weekend with 23 and I am not letting go now.