Wright's Equation and Hardiman's Method are both based on the principle that the inbreeding of an individual is one half the relationship of its sire and dam, however the calculations involve different data and so the inbreeding coefficients produced by them are not interchangeable and should not be compared with each other. Wright's Equation is haphazardly calculated to any number of generations, whereas Hardiman's Method is always calculated to five generations. Wright's Equation considers duplicated ancestors only if they are common to both sire and dam, whereas Hardiman's Method considers all duplicated ancestors. Wrights Equation considers inbred ancestors only if they are duplicated ancestors, whereas Hardiman's Method considers all inbred ancestors. It should be noted here that an inbreeding coefficient is of little value without a standard with which it can be compared, so the proposed Register of Inbreeding Coefficients will be used to calculate a breed average for comparison.
STANDARD INBREEDING COEFFICIENT  includes only
the subject's inbreeding in the first five generations
CUMULATIVE INBREEDING COEFFICIENT  includes all inbreeding in the subject's
pedigree back as far as records allow
See REGISTER OF INBREEDING COEFFICIENTS

Fx is the inbreeding coefficient of the horse in question, Fa is the inbreeding coefficient of the common ancestor, n1 is the number of generations from the sire to the common ancestor, and n2 is the number of generations from the dam to the common ancestor.
CEDRIC  PHANTOM  WALTON 
Walton mare  WALTON  
Cedric is the result of the mating of halfsibs, both his parents
being by Walton. If Walton carries a gene with two different alleles, the one
which is passed to Phantom has a 50% probability of being passed to Cedric.
There is also a 50% probability that the Walton mare will receive the same allele
from Walton and a 50% probability of it being passed to Cedric. The probability
that Cedric will be homozygous for this allele is 0.5 x 0.5 x 0.5 = 0.125 or
12.5%. If Walton were the only common ancestor, the inbreeding coefficient for
Cedric would be 12.5%.
Simply put, Cedric's inbreeding coefficient is found by calculating ½ to the
power n, where n is the number of individuals from Cedric to the common ancestor
Walton and back to Cedric on the other side of the pedigree, less Cedric. This
makes n equal to Phantom  Walton  Walton mare, or 3. The calculation therefore
is (½)³ or (½ x ½ x ½), which equals one eighth or 12.5%.
In the equation quoted above n1 = 1 (Phantom) and n2 = 1 (Walton mare). Walton,
the common ancestor, is represented by 1. If Walton is also inbred, then Cedric's
inbreeding coefficient would be 12.5 x (1 plus the inbreeding coefficient of
Walton, the common ancestor). If the common ancestor is not inbred then Fa =
0, therefore this part of the equation can be ignored because (1+Fa) = 1.
If Cedric had more than one common ancestor then calculations
would be made for each and added together to give his inbreeding
coefficient.
On the face of it Wright's Equation works, however closer examination reveals inherent defects.
OMAR  GODOLPHIN ARABIAN  
Lath mare  LATH  GODOLPHIN ARABIAN  
In the above pedigree Omar is inbred to Godolphin Arabian (1 x 3), so the value for n in the equation equals Godolphin Arabian  Lath  Lath mare or 3. This gives an inbreeding coefficient of 12.5%, the same as that for Cedric. The problem is Omar is more closely inbred than Cedric. Cedric inherited 25% of his genes from Walton through Phantom and 25% of his genes from Walton through Walton mare, making a total of 50%, which when divided by four gives an inbreeding coefficient of 12.5%. Omar, on the other hand, inherited 50% of his genes from Godolphin Arabian as his sire and 12.5% of his genes from Godolphin Arabian through Lath mare, making a total of 62.5%, which when divided by four gives an inbreeding coefficient of 15.625%.
The value of n in Wright's Equation does not take into consideration the positions of the common ancestor in the pedigree.
If Cedric's grandsire Walton was inbred to A (2 x 2), Cedric's
inbreeding coefficient would be .125 x 1.125 = .140625 or 14.0625%.The increase
of 1.5625% represents the total influence of A which appears four times in the
fourth generation of the pedigree of Cedric. Cedric inherited 25% of his genes
from A, which when divided by four gives an inbreeding coefficient of 6.25%.
Cedric's inbreeding coefficient would therefore be 12.5% + 6.25% = 18.75%.
If Omar's sire Godolphin Arabian was inbred to B (2 x 2), Omar's inbreeding
coefficient would also be .125 x 1.125 = .140625 or 14.0625%. The increase of
1.5625% represents the total influence of B which appears twice in the third
generation and twice in the fifth generation of the pedigree of Omar. Omar inherited
25% of his genes from B in the third generation and 6.25% of his genes from
B in the fifth generation, making a total of 31.25%, which when divided by four
gives an inbreeding coefficient of 7.8125%. Omar's inbreeding coefficient would
therefore be 15.625% + 7.8125% = 23.4375%.
Multiplying an inbreeding coefficient by one plus the inbreeding coefficient of a common ancestor severely underestimates the total amount of inbreeding in a pedigree.
W E Jones in Genetics of the Horse makes the following statements concerning Wright's Equation:Page 189  "To determine if there is any inbreeding, one observes the material on the sire's side of the pedigree to see if any animal is common with what is on the dam's side of the pedigree".
Page 189  "The amount of inbreeding is usually expressed in a percentage, which can be considered to be an estimate of the percentage of the total genes that have been put in the homozygous state. This estimate is always less than the actual because our records are never extensive enough to show all of the relationships that ever existed".
Page 190  "The equation for calculating the coefficent of inbreeding as proposed by Wright may look somewhat complicated to one without much background in mathematics. The coefficient of inbreeding is a fraction which when multiplied by 100 gives the percentage of inbreeding. The formula is based on the principle that the inbreeding of an individual is one half the relationship of its sire and dam".
In fact, an inbreeding coefficient calculated using Wright's Equation is neither an estimation of the number of genes put into the homozygous state nor an estimation of the percentage of inbreeding. It is merely the probability that identical alleles will be inherited from ancestors common to both sire and dam.
Wright's Equation considers duplicated ancestors only if they are common to both sire and dam, but if the inbreeding of an individual is one half the relationship of its sire and dam, then duplicated ancestors wholly contained within the pedigrees of either the sire or the dam should also be considered because ultimately they will trace to ancestors common to both sire and dam. The following pedigree is an example:
HIGH BIRD 1933 
HIGH TIME 1916 
ULTIMUS 1906 
COMMANDO 1898 
DOMINO  HIMYAR 
Mannie Gray  
Emma C  DAREBIN  
Guenn  
Running Stream 1898 
DOMINO  HIMYAR  
Mannie Gray  
Dancing Water  ISONOMY  
Pretty Dance  
Noonday 1898 
DOMINO 1891 
HIMYAR  ALARM  
Hira  
Mannie Gray  ENQUIRER  
Lizzie G  
Sundown 1887 
SPRINGFIELD  ST ALBANS  
Viridis  
Sunshine  THORMANBY  
Sunbeam  
Billie Dove 1922 
ATHELING 1913 
DESMOND 1896 
ST SIMON  GALOPIN  
St Angela  
L'Abesse de Jouarre  TRAPPIST  
Festive  
Wood Daisy 1906 
CYLLENE  BONA VISTA  
Arcadia  
Mountain Daisy  AYRSHIRE  
Light of Other Days  
Polistena 1912 
POLYMELUS 1902 
CYLLENE  BONA VISTA  
Arcadia  
Maid Marian  HAMPTON  
Quiver  
Imola 1901 
ST HILAIRE  ST SIMON  
Distant Shore  
Yola  BONA VISTA  
Doralice 
HIGH BIRD has no ancestors in the first five generations which are common to both sire and dam.
The sire HIGH TIME is inbred to DOMINO (3 x 3) x 2
The paternal grandsire ULTIMUS is inbred to DOMINO 2 x 2
The dam Billie Dove is inbred to CYLLENE 3 x 3, ST SIMON 3 x 4 and BONA VISTA
4 x (4 x 4)
The maternal grandam Polistena is inbred to BONA VISTA 3 x 3
The following inbreeding coefficients are produced by Wright's Equation using only the information contained in this five generation pedigree:
HIGH BIRD = 0% HIGH TIME = 12.5% ULTIMUS = 12.5% Billie Dove = 6.25% Polistena = 3.125%
The inbreeding coefficient of 0% for HIGH BIRD produced by Wright's Equation is impossible. If his pedigree is extended to nine generations the following ancestors are common to both sire and dam:
Banter (9 x 9 x 9 x 9 x 9) x (9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9)
BAY MIDDLETON (9 x 9 x 8 x 7) x (8 x 9 x 9)
BIRDCATCHER (8 x 9 x 9 x 9 x 8 x 7) x (8 x 9 x 9 x 9)
CAMEL (9 x 9 x 9 x 9 x 9 x 9) x (9 x 9 x 9 x 9 x 8 x 9 x 9)
CATTON 9 x 9
Cerberus mare (9 x 9) x 9
Decoy (9 x 8) x 8
DONCASTER 6 x (7 x 7 x 7)
ECONOMIST 9 x (8 x 9)
GLENCOE (9 x 9 x 9 x 9 x 9 x 9 x 9 x 8 x 9 x 9 x 8) x (8 x 9)
Guiccioli (9 x 9 x 9 x 8 x 9 x 8) x 9
ISONOMY 5 x (6 x 6)
KING TOM 8 x (6 x 8 x 8 x 7 x 8)
LANERCOST (9 x 9 x 8) x (9 x 8)
LOTTERY 8 x 9
MELBOURNE (7 x 9) x (9 x 8 x 8 x 9)
MULEY (9 x 9 x 8) x (9 x 9)
ORLANDO (8 x 8 x 9 x 7 x 7) x (9 x 9 x 8)
PALMYRA 7 x (9 x 9)
PANTALOON (9 x 9 x 9 x 9 x 8 x 8 x 7) x (9 x 9 x 9 x 8 x 9 x 9 x 9 x 9)
Pasquinade (9 x 8) x 9
Phryne 7 x 9
Pocahontas (9 x 9 x 9 x 8 x 8 x 8 x 7) x (7 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9
x 8 x 9 x 9)
Rebecca 7 x 9
RIFLEMAN 9 x 8
SCOTTISH CHIEF 7 x 6
SIR HERCULES (9 x 9 x 9 x 8 x 9 x 8) x 9
STOCKWELL (8 x 8 x 7 x 7 x 7 x 6) x (8 x 8 x 9 x 8 x 8 x 8 x 8)
SULTAN (9 x 9 x 9 x 8 x 8) x (9 x 9)
TAURUS2 8 x 9
THE BARON (9 x 9 x 8 x 8 x 8 x 7) x (9 x 9 x 9 x 9 x 9 x 9 x 9)
THE FLYING DUTCHMAN 9 x (7 x 9 x 8)
THORMANBY (8 x 5) x (8 x 8 x 8 x 8 x 8)
TOUCHSTONE (9 x 8 x 9 x 9 x 9 x 9 x 8 x 8 x 8) x (8 x 8 x 9 x 9 x 9 x 9 x 8
x 9 x 8 x 9 x 8)
VELOCIPEDE 9 x 9
WHALEBONE (9 x 9) x 9
WHISKER (9 x 8) x 9
The method I am proposing produces the following inbreeding coefficients using only the information contained in this five generation pedigree:
HIGH BIRD = 18.75% HIGH TIME = 18.75% ULTIMUS = 12.5% Billie Dove = 18.75% Polistena = 6.25%
CEDRIC  PHANTOM (12.5%)  WALTON (6.25%) 
Walton mare (12.5%)  WALTON (6.25%)  
Cedric's inbreeding coefficient of 12.5% is calculated for an ancestor which appears twice in the second generation of his pedigree, therefore each appearance in the second generation is worth 6.25%. The total for each generation is 25%, which is the probability of an allele being passed from Walton to Phantom to Cedric. Since the total for each generation is 25, the value for each position in the pedigree can be summarised as follows:
1st Generation = 12.5
2nd Generation= 6.25
3rd Generation = 3.125
4th Generation = 1.5625
5th Generation = .78125
There are 32 ancestors in the fifth generation, each contributing .78125 of the whole. Since at least two positions in the pedigree are required for inbreeding and the maximum of 25 cannot be reached, that leaves 30 possible basic inbreeding coefficients within five generations. Each basic coefficient, which is a multiple of .78125, represents the number of ancestors in the 5th generation that are contained within the pedigree of the common ancestor. It should be noted that there are many more combinations of inbreedings, but there are only 30 possible basic inbreeding coefficients.
Inbreeding notations

Basic coefficients

1 x 2 x 3 x 4 x 5  24.21875 
1 x 2 x 3 x 4  23.4375 
1 x 2 x 3 x 5  22.65625 
1 x 2 x 3  21.875 
1 x 2 x 4 x 5  21.09375 
1 x 2 x 4  20.3125 
1 x 2 x 5  19.53125 
1 x 2  18.75 
1 x 3 x 4 x 5  17.96875 
1 x 3 x 4  17.1875 
1 x 3 x 5  16.40625 
1 x 3  15.625 
1 x 4 x 5  14.84375 
1 x 4  14.0625 
1 x 5  13.28125 
2 x 2  12.5 
2 x 3 x 4 x 5  11.71875 
2 x 3 x 4  10.9375 
2 x 3 x 5  10.15625 
2 x 3  9.375 
2 x 4 x 5  8.59375 
2 x 4  7.8125 
2 x 5  7.03125 
3 x 3  6.25 
3 x 4 x 5  5.46875 
3 x 4  4.6875 
3 x 5  3.90625 
4 x 4  3.125 
4 x 5  2.34375 
5 x 5  1.5625 
The inbreeding coefficients have to be modified if the common ancestor is also inbred. The movement of an ancestor back one generation in a pedigree halves its influence, therefore the inbreeding coefficient of an inbred ancestor has to be halved to compensate. The value of an inbreeding coefficient for each generation is calculated as follows:
Generation 0  Inbreeding Coefficient
Generation 1  Divide by 2
Generation 2  Divide by 4
Generation 3  Divide by 8
Generation 4  Divide by 16
Generation 5  Divide by 32
0  1  2  3  4 
D  A  B  
C  B  
E  A  B  
C  B  
In the above pedigree D is inbred to A (1 x 2).
The inbreeding coefficient for D is therefore 12.5 + 6.25 = 18.75.
A, however, is inbred to B (1 x 2)
and appears in two different generations. The inbreeding coefficient for A
is also 18.75.
The movement of an ancestor back one generation in a pedigree halves its influence,
so the modified coefficient for A in generation 1 will be 9.375
and in generation 2 it will be 4.6875. The influence of A in
the pedigree is therefore 9.375 + 4.6875 = 14.0625. The inbreeding coefficient
for D will be 18.75 + 14.0625 = 32.8125.
In the above pedigree B appears once in generation
2, twice in generation 3 and once in generation 4. The values for these positions
in the pedigree are 6.25, 3.125, 3.125 and 1.5625. The addition of these figures
gives 14.0625, which is the influence of A in the pedigree.
This pedigree contains new and conjectural
information of a radical nature  See
CONFUSED PEDIGREES AND MISTAKEN IDENTITIES
DARCY'S YELLOW TURK, DARCY'S WHITE TURK AND HELMSLEY
TURK
GARDINER MARE, HUTTON'S SPOT AND ALCOCK'S ARABIAN
LAYTON GREY BARB, ROCKWOOD, TAFFOLET BARB AND TREGONWELL'S
BARB MARE
HIGHLANDER, MERLIN AND WOODCOCK
BLACKATOP, OLD MONTAGUE MARE, PULLEINE'S CHESNUT
ARABIAN AND WHITESHIRT MARE
SNAKE, CONEYSKINS, LISTER'S TURK AND BYERLEY'S
TURK
Old Bald Peg = FAIRFAX'S MOROCCO BARB  [HELMSLEY TURK]   >  <    Leedes Bald Peg  Lawson's Barb Mare = DARCY'S YELLOW TURK = Old Morocco Mare [Young Bald Peg]  [Dodsworth's dam]  [DODSWORTH]     [Merlin's grandam]  [MERLIN'S GRANDSIRE]                      DARCY'S WHITE TURK = Pierson's Bay mare Barb Mare     [DARCY'S DIAMOND]       [PLACE'S WHITE TURK]       [BURNET'S WHITE BARB]       [PLACE'S WHITE TRUGUNWELL TURK]               >  <>  <>  <      \ /     Darcy's Grey Royal mare = BRIMMER SPANKER    [Lonsdale Arabian Mare]                 \ /     >  <>  <          >  <               \ /    \ / Yellow Bald Peg mare = HAUTBOY Arlington Barb Mare  BYERLEY'S TURK = Charming Jenny [Chesnut Peg]  [ROCKWOOD] [Layton Barb Mare]  [LISTER'S TURK]  [Wyvill's Roan Mare]   [PULLEINE'S WHITE TURK]   [RUTLAND BLACKLEGS]    [PULLEINE'S OLD ARABIAN]   1678                \ /    Bay Peg mare GREY HAUTBOY = Darcy's Pet Mare PELHAM'S JIGG BROTHER TO SNAKE by Leedes  [LAYTON GREY BARB]  [Old Grey Royal] [LISTER'S SNAKE]  Arabian   [Tregonwell Barb mare]      [Darcy's Oldest Royal Mare]      [Clubfoot]        >  <          BLUE CAP   CLUMSEY Grey Wilkes  CURWEN'S BAY BARB mare     [Old Wilkes]                      \ / \ /   mare CHAMPION FOX SON OF JIGG = mare   by Harpham Arabian  1714 [SMITH'S SON OF SNAKE]     1707         \ /    mare  HENEAGE'S JIGG          \ / \ / BOLTON GOLIAH = mare 1730       HUNT'S JIGG   1741    \ / JIGGOFJIGGS 1745
The inbreeding coefficient for JiggofJiggs is calculated as follows:
0  1  2  3  4  5 
JIGGOFJIGGS 28.125 17.236328125 12.109375 (57.470703125) 
HUNT'S JIGG 03.125 08.056640625 06.0546875 (17.236328125) 
BOLTON GOLIAH 02.34375 04.6875 01.025390625 (08.056640625) 
FOX 02.05078125 02.05078125 00.5859375 (04.6875) 
CLUMSEY 01.611328125 00.146484375 00.29296875 (02.05078125) 
GREY HAUTBOY (00.146484375) 
Darcy's Pet Mare (00.29296875) 

Bay Peg (00.5859375) 
LEEDES ARABIAN  
Yellow Bald Peg 

Champion mare (01.025390625) 
CHAMPION (01.025390625) 
HARPHAM ARABIAN  
Hautboy mare 00.732421875 00.146484375 00.146484375 (01.025390625) 

Blue Cap mare  BLUE CAP  
Heneage's Jigg mare (06.0546875) 
HENEAGE'S JIGG  SON OF JIGG  PELHAM'S JIGG  
Grey Wilkes  
Curwen's Bay Barb mare 
CURWEN'S BAY BARB  
Brother to Snake mare  BROTHER TO SNAKE  LISTER'S TURK  
Charming Jenny  
Heneage's Jigg mare 06.25 04.6875 01.171875 (12.109375) 
HENEAGE'S JIGG (04.6875) 
SON OF JIGG 02.05078125 00.5859375 02.05078125 (04.6875) 
PELHAM'S JIGG (00.5859375) 
BYERLEY'S TURK  
Charming Jenny (00.5859375) 

Grey Wilkes 01.611328125 00.146484375 00.29296875 (02.05078125) 
GREY HAUTBOY (00.146484375) 

Darcy's Pet Mare (00.29296875) 

Curwen's Bay Barb mare 
CURWEN'S BAY BARB  
Brother to Snake mare (01.171875) 
BROTHER TO SNAKE (01.171875) 
LISTER'S TURK  
Charming Jenny (01.171875) 
SPANKER  
Old Morocco Mare  
0  1  2  3  4  5 
Details of each specific inbreeding:
JIGGOFJIGGS inbred to Heneage's Jigg mare 2 x 1 = 18.75
JIGGOFJIGGS inbred to BYERLEY'S TURK=LISTER'S TURK 5 x (5 x 4) = 3.125
JIGGOFJIGGS inbred to Charming Jenny 5 x (5 x 4) = 3.125
JIGGOFJIGGS inbred to Darcy's Pet Mare 5 x 5 = 1.5625
JIGGOFJIGGS inbred to GREY HAUTBOY 5 x 5 = 1.5625
Total SIC for JIGGOFJIGGS = 28.125
HUNT'S JIGG inbred to Darcy's Pet Mare 4 x 5 = 2.34375
HUNT'S JIGG inbred to GREY HAUTBOY 4 x 5 = 2.34375
HUNT'S JIGG inbred to SPANKER 5 x 5 = 1.5625
Total SIC for HUNT'S JIGG = 6.25
Heneage's Jigg mare inbred to BYERLEY'S TURK=LISTER'S TURK 4 x 3 = 4.6875
Heneage's Jigg mare inbred to Charming Jenny 4 x 3 = 4.6875
Heneage's Jigg mare inbred to Old Morocco Mare 5 x (5 x 4) = 3.125
Total SIC for Heneage's Jigg mare = 12.5
BOLTON GOLIAH inbred to HAUTBOY 4 x 4 = 3.125
BOLTON GOLIAH inbred to Darcy's Grey Royal=Lonsdale Arabian Mare (5 x 4) x 5
= 3.125
BOLTON GOLIAH inbred to DARCY'S WHITE TURK (5 x 4) x 5 = 3.125
Total SIC for BOLTON GOLIAH = 9.375
FOX inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (5 x 4 x 5) x (5 x 4) = 5.46875
FOX inbred to DARCY'S YELLOW TURK (5 x 4) x 4 = 3.90625
FOX inbred to Old Morocco Mare (5 x 4) x 4 = 3.90625
FOX inbred to Old Bald Peg 5 x (5 x 4) = 3.125
Total SIC for FOX = 16.40625
SON OF JIGG inbred to Old Morocco Mare (4 x 3) x (5 x 4) = 7.03125
SON OF JIGG inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (5 x 4) x (5 x 4
x 5) = 5.46875
SON OF JIGG inbred to DARCY'S YELLOW TURK 4 x (5 x 4) = 3.90625
Total SIC for SON OF JIGG = 16.40625
CLUMSEY inbred to Darcy's Grey Royal=Lonsdale Arabian Mare 3 x 2 = 9.375
CLUMSEY inbred to DARCY'S WHITE TURK 3 x 2 = 9.375
CLUMSEY inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (4 x 5) x (3 x 4) = 7.03125
Total SIC for CLUMSEY = 25.78125
Grey Wilkes inbred to Darcy's Grey Royal=Lonsdale Arabian Mare 3 x 2 = 9.375
Grey Wilkes inbred to DARCY'S WHITE TURK 3 x 2 = 9.375
Grey Wilkes inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (4 x 5) x (3 x 4)
= 7.03125
Total SIC for Grey Wilkes = 25.78125
Charming Jenny inbred to Old Morocco Mare 2 x 1 = 18.75
Total SIC for Charming Jenny = 18.75
Darcy's Pet Mare inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK 2 x 3 = 9.375
Total SIC for Darcy's Pet Mare = 9.375
Yellow Bald Peg inbred to FAIRFAX'S MOROCCO BARB 3 x 2 = 9.375
Yellow Bald Peg inbred to Old Bald Peg 3 x 2 = 9.375
Total SIC for Yellow Bald Peg = 18.75
Hautboy mare inbred to DARCY'S DIAMOND=DARCY'S WHITE TURK 2 x 3 = 9.375
Hautboy mare inbred to DARCY'S YELLOW TURK=MERLIN'S GRANDSIRE 3 x (3 x 4) =
7.8125
Hautboy mare inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (3 x 4) x 4 = 6.25
Total SIC for Hautboy mare = 23.4375
HAUTBOY inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK 2 x 3 = 9.375
Total SIC for HAUTBOY = 9.375
Brimmer mare inbred to DARCY'S YELLOW TURK=MERLIN'S GRANDSIRE 2 x 3 = 9.375
Total SIC for Brimmer mare = 9.375
METHOD ONE
Working forwards through the pedigree
6  HAUTBOY = modified SIC of 0.146484375 
6  Brimmer mare = modified SIC of 0.146484375 
5  Darcy's Pet Mare = modified SIC of 0.29296875 
5  Yellow Bald Peg = modified SIC of 0.5859375 
5  Hautboy mare = modified SIC of 0.732421875 + modified SIC for HAUTBOY in generation 6 of 0.146484375 + modified SIC for Brimmer mare in generation 6 of 0.146484375 = 1.025390625 
5  Charming Jenny = half the modified SIC in generation 4 of 1.171875 = 0.5859375 
4  CLUMSEY = modified SIC of 01.611328125 + modified SIC for HAUTBOY in generation 6 of 0.146484375 + modified SIC for Darcy's Pet Mare in generation 5 of 0.29296875 = 02.05078125 
4  Grey Wilkes = modified SIC of 01.611328125 + modified SIC for HAUTBOY in generation 6 of 0.146484375 + modified SIC for Darcy's Pet Mare in generation 5 of 0.29296875 = 02.05078125 
4  Charming Jenny = modified SIC of 1.171875 
3  FOX = modified SIC of 02.05078125 + modified CIC for CLUMSEY in generation 4 of 02.05078125 + modified SIC for Yellow Bald Peg in generation 5 of 0.5859375 = 04.6875 
3  SON OF JIGG = modified SIC of 02.05078125 + modified SIC for Charming Jenny in generation 5 of 0.5859375 + modified CIC for Grey Wilkes in generation 4 of 02.05078125 = 04.6875 
2  BOLTON GOLIAH = modified SIC of 02.34375 + modified CIC for FOX in generation 3 of 04.6875 + modified CIC for Hautboy mare in generation 5 of 1.025390625 = 08.056640625 
2  Heneage's Jigg mare = half the modified CIC in generation 1 of 12.109375 = 06.0546875 
1  HUNT'S JIGG = modified SIC of 03.125 + modified CIC for BOLTON GOLIAH in generation 2 of 08.056640625 + modified CIC for Heneage's Jigg mare in generation 2 of 06.0546875 = 17.236328125 
1  Heneage's Jigg mare = modified SIC of 06.25 + modified CIC for SON OF JIGG in generation 3 of 04.6875 + modified SIC for Charming Jenny in generation 4 of 01.171875 = 12.109375 
0  JIGGOFJIGGS = SIC of 28.125 + modified CIC for HUNT'S JIGG in generation 1 of 17.236328125 + modified CIC for Heneage's Jigg mare in generation 1 of 12.109375 = 57.470703125 
METHOD TWO
Working backwards through the pedigree
Inbred Horse  SIC  Modified SIC  
0  JIGGOFJIGGS  28.125  28.125  
1  HUNT'S JIGG  6.25  ÷ 2  03.125 
1  Heneage's Jigg mare  12.5  ÷ 2  06.25 
2  BOLTON GOLIAH  9.375  ÷ 4  02.34375 
2  Heneage's Jigg mare  12.5  ÷ 4  03.125 
3  FOX  16.40625  ÷ 8  02.05078125 
3  SON OF JIGG  16.40625  ÷ 8  02.05078125 
4  CLUMSEY  25.78125  ÷ 16  01.611328125 
4  SON OF JIGG  16.40625  ÷ 16  01.025390625 
4  Grey Wilkes  25.78125  ÷ 16  01.611328125 
4  Charming Jenny  18.75  ÷ 16  01.171875 
5  Darcy's Pet Mare  9.375  ÷ 32  00.29296875 
5  Yellow Bald Peg  18.75  ÷ 32  00.5859375 
5  Hautboy mare  23.4375  ÷ 32  00.732421875 
5  Grey Wilkes  25.78125  ÷ 32  00.8056640625 
5  Charming Jenny  18.75  ÷ 32  00.5859375 
5  Charming Jenny  18.75  ÷ 32  00.5859375 
5  Darcy's Pet Mare  9.375  ÷ 32  00.29296875 
6  HAUTBOY  9.375  ÷ 64  00.146484375 
6  HAUTBOY  9.375  ÷ 64  00.146484375 
6  Brimmer mare  9.375  ÷ 64  00.146484375 
6  Charming Jenny  18.75  ÷ 64  00.29296875 
6  Darcy's Pet Mare  9.375  ÷ 64  00.146484375 
6  HAUTBOY  9.375  ÷ 64  00.146484375 
7  HAUTBOY  9.375  ÷ 128  00.0732421875 
Total CIC for JIGGOFJIGGS  57.470703125 
METHOD THREE
Register of Inbreeding Coefficients
The figure of 57.470703125, arrived at by both Method One and Method Two above, is the cumulative inbreeding coefficent for JiggofJiggs and includes all the inbreeding in his pedigree back as far as records allow. The standard inbreeding coefficient for JiggofJiggs of 28.125 is less than half of this total, so it is clear that the inbreeding carried forward from previous generations is still valid but the methods of calculation are cumbersome and time consuming.
It is proposed that a Register of Inbreeding Coefficients of all stallions and mares be compiled, so that any Thoroughbred's cumulative inbreeding coefficient may be found by first calculating the standard inbreeding coefficient and adding to it half the value of each of the parents cumulative inbreeding coefficients as taken from the register.
Using this method and beginning with the earliest inbred ancestor, the cumulative inbreeding coefficient for JiggofJiggs would be calculated as follows:
Brimmer mare (9.375) 
BRIMMER (0) 
DARCY'S YELLOW TURK *  
Darcy's Diamond mare (0) 

Pierson's Bay Mare  MERLIN'S GRANDSIRE *  
Brimmer mare inbred to DARCY'S YELLOW TURK=MERLIN'S
GRANDSIRE 2 x 3 = 9.375
Total SIC and CIC for Brimmer mare = 9.375
HAUTBOY (09.375) 
DARCY'S WHITE TURK (0) 
HELMSLEY TURK *  
Lonsdale Arabian Mare (0) 

Old Morocco Mare  FAIRFAX'S MOROCCO BARB *  
HAUTBOY inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY
TURK 2 x 3 = 9.375
Total SIC and CIC for HAUTBOY = 9.375
Hautboy mare (32.8125) 
HAUTBOY (09.375) 
DARCY'S WHITE TURK *  HELMSLEY TURK **  
Lonsdale Arabian Mare  DARCY'S YELLOW TURK *** 

Old Morocco Mare  FAIRFAX'S MOROCCO BARB **  
Brimmer mare (09.375) 
BRIMMER  DARCY'S YELLOW TURK *** 

Darcy's Diamond mare  DARCY'S DIAMOND *  HELMSLEY TURK **  
Pierson's Bay Mare  MERLIN'S GRANDSIRE***  
Hautboy mare inbred to DARCY'S DIAMOND=DARCY'S
WHITE TURK 2 x 3 = 9.375
Hautboy mare inbred to DARCY'S YELLOW TURK=MERLIN'S GRANDSIRE 3 x (3 x 4) =
7.8125
Hautboy mare inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (3 x 4) x 4 = 6.25
Total SIC for Hautboy mare = 23.4375
Half CIC for HAUTBOY = 4.6875
Half CIC for Brimmer mare = 4.6875
Total CIC for Hautboy mare = 32.8125
Yellow Bald Peg (18.75) 
SPANKER (0) 

Old Morocco Mare  FAIRFAX'S MOROCCO BARB *  
Old Bald Peg **  
Leedes Bald Peg (0) 
FAIRFAX'S MOROCCO BARB *  
Old Bald Peg **  
Yellow Bald Peg inbred to FAIRFAX'S MOROCCO BARB 3 x 2 = 9.375
Yellow Bald Peg inbred to Old Bald Peg 3 x 2 = 9.375
Total SIC and CIC for Yellow Bald Peg = 18.75
Darcy's Pet Mare (09.375) 
DARCY'S WHITE TURK (0) 
HELMSLEY TURK *  
Darcy's Grey Royal (0) 

Old Morocco Mare  FAIRFAX'S MOROCCO BARB *  
Darcy's Pet Mare inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY
TURK 2 x 3 = 9.375
Total SIC and CIC for Darcy's Pet Mare = 9.375
Charming Jenny (18.75) 
SPANKER (0) 

Old Morocco Mare *  
Old Morocco Mare * (0) 

Charming Jenny inbred to Old Morocco Mare 2 x 1 = 18.75
Total SIC and CIC for Charming Jenny = 18.75
Grey Wilkes (32.8125) 
GREY HAUTBOY (04.6875) 
HAUTBOY (09.375) 
DARCY'S WHITE TURK *  HELMSLEY TURK ***  
Lonsdale Arabian Mare **  
Old Morocco Mare  FAIRFAX'S MOROCCO BARB ***  
Darcy's Pet Mare (09.375) 
DARCY'S WHITE TURK *  HELMSLEY TURK ***  
Darcy's Grey Royal **  
Old Morocco Mare  FAIRFAX'S MOROCCO BARB ***  
Grey Wilkes inbred to Darcy's Grey Royal=Lonsdale Arabian Mare
3 x 2 = 9.375
Grey Wilkes inbred to DARCY'S WHITE TURK 3 x 2 = 9.375
Grey Wilkes inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (4 x 5) x (3 x 4)
= 7.03125
Total SIC for Grey Wilkes = 25.78125
Half CIC for GREY HAUTBOY = 2.34375
Half CIC for Darcy's Pet Mare = 4.6875
Total CIC for Grey Wilkes = 32.8125
CLUMSEY (32.8125) 
GREY HAUTBOY (04.6875) 
HAUTBOY (09.375) 
DARCY'S WHITE TURK *  HELMSLEY TURK ***  
Lonsdale Arabian Mare **  
Old Morocco Mare  FAIRFAX'S MOROCCO BARB ***  
Darcy's Pet Mare (09.375) 
DARCY'S WHITE TURK *  HELMSLEY TURK ***  
Darcy's Grey Royal **  
Old Morocco Mare  FAIRFAX'S MOROCCO BARB ***  
CLUMSEY inbred to Darcy's Grey Royal=Lonsdale Arabian Mare 3
x 2 = 9.375
CLUMSEY inbred to DARCY'S WHITE TURK 3 x 2 = 9.375
CLUMSEY inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (4 x 5) x (3 x 4) = 7.03125
Total SIC for CLUMSEY = 25.78125
Half CIC for GREY HAUTBOY = 2.34375
Half CIC for Darcy's Pet Mare = 4.6875
Total CIC for CLUMSEY = 32.8125
SON OF JIGG (37.5) 
PELHAM'S JIGG (9.375) 

Charming Jenny (18.75) 
SPANKER  DARCY'S YELLOW TURK ** 

Old Morocco Mare *  FAIRFAX'S MOROCCO BARB ***  
Old Morocco Mare *  FAIRFAX'S MOROCCO BARB ***  
Grey Wilkes (32.8125) 
GREY HAUTBOY  HAUTBOY  DARCY'S WHITE TURK  HELMSLEY TURK ***  
Lonsdale Arabian Mare  DARCY'S YELLOW TURK ** 

Old Morocco Mare *  
Darcy's Pet Mare  DARCY'S WHITE TURK  HELMSLEY TURK ***  
Darcy's Grey Royal  DARCY'S YELLOW TURK ** 

Old Morocco Mare *  FAIRFAX'S MOROCCO BARB ***  
SON OF JIGG inbred to Old Morocco Mare (4 x 3) x (5 x 4) = 7.03125
SON OF JIGG inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (5 x 4) x (5 x 4
x 5) = 5.46875
SON OF JIGG inbred to DARCY'S YELLOW TURK 4 x (5 x 4) = 3.90625
Total SIC for SON OF JIGG = 16.40625
Half CIC for PELHAM'S JIGG = 4.6875
Half CIC for Grey Wilkes = 16.40625
Total CIC for SON OF JIGG = 37.5
FOX (37.5) 
CLUMSEY (32.8125) 
GREY HAUTBOY  HAUTBOY  DARCY'S WHITE TURK  HELMSLEY TURK * 
Lonsdale Arabian Mare  DARCY'S YELLOW TURK ** 

Old Morocco Mare ***  
Darcy's Pet Mare  DARCY'S WHITE TURK  HELMSLEY TURK *  
Darcy's Grey Royal  DARCY'S YELLOW TURK ** 

Old Morocco Mare ***  FAIRFAX'S MOROCCO BARB *  
Old Bald Peg ****  
Bay Peg (9.375) 

Yellow Bald Peg (18.75) 
SPANKER  DARCY'S YELLOW TURK ** 

Old Morocco Mare ***  FAIRFAX'S MOROCCO BARB *  
Old Bald Peg ****  
Leedes Bald Peg  FAIRFAX'S MOROCCO BARB *  
Old Bald Peg ****  
FOX inbred to FAIRFAX'S MOROCCO BARB=HELMSLEY TURK (5 x 4 x
5) x (5 x 4) = 5.46875
FOX inbred to DARCY'S YELLOW TURK (5 x 4) x 4 = 3.90625
FOX inbred to Old Morocco Mare (5 x 4) x 4 = 3.90625
FOX inbred to Old Bald Peg 5 x (5 x 4) = 3.125
Total SIC for FOX = 16.40625
Half CIC for CLUMSEY = 16.40625
Half CIC for Bay Peg = 4.6875
Total CIC for FOX = 37.5
BOLTON GOLIAH (32.2265625) 
FOX (37.5) 
CLUMSEY  GREY HAUTBOY  HAUTBOY *  DARCY'S WHITE TURK ** 
Lonsdale Arabian Mare ***  
Darcy's Pet Mare  DARCY'S WHITE TURK **  
Darcy's Grey Royal ***  
Champion mare (8.203125) 
CHAMPION (16.40625) 

Hautboy mare (32.8125) 
HAUTBOY *  DARCY'S WHITE TURK **  
Lonsdale Arabian Mare ***  
BOLTON GOLIAH inbred to Darcy's Grey Royal=Lonsdale Arabian
Mare (5 x 4) x 5 = 3.125
BOLTON GOLIAH inbred to DARCY'S WHITE TURK (5 x 4) x 5 = 3.125
BOLTON GOLIAH inbred to HAUTBOY 4 x 4 = 3.125
Total SIC for BOLTON GOLIAH = 9.375
Half CIC for FOX = 18.75
Half CIC for Champion mare = 4.1015625
Total CIC for BOLTON GOLIAH = 32.2265625
Heneage's Jigg mare (24.21875) 
HENEAGE'S JIGG (18.75) 
SON OF JIGG (37.5) 
PELHAM'S JIGG  BYERLEY'S TURK *  
Charming Jenny **  
Old Morocco Mare ***  
Brother to Snake mare (4.6875) 
BROTHER TO SNAKE (9.375) 
LISTER'S TURK *  
Charming Jenny ** (18.75) 
SPANKER  
Old Morocco Mare ***  
Old Morocco Mare ***  
Heneage's Jigg mare inbred to BYERLEY'S TURK=LISTER'S TURK 4
x 3 = 4.6875
Heneage's Jigg mare inbred to Charming Jenny 4 x 3 = 4.6875
Heneage's Jigg mare inbred to Old Morocco Mare 5 x (5 x 4) = 3.125
Total SIC for Heneage's Jigg mare = 12.5
Half CIC for HENEAGE'S JIGG = 9.375
Half CIC for Brother to Snake mare = 2.34375
Total CIC for Heneage's Jigg mare = 24.21875
HUNT'S JIGG (34.47265625) 
BOLTON GOLIAH (32.2265625) 
FOX  CLUMSEY  GREY HAUTBOY *  
Darcy's Pet Mare **  
Bay Peg  
Yellow Bald Peg  SPANKER ***  
Heneage's Jigg mare (24.21875) 
HENEAGE'S JIGG  SON OF JIGG  
Grey Wilkes  GREY HAUTBOY *  
Darcy's Pet Mare **  
Brother to Snake mare  BROTHER TO SNAKE  
Charming Jenny  SPANKER ***  
HUNT'S JIGG inbred to Darcy's Pet Mare 4 x 5 = 2.34375
HUNT'S JIGG inbred to GREY HAUTBOY 4 x 5 = 2.34375
HUNT'S JIGG inbred to SPANKER 5 x 5 = 1.5625
Total SIC for HUNT'S JIGG = 6.25
Half CIC for BOLTON GOLIAH = 16.11328125
Half CIC for Heneage's Jigg mare = 12.109375
Total CIC for HUNT'S JIGG = 34.47265625
JIGGOFJIGGS (57.470703125) 
HUNT'S JIGG (34.47265625) 
BOLTON GOLIAH  FOX  CLUMSEY  GREY HAUTBOY ** 
Darcy's Pet Mare ***  
Heneage's Jigg mare *  
Brother to Snake mare  BROTHER TO SNAKE  LISTER'S TURK ****  
Charming Jenny *****  
Heneage's Jigg mare * (24.21875) 
HENEAGE'S JIGG  SON OF JIGG  PELHAM'S JIGG  BYERLEY'S TURK ****  
Charming Jenny *****  
Grey Wilkes  GREY HAUTBOY **  
Darcy's Pet Mare ***  
Brother to Snake mare  BROTHER TO SNAKE  LISTER'S TURK ****  
Charming Jenny *****  
JIGGOFJIGGS inbred to Heneage's Jigg mare 2 x
1 = 18.75
JIGGOFJIGGS inbred to BYERLEY'S TURK=LISTER'S TURK 5 x (5 x 4) = 3.125
JIGGOFJIGGS inbred to Charming Jenny 5 x (5 x 4) = 3.125
JIGGOFJIGGS inbred to Darcy's Pet Mare 5 x 5 = 1.5625
JIGGOFJIGGS inbred to GREY HAUTBOY 5 x 5 = 1.5625
Total SIC for JIGGOFJIGGS = 28.125
Half CIC for HUNT'S JIGG = 17.236328125
Half CIC for Heneage's Jigg mare = 12.109375
Total CIC for JIGGOFJIGGS = 57.470703125
It is proposed that Hardiman's Coefficient always be rounded to two decimal places. The following method is recommended:
1. Calculate the SIC in full and round to two decimal places.
2. Add together the parent's CIC's, divide by two, add to the SIC and then round to two decimal places.
Using this method and beginning with the earliest inbred ancestor, the cumulative inbreeding coefficient for JiggofJiggs would be calculated as follows:
Brimmer mare
Total SIC = 9.375 = 9.38
Total CIC = 0 + 0 = 0 ÷ 2 = 0 + 9.38 = 9.38
HAUTBOY
Total SIC = 9.375 = 9.38
Total CIC = 0 + 0 = 0 ÷ 2 = 0 + 9.38 = 9.38
Hautboy mare
Total SIC = 23.4375 = 23.44
Total CIC = 9.38 + 9.38 = 18.76 ÷ 2 = 9.38 + 23.44 = 32.82
Yellow Bald Peg
Total SIC = 18.75
Total CIC = 0 + 0 = 0 ÷ 2 = 0 + 18.75 = 18.75
Darcy's Pet Mare
Total SIC = 9.375 = 9.38
Total CIC = 0 + 0 = 0 ÷ 2 = 0 + 9.38 = 9.38
Charming Jenny
Total SIC = 18.75
Total CIC = 0 + 0 = 0 ÷ 2 = 0 + 18.75 = 18.75
Grey Wilkes
Total SIC = 25.78125 = 25.78
Total CIC = 4.69 + 9.38 = 14.07 ÷ 2 = 7.035 + 25.78 = 32.815 = 32.82
CLUMSEY
Total SIC = 25.78125 = 25.78
Total CIC = 4.69 + 9.38 = 14.07 ÷ 2 = 7.035 + 25.78 = 32.815 = 32.82
SON OF JIGG
Total SIC = 16.40625 = 16.41
Total CIC = 9.38 + 32.82 = 42.20 ÷ 2 = 21.10 + 16.41 = 37.51
FOX
Total SIC = 16.40625 = 16.41
Total CIC = 32.82 + 9.38 = 42.20 ÷ 2 = 21.10 + 16.41 = 37.51
BOLTON GOLIAH
Total SIC = 9.375 = 9.38
Total CIC = 37.51 + 8.21 = 45.72 ÷ 2 = 22.86 + 9.38 = 32.24
Heneage's Jigg mare
Total SIC = 12.5
Total CIC = 18.76 + 4.69 = 23.45 ÷ 2 = 11.725 + 12.5 = 24.225 = 24.23
HUNT'S JIGG
Total SIC = 6.25
Total CIC = 32.24 + 24.23 = 56.47 ÷ 2 = 28.235 + 6.25 = 34.485 = 34.49
JIGGOFJIGGS
Total SIC = 28.125 = 28.13
Total CIC = 24.49 + 24.23 = 58.72 ÷ 2 = 29.36 + 28.13 = 57.49
The difference between 57.49 and 57.470703125 of less than 0.02 is negligible.