T-Model Fingerprint Calculator ©
Version 3.0
By Henry Templeman
Introduction
When a number of friction ridge formations in two fingerprint impressions are found to correspond in shape and position, the probability to find
even a very small amount of the most common occurring ridge formations that match is usually in the millions or billions to 1. As a result, a
small amount of highly discriminating corresponding friction ridge formations found in two fingerprint impressions can be defined such that the
reciprocal of the match probability exceeds the world fingerprint population many fold. Once the rarity of a small amount of corresponding ridge
formations is estimated, objective criteria can be used to report that with reasonable scientific certainty the amount is significant enough to
establish inference for source attribution to a particular individual.
Fingerprint ridge formation frequency is estimated by determining its frequency of occurrence (with refinement for ridge formations impacted by
diminishing area pattern force), the frequency of its position based on intervening ridge count to its nearest neighbor, qualitative metrics in the
form of reduction factors for reduced levels of ridge formation clarity and reliability, e.g., 100%, 75%, 50%, 25%) and for reduced levels of
quality of agreement, e.g., 100%, 75%, 50%, 25%, and application of the product rule, multiplying the frequencies and values together across all
ridge formations found in two impressions. The final product represents the significance or discrimination power of the aggregate (quantity and
quality) amount of matching ridge formations present in two fingerprint impressions.
To ensure a reasonable degree of scientific certainty has been attained regarding inference for source attribution, a threshold probability value (p)
is recommended for purposes of routine casework for crimes committed in the United States and based on a total United States population of 300
million (Note: The relevant population variable is not fixed and may be defined by the examiner for the case at hand).
The T-Model Fingerprint Calculator establishes source attribution to an individual if the Fingerprint Match Probability (FMP) of the fingerprint
profile from the latent satisfies the following condition:
FMP < 1 - (1-α) 1/N
where α = 0.00001, representing a confidence level of 99.999%, and, for example, if N = 66 billion, e.g., the number equal to the approximate
total number of fingerprint parts (22) per fingerprint (10) in the total human population of the United States (300,000,000) such that:
FMP < 1 – (.99999) 1/66,000,000,000
FMP < 1 - .00000000001515
FMP < 0.99999999998484
Therefore, if the fingerprint match probability is less than the probability for 1 out of the total number of parts per fingerprint in the relevant
fingerprint population for the case at hand, or in the above example, 1/66 billion, then the following statement can be reported where X and Y
represent known and unknown fingerprints, respectively:
“Fingerprint exemplar X is the source of fingerprint evidence Y to a reasonable degree of scientific certainty.”
The T-Model Fingerprint Calculator calculates the following values based on relevant fingerprint population for the case at hand and
the quantitative interpretation and qualitative assessment of matching fingerprint ridge features found in two fingerprint impressions in
order to infer positive fingerprint identification to a single source:
Likelihood Ratio
Likelihood Ratio is the aggregate weight for the fingerprint evidence based on information for the case at hand. The T-Model uses the product
rule to define the aggregate weight as a positive number for a given amount of matching ridge features found in two impressions based on the
relevant fingerprint population for the case at hand.
Fingerprint Match Probability
Fingerprint Match Probability is the chance that an arrangement of fingerprint ridge formations matches within a given population.
Estimated (Conservative and Lower-bound) Number of Look-alikes in the Relevant Fingerprint Population
The following fingerprint population groups are based on US Census Bureau estimates and should be used to calculate the estimated, conservative
(lower-bound) number of fingerprint look-alikes in the relevant fingerprint population for the case at hand:
1.
2.
3.
4.
5.
6.
7.
Greater San Francisco Bay Area of 18-65 year olds = 77,000,000
California Department of Justice Criminal AFIS Database = 100,000,000
State of California of 18-65 year olds = 228,000,000
FBI IAFIS Database = 550,000,000
United States of 18-65 year olds= 1,116,000,000
United States Total = 3,000,000,000 (default)
World 18-65 year olds = 24,552,000,000
Inference for identification to a Single Source
Inference of fingerprint identification is established when the final Fingerprint Match Probability (FMP) is less then the reciprocal of the total
number of fingerprint parts multiplied by the total number of fingerprint defined by the case at hand. Therefore, if the FMP is less than the
probability for 1 out of the total number of parts per fingerprint in the relevant fingerprint population for the case at hand then positive
identification with an reasonable degree of scientific certainty can be established.
Number of Fingerprint Parts Calculator
Fingerprint source attribution can be made on partial, fragmented “parts” of whole, complete fingerprints. The following formula defines the
value “P” for any aggregate amount of matching ridge features found in two impressions:
T ^ P = 10^240
Where,
T = T-Value or total match probability for an aggregate amount of ridge feature.
P = Number of “parts” in a hypothetical fingerprint
F = 10^240 (the total weight for the average flat fingerprint)*
NOTE
The total weight for the average flat fingerprint was defined as 2.45 x 10^239. For purposes of conservativeness this figure is rounded up to the
nearest factor of 10 and defined as 10^240. The log of 10^240 divided by the log of the total value (T) for the aggregate quantitative - qualitative
volume of ridge formations found in agreement between a latent fingerprint impression and an exemplar establishes the numbers of parts (P)
where the part represents the amount of ridge detail, for example, in a latent. P is the exponential power that T must be raised to equal the value
for the average flat fingerprint (F).
Number of Look-alikes Calculator
L = (P) (R)/T
Where,
L = Number of Look-alikes
R = Relevant Fingerprint Population
P = Number of parts in the whole average flat fingerprint
T = T-Value or total quantitative-qualitative value or weight for the particular arrangement of ridge formations in a single impression
or in agreement in two impressions
The number of look-alikes (L) present in a given fingerprint population is calculated by multiplying relevant fingerprint population
(R) to the number of parts (P) divided by the T-Value (T) for the latent or pair of corresponding impressions. The above formula is
used to define the number of look-alikes (L) likely to exist in a given fingerprint population.
Inference for Positive identification
The T-Model infers positive identification based on the definition for “identification” as to mean one person, however, it should not be
confused with “uniqueness” or one and only one to the exclusion of all others that exist, have existed, or will exist in the world. When
deducing positive identification there often is little need to establish that a fingerprint sample is found in only one person in the entire
world. Instead, source attribution is considered in the context of the case, and rarely would the entire world’s population be
considered as the pool of plausible contributors of any fingerprint evidence sample.
Inference for positive identification depends on relevant population. For purposes of accuracy, especially when dealing with small
known population groups, the variable for relevant fingerprint population remains an open field to be defined based on the case at
hand. In practice, fingerprint match probability is calculated for a number of relevant population groups residing in the geographic
area where the crime was committed. When there is no reason to believe that a smaller population group is relevant, it is
recommended to set the fingerprint population group to 3 billion, roughly equivalent to a total fingerprint population in the United
States. As a result, the default number of parts per fingerprint, e.g., 22, is multiplied by 3 billion, which subsequently defines the
fingerprint match probability threshold needed to establish positive identification for routine casework as 1/66 billion.
In general, however, inference for positive identification is defined as follows:
If L >1, then No Identification
If L  1, then Positive Identification
Where,
L equals the estimated, conservative (lower-bound) number of fingerprint “look-alikes” in a given fingerprint population..
DATA TABLES
Ridge Feature Weights (Inverse Probability Values)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Continuous ridge unit
Pore
Ending ridge unit in funnel
Ending Ridge Not in funnel
Ending/bifurcating ridge unit in funnel
Bifurcating ridge unit in funnel
Ending/bifurcating ridge unit not in funnel
Bifurcating ridge unit not in funnel
Single ridge unit (dot)
Core area (1mm x 1mm)
Delta (1mm x 1mm)
Crease
Trifurcating ridge unit
Scar
Other
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
1.15
5
10.00
14.25
14.375
18.75
20.50
26.75
98
209
453
634
23,136
26,224
23,136
Weights for Intervening Ridge Count to Nearest Neighbor (Inverse Probability Values)
1.
2.
3.
4.
5.
6.
7.
0-1 intervening ridges to nearest neighbor
2 intervening ridges to nearest neighbor
3 intervening ridges to nearest neighbor
4 intervening ridges to nearest neighbor
5 intervening ridges to nearest neighbor
6 intervening ridges to nearest neighbor
7 intervening ridges to nearest neighbor
=
=
=
=
=
=
=
1.0
2.5
9.5
26.5
50.0
188.5
377.5
Ridge Feature Clarity / Reliability Grade Scale – ANALYSIS
No Distortion:
Ridge feature appears visually clear and reliable, e.g., consistent with normal ridge structure.
Weak Distortion:
Ridge feature appears visually unclear or unreliable, and within tolerance to include.
Moderate Distortion:
Ridge feature appears visually unclear and unreliable, and within tolerance to include.
Strong Distortion:
Ridge feature appears obstructed however the orientation and relative position are reliably predictable.
Extreme Distortion:
Ridge feature appears too distorted to analyze.
NOTE: 1/P denotes neutralization of ridge feature weight, e.g. a ridge feature quantitative-qualitative value of 1.
Verbal
Statement
Grade
No
Distortion
Weak
Distortion
Moderate
Distortion
Strong
Distortion
Complete Reduction
Distortion
Factor
Excellent
A
Yes
No
No
No
No
1.00
Above Average
B
No
Yes
No
No
No
0.75
Average
C
No
No
Yes
No
No
0.50
Below Average
D
No
No
No
Yes
No
0.25
Fail
F
No
No
No
No
Yes
1/P
Ridge Feature Quality of Agreement Grade Scale - COMPARISON
Ridge Feature Type:
Continuous ridge unit, ending ridge unit, bifurcating ridge unit, dot, pore, core, delta, crease, scar, etc.
Ridge Path:
Feature ridge unit slants to the right, left, or not; angle of feature ridge unit is narrow, normal, wide, etc.
Spatial Relationship:
To Nearest Neighbor(s)
Less than or equal to a friction ridge skin elasticity threshold of 20% as measured from exemplar.
NOTE: 1/P denotes neutralization of ridge feature weight, e.g. a ridge feature quantitative-qualitative agreement value of 1.
Verbal
Statement
Ridge Type
Ridge
Agrees
Path Agrees
(Connectivity) (Slant/Angle)
Spatial Relationship to
Nearest Neighbor(s) Agrees
1
2
3
Reduction
Factor
Grade
Excellent
A
Yes
Yes
Yes
Yes
Yes
1.00
Above Average
B1
B2
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
No
Yes
0.75
Average
C1
C2
C3
Yes
Yes
No
Yes
No
Yes
Yes
Yes
Yes
No
Yes
Yes
No
No
Yes
0.50
Below Average
D1
D2
D3
D4
Yes
Yes
No
No
Yes
No
No
Yes
No
Yes
Yes
Yes
No
No
Yes
Yes
No
No
Yes
No
0.25
Fail
F1
F2
F3
Yes
No
No
No
No
Yes
No
Yes
Yes
No
Yes
No
No
No
No
1/P