NISTIR 7271

The Myth of Goats:

How many people have fingerprints 

that are hard to match? 

Austin Hicklin, Mitretek Systems

Craig Watson, NIST

Brad Ulery, Mitretek Systems

 
NISTIR 7271

The Myth of Goats: 

How many people have fingerprints that are hard to match? 

Austin Hicklin 

Brad Ulery 

Mitretek Systems 

Craig Watson 

U.S. DEPARTMENT OF 

COMMERCE 

Technology Administration 

National Institute of 

Standards and Technology 

Information Access Division 

Gaithersburg, MD 20899 

September 2005

U.S. DEPARTMENT OF COMMERCE

Carlos M. Gutierrez, Secretary

TECHNOLOGY ADMINISTRATION

Michelle O’Neill, Acting Under Secretary of Commerce for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

William A. Jeffrey, Director

 
The Myth of Goats: 

How many people have fingerprints that are hard to match? 

Austin Hicklin, Mitretek Systems 

Craig Watson, NIST 

Brad Ulery, Mitretek Systems 

13 September 2005 

Abstract 

The proportion of people who have fingerprints that are particularly hard to match (also 

known as “Goats”) is a topic of great interest in biometrics, especially for those involved 

in the design, development, or evaluation of fingerprint-based identification or 

verification systems. There have been a variety of statements made in the recent past that 

a small percentage of people (usually 2%) cannot be fingerprinted due to poor quality 

fingers. This study shows these statements are based on misconceptions: the fact that 

some small percentage of fingerprints may be hard to match does not mean that a 

corresponding percentage of people are hard to match. 

This study describes the results of tests using fingerprint data collected operationally by 

US-VISIT. Ten sets of right and left index fingerprints from each of 6,000 individuals 

were used in the evaluation. Two of the more accurate matchers from the NIST Software 

Development Kit (SDK) tests were used. 

The definition of a Goat, or person whose fingerprints are intrinsically hard to match, 

varies. However, results clearly show that the proportion of Goats is very small, 

regardless of the definition. None of the 6,000 subjects had fingers that were always hard 

to match (with single-finger mate scores worse than a threshold corresponding to a 

verification False Accept Rate of 1%); less than 0.05% of the subjects had fingers that 

were usually hard to match; less than 0.3% of the subjects had fingers that were hard to 

match even a quarter of the time. 

Many individuals were particularly easy to match: for 77% to 81% of subjects, every

fingerprint comparison had mate scores better than a threshold corresponding to a 

verification False Accept Rate of 10-6 (0.0001%). 

This study concludes that for the subject population (frequent users of US-VISIT) 

fingerprints that are hard to match cannot generally be attributed to intrinsic 

characteristics of a person’s fingerprints, but should be attributed to collection problems 

or other characteristics of the specific fingerprints used. Note that these results should be 

generalized with caution: results obtained using less accurate matchers, data from a 

source with lower operational quality controls, or substantively different subject 

populations would be likely to differ.

 
GOATS 

Contents 

1 Introduction ...................................................................................................5

2 Background....................................................................................................5

3 Experiment Description ...............................................................................9

3.1 Data.................................................................................................................9

3.2 Thresholds....................................................................................................10

4 Distribution of Mate Scores .......................................................................12

4.1 Overall Distribution of Mate Scores.........................................................12

4.2 Distribution of Mate Scores by Subject....................................................14

5 Image Quality Values .................................................................................18

6 Correspondence between Fingers ............................................................20

7 Correspondence between Matchers .........................................................21

8 Conclusions..................................................................................................22

9 References ....................................................................................................24

Disclaimer 

This work was performed for the Department of Homeland Security (US-VISIT 

Program) and the National Institute of Standards and Technology. Mitretek 

Systems was funded by the Department of Homeland Security, under contract to 

the U.S. Department of Interior, Contract NBCH-D-02-0039, Delivery Order 

D0200390054. 

13 SEPTEMBER 2005 4/24 
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1 Introduction 

Failures to match are obviously of serious concern in biometric systems. 

Every biometric system encounters some cases that cannot be acquired, 

enrolled, and/or matched. The reasons for these failures can generally be 

attributed to collection problems (due to problems with the operator, 

subject, collection devices, or software), or to intrinsic characteristics of the 

subject. This distinction is important, because failures due to collection 

problems can be lessened or eliminated with better quality control, but 

failures due to intrinsic characteristics of the subject limit the effectiveness 

of that biometric. 

Various statements have been made about the proportion of the general 

population that is difficult to match using fingerprints: 2% is most 

frequently cited. For large-scale operational systems such as US-VISIT, 2% 

of the overall population is a very large number of people, and therefore 

of concern. This study attempts to verify or contradict the assumption that 

there is such a proportion of the population that is difficult to match using 

fingerprints. 

The concept of a biometric menagerie was introduced in 1997 by Joseph 

Campbell1 and expanded by George Doddington2, defining 

• sheep (subjects who are easily matched), 

• goats (subjects who are particularly difficult to match), 

• lambs (subjects exceptionally vulnerable to impersonation), and 

• wolves (subjects exceptionally successful at impersonation). 

The term “Goat” is now widely used in biometrics to refer to a person 

who is intrinsically difficult to match. 

2 Background 

There have been a variety of statements made in the recent past that a 

small percentage of people cannot be fingerprinted due to poor quality 

fingers. Most of these cite (directly or indirectly) a 2002 NIST report,3

which made the following statements: 

 

1 See References [Campbell] 

2 See References [Doddington] 

3 See References [NIST2002] 

13 SEPTEMBER 2005 5/24 
GOATS 

(A)“Tests by NIST using INS data show that for approximately 2% of the 

fingers in the INS database, the friction ridges are too damaged to be 

matched with existing technology.” [pg. 2] 

(B) “We conclude that approximately 2% of individuals in the general 

population may not be easily fingerprinted.” [pg. 15] 

(C) “Not all subjects can be easily fingerprinted with existing technology 

resulting in a 2% failure to acquire rate.” [pg.21] 

A 2003 GAO Report,4 citing the above NIST report, stated, 

(D)“Approximately 2 percent of the population cannot provide good 

fingerprint images.” [pg 11] 

The NIST report was partly based on a 2000 Mitretek study for DOJ,5

which stated, 

(E) “The quality of approximately 2 percent of INS IDENT flat fingerprints is 

so poor that it renders them virtually impossible to match using current 

IAFIS technology, and an additional 3 percent would be very unlikely to 

match.” [pg vii] 

Each of these statements can be misinterpreted or misapplied. There are 

several issues involved here, which are key to defining what Goats are: 

Problem fingerprints as opposed to people with problem fingers 

The fact that a given percentage of fingerprints in a database may 

be hard to match does not mean that a corresponding percentage of 

people have fingers that are always hard to match. A fingerprint is 

often hard to match for a variety of reasons that are specific to that 

individual image, such as poor quality control in data collection, 

that do not reflect on the ability of the person to provide good 

fingerprints in the future. Every person can produce poor-quality 

fingerprints. Note that all of the statements cite the same 2% figure 

even though statements (A), (C) and (E) refer to fingerprints, and 

statements (B) and (D) refer to people. 

Population and data source 

All of these statements refer to INS6 recidivist data, collected by 

what was then INS (now BICE7) from illegal immigrants, under 

 

4 See References [GAO] 

5 See References [IQS] 

6 Immigration and Naturalization Service, U.S. Department of Justice 

7 Bureau of Immigration and Customs Enforcement, U.S. Department of Homeland Security 

13 SEPTEMBER 2005 6/24 
GOATS 

difficult operational conditions, using fingerprint scanners with 

less-than-ideal image quality. Statistics based on this population 

(mostly composed of manual laborers) cannot be extrapolated to 

the overall human population, and the distribution of image 

qualities cannot be assumed to apply to other sources of data. Some 

population characteristics that are known or believed to be 

associated with lower fingerprint matching accuracy include 

manual labor that damages the skin (through abrasion or 

chemicals), age, and small physical size. Data sources that come 

from populations that differ substantially in these terms should be 

expected to differ in ease of matching. 

Matching technology 

None of the statements was based on state-of-the-art technology for 

the types of fingerprints used. The NIST test was based on the 

VTB,8 which was shown to be roughly average in performance 

when compared against a range of other matchers in the FpVTE9

and SDK10 evaluations. The results in (D) used flat fingerprints on a 

system specifically optimized for rolled fingerprints. Some systems 

available today are much more accurate, especially with poorquality single-finger flat images. Determining which individuals 

are Goats also depends on the matching algorithm in ways beyond 

overall accuracy: fingerprints that cause problems for any one 

algorithm will overlap with fingerprints that cause problems for 

others, but will often include some cases that are particularly 

difficult solely for that algorithm. 

Difficulty of matching 

Except in extreme cases, there is no absolute line defining 

fingerprints that are hard to match from those that are easy to 

match: hard (or easy) to match could be defined in a variety of 

ways. Goats could be defined in absolute terms, as people whose 

fingerprints are consistently matched below a given threshold11, 

based on evaluation and operational experience. A different 

definition of Goats could be in relative terms, defined as people 

 

8 The NIST Verification Test Bed (VTB) is an export-controlled open source fingerprint matcher: 

see References [VTB] 

9 See References [FpVTE] 

10 See References [SDK] 

11 Matcher score thresholds are set to trade off false matches against false rejects. 

13 SEPTEMBER 2005 7/24 
GOATS 

who are harder to match than others, but who may or may not 

actually be hard to match in absolute terms. 

Number of fingers 

For biometrics such as iris or fingerprint, for which one subject can 

provide multiple samples (two eyes or ten fingers), failures to 

match can be based on each sample, or each subject. Many people 

have hard to match little fingers, but very few have ten hard to 

match fingers: does a Goat have one poor-quality finger, or are all 

ten fingers poor quality? 

Many evaluations have been conducted that can be used to determine the 

proportion of the fingerprints in the test that were difficult to match, using 

a specific set of matcher technologies. In most evaluations the proportion 

of fingerprints that failed to match (false rejects) can readily be 

determined, for a given matcher, at a given threshold or false accept rate 

(FAR). Unfortunately, without multiple fingerprints per finger (and per 

person), these studies reflect the proportion of problem fingerprints, and 

say nothing about whether these were caused by intrinsic characteristics 

of the subjects. 

The only study known to have evaluated the consistency of intra-subject 

fingerprint matching accuracy is the small-scale study reported in 

[NIST2002]. In that study, 100 subjects with 30 sets of right and left index 

fingerprints each were evaluated using the VTB matcher. Two of the 

subjects were found to be problematic: 

“Two of the match blocks [i.e. subjects] had average match scores that 

were so low that they were only marginally distinguishable from nonmatch blocks. When the 30 images of each of the marginal match blocks 

were examined, it was found that the friction ridges of these 

individuals were abraded to the point where no ridges were present. 

This did not appear to be an equipment problem. The images had 

sufficient contrast and were not blurred. The fingers did not have 

detectable or repeatable friction ridge patterns.” [pg 14-15] 

The NIST study was appropriately designed and conducted, but as stated 

above there were several issues that limited how the results could be 

generally applied: 

• Only 100 subjects were available. This sample size is not large enough 

to make a definitive statement about a 2% rate with high confidence. 

13 SEPTEMBER 2005 8/24 
GOATS 

This limits the level of certainty of measurements, so that 2/100 can 

only be stated as 2% ± 2.7% (95% confidence)12, or 0.0% to 4.7%. 

• The matcher used was not one of the more accurate matchers available. 

• The population involved was limited to illegal aliens apprehended on 

the Mexican-US border, most of whom were manual laborers. 

• The capture devices used were not representative of the more accurate 

livescan devices now available. 

• Operational quality control for fingerprint capture was limited. 

No studies are known to have been conducted to determine the 

proportion of people in the general population with hard to match 

fingerprints, using a large number of subjects with multiple fingerprints 

per finger, and accurate matchers. The current study seeks to fill this gap, 

and expand upon the previous NIST work. 

3 Experiment Description 

The primary objectives of this study were to determine the proportion of 

the US-VISIT population for whom 

• One finger is always or usually particularly difficult to match 

• Both fingers are always or usually particularly difficult to match 

• One finger is always or usually particularly easy to match 

• Both fingers are always or usually particularly easy to match 

3.1 Data 

NIST has a large variety of fingerprint data available. One set in 

particular, the US-VISIT Point of Entry dataset (POE) contains all 

fingerprints collected by US-VISIT between January and June 2004. The 

POE dataset included left and right index fingerprints from 4.2 million 

subjects. Note that no Failures to Enroll (FTEs) were excluded from this 

data: the overall dataset includes every single non-amputee who entered 

the United States with a U.S. Visa.13 All mating information (knowing 

which fingerprints belonged to the same person) was determined through 

document numbers, not through use of a fingerprint matcher. Two subsets 

of the POE data were used in this study: 

 

12 This is assuming a binomial distribution; otherwise, the confidence bands will be larger. 

13 Amputees account for much less than 0.1% of the US-VISIT population. [ref. Neal Latta, USVISIT] 

13 SEPTEMBER 2005 9/24 
GOATS 

Multi-Instance Subset of POE 

Of the 4.2 million subjects, approximately 6,600 had ten or more 

sets of fingerprints in the POE dataset. From these, ten sets of 

fingerprints (left and right index) were selected from each of 6,000 

subjects.14 Two of the more accurate SDK matchers (Matchers H 

and I) were used to match each finger for a subject against all of the 

other corresponding fingers from the same subject. Since ten sets of 

fingerprints were available from each subject, each matcher 

generated 90 scores per finger, or 360 scores per person: the MultiInstance Subset of POE included 2,160,000 scores in all.15

Note that this population represents individuals who were 

processed by US-VISIT ten or more times in a six month period. 

While the overall US-VISIT population is to some extent a crosssection of the world’s population, this multi-instance population is 

primarily composed of flight crews and business travelers. 

Overall Subset of POE 

Another random selection of 61,996 subjects16 from the overall USVISIT-POE dataset was made, with two sets of fingerprints (left and 

right index) from each subject. The score distributions from this 

dataset from the H and I matchers were used to determine the 

extent to which the Multi-Instance Subset of POE corresponded to 

the overall US-VISIT population. 

3.2 Thresholds 

For this study, thresholds were required to correspond to the nebulous 

concepts of “Hard to match” and “Easy to match.” The thresholds used 

were not absolute: whether something is hard to match is an applicationdependent concept. As rough guidelines for the purposes of this study, 

 

14 Both subjects and sets of fingerprints were randomly selected. 6,000 subjects were used because 

6,000-subject matrices were standard in the SDK tests. 

15 The matchers used were not fully symmetric: matching A against B generally results in scores 

that are similar to but not precisely the same as matching B against A. Of the 90 scores per finger, 

therefore, 45 were redundant. 

16 62,000 subjects were randomly selected; 4 subjects could not be processed due to invalid file 

formatting. 

13 SEPTEMBER 2005 10/24 
GOATS 

• scores associated with a verification FAR17 of 10-2 or worse can be 

considered hard to match, and 

• scores associated with a verification FAR of 10-6 or better can be 

considered easy to match.18 

The categories used in this study to define difficulty of matching in terms 

of FAR are shown in Table 1. 

Score Thresholds 

in terms of False 

Accept Rates 

Categories used in this study 

FAR=1 Unusable 

10 0 > FAR ≥ 10-2 Hard to match 

10-2 > FAR ≥ 10-6 Debatable (between hard and 

easy to match) 

FAR < 10-6 Easy to match 

Table 1: Categories of thresholds, defined in terms of 1:1 False Accept Rates 

For a subject/finger to be always hard to match, the maximum score of all 

of the cross-comparisons must be worse than a specific score threshold. 

For a subject/finger to be usually hard to match, the median score of all of 

the cross-comparisons must be worse than a specific score threshold. 

The mate and non-mate score distributions were determined for the POE 

data using two of the most accurate matchers from the NIST SDK 

evaluations,19 Matcher H and Matcher I. For reference, the associations 

between False Accept and True Accept Rates (as calculated in the SDK 

tests on the US-VISIT POE data) are shown in Table 2. 

 

17 The False Accept Rates stated throughout the paper are 1:1 (verification) FARs, based on singlefinger matching. 

18 Note that a verification FAR of 10-6 on a single-finger search would not by itself translate to a 

definitive search against a large identification system (with a gallery in the millions). Such 

systems rely on the use of multiple fingers to achieve those levels of accuracy. 

19 See References: [SDK] 

13 SEPTEMBER 2005 11/24 
GOATS 

False and True Accept Rates 

FAR TAR 

 Matcher I Matcher H 

 R.Index L.Index R.Index L.Index 

1 10 0 100.0% 100.0% 100.0% 100.0% 

0.1 10-1 99.5% 99.5% 99.7% 99.7% 

0.01 10-2 99.2% 99.2% 99.4% 99.3% 

0.001 10-3 99.0% 98.9% 99.2% 99.1% 

0.0001 10-4 98.7% 98.5% 98.9% 98.7% 

0.00001 10-5 98.3% 98.0% 98.5% 98.0% 

0.000001 10-6 97.9% 97.2% 97.9% 97.4% 

Table 2: False and True Accept Rates for the matchers used in the study on US-VISIT 

POE Data, as measured in the NIST SDK tests 

4 Distribution of Mate Scores 

This section describes the key results of the study, the overall distribution 

of mate scores and the distribution of mate scores by subject. 

4.1 Overall Distribution of Mate Scores 

Since the population in the multi-instance dataset differs to some extent 

from the overall US-VISIT population, it is necessary to demonstrate that 

the multi-instance and overall datasets correspond in their distributions, 

so that findings related to the multi-instance data can be reasonably 

expected to apply to the overall US-VISIT population. 

Table 3 and Table 4 show the distribution of scores in terms of False 

Accept Rates for the overall US-VISIT dataset, and for the Multi-Instance 

Subset of POE. Note the degree of correspondence between the 

distributions. 

13 SEPTEMBER 2005 12/24 
GOATS 

Overall Subset of POE 

Distribution of scores in terms of False Accept Rates 

log(FAR) Right Index Left Index 

 Matcher H Matcher I Matcher H Matcher I 

0 0.60% 0.03% 0.48% 0.05% 

0 to -1 0.03% 0.47% 0.05% 0.36% 

-1 to -2 0.04% 0.22% 0.07% 0.34% 

-2 to -3 0.20% 0.23% 0.36% 0.41% 

-3 to -4 0.28% 0.28% 0.41% 0.46% 

-4 to -5 0.30% 0.38% 0.52% 0.68% 

-5 to -6 0.41% 0.59% 0.69% 0.96% 

<-6 98.16% 97.81% 97.41% 96.74% 

Scores 61,996 61,996 61,996 61,996 

Subjects 61,996 61,996 61,996 61,996 

 Table 3: Distribution of Overall Subset of POE scores in terms of False Accept Rates 

Multi-Instance Subset of POE 

Distribution of scores in terms of False Accept Rates 

log(FAR) Right Index Left Index 

 Matcher H Matcher I Matcher H Matcher I 

0 0.56% 0.03% 0.40% 0.04% 

0 to -1 0.04% 0.46% 0.05% 0.30% 

-1 to -2 0.05% 0.24% 0.06% 0.28% 

-2 to -3 0.22% 0.24% 0.27% 0.30% 

-3 to -4 0.30% 0.30% 0.34% 0.38% 

-4 to -5 0.35% 0.43% 0.41% 0.52% 

-5 to -6 0.48% 0.63% 0.56% 0.80% 

<-6 98.01% 97.66% 97.92% 97.37% 

Scores 540,000 540,000 540,000 540,000 

Subjects 6,000 6,000 6,000 6,000 

Table 4: Distribution of Multi-Instance Subset of POE scores in terms of False Accept 

Rates 

These results are shown graphically in Figure 1. 

13 SEPTEMBER 2005 13/24 
GOATS 

Comparison of Overall VISIT-POE with Multi-Instance Subset

Mate Scores in Terms of log(False Accept Rate)

(Right & Left Index Fingers, SDK (H) and (I) matchers)

0%

1%

2%

3%

4%

5%

MultiInst

F02 - H

Overall

F02 - H

MultiInst

F02 - I

Overall

F02 - I

MultiInst

F07 - H

Overall

F07 - H

MultiInst

F07 - I

Overall

F07 - I

Proportion of Mate Scores

<-6

-5 to -6

-4 to -5

-3 to -4

-2 to -3

-1 to -2

0 to -1

0

log(FAR)

Matcher (H)

Right Index

Matcher (I)

Right Index

Matcher (H)

Left Index

Matcher (I)

Left Index

Figure 1: Comparison of matcher scores from the Overall and Multi-Instance subsets 

of US-VISIT-POE data 

Further analysis of the actual scores in the tails of the distributions (e.g. 

the 1st percentile and 0.1 percentile) also showed close correspondence. 

4.2 Distribution of Mate Scores by Subject 

When the 10 fingerprints for each person’s finger were matched, all crosscomparisons yielded 90 scores for each matcher. This analysis is based on 

the distribution of the minimum, 1st quartile, median, average, 3rd quartile, 

and maximum values of these scores.20 Figure 2 shows the median score, 

interquartile distance (difference between 1st and 3rd quartiles), minima, 

and maxima for all right index fingers, sorted by median, using the 

Matcher H matcher.21 Note that the scores vary substantially, both in 

terms of median values and inter-quartile distance, but that only a very 

small proportion of the scores fall within the FAR range of 1 to 10-6: the 

 

20 The redundancy in the scores (inclusion of both A:B and B:A comparisons) does not affect these 

measures, but would affect measures such as standard deviation. 

21 The actual matcher scores are omitted, as they are considered proprietary. 

13 SEPTEMBER 2005 14/24 
GOATS 

overwhelming majority of scores are far better than even the easy to 

match threshold. Note in Figure 2 that the threshold of FAR=1 cannot be 

differentiated from FAR=10-2 at this scale. 

Distribution of 90 mated scores per subject

Scores from (H) Matcher, Right Index finger

Subjects, sorted by median score

Matcher Scores

Min/Max

Median

Interquartile

distance

FAR=10-6

FAR=1

FAR=10-2

Figure 2: Distribution of matcher scores from the (H) matcher (right index fingers), 

showing median scores (blue line), 1st and 3rd quartiles (gray lines), and 

minima/maxima (red points) 

There is a clear relationship between subject and the distribution of 

matcher scores: in other words, some people are harder (or easier) to 

match than others. 

Table 5 and Table 6 show greater detail for the score distributions. The 

highlighted regions of these tables show that: 

No subject was always hard to match 

No subjects (for either finger, either matcher) had maximum scores 

worse than a FAR of 10-2. 

13 SEPTEMBER 2005 15/24 
GOATS 

Less than 0.03% of subjects had fingers that were usually hard to match 

For the H matcher, no subject (for either finger) had a median score 

worse than a FAR of 10-2, but for the I matcher, 0.02%-0.03% of the 

population22 had median scores worse than a FAR of 10-2. 

Less than 0.3% of subjects had fingers that were hard to match even a 

quarter of the time. 

Between 0.08% and 0.32% of the population had a 1st Quartile 

worse than a FAR of 10-2. 

6.3% of subjects had fingers that were ever hard to match. 

The minimum score for 6% of subjects was worse than a FAR of 10-

2. Most hard to match fingerprints are the worst scores for their 

subjects, and are not generally representative of their subjects. Note 

that the H and I matcher differed substantially on the proportion of 

unusable (FAR=1) scores. 

About 80% of subjects were always easy to match 

• 77.0-80.9% of the subjects had a minimum score better than a threshold 

of 10-6. 

More than 99.5% of subjects were usually easy to match 

• 99.5-99.7% of the subjects had a median score better than a threshold of 

10-6. 

 

22 Ranges show range of measured values for the two matchers and left and right index fingers. 

13 SEPTEMBER 2005 16/24 
GOATS 

 Summary of Cumulative Distribution, Right Index 

Finger Matcher Type Hard to match Easy to 

match 

 FAR=1 FAR≥10-1 FAR≥10-2 FAR≥10-3 FAR≥10-4 FAR≥10-5 FAR≥10-6 FAR<10-6

Min 5.15% 5.68% 6.33% 8.18% 11.10% 14.32% 19.07% 80.93% 

Quartile1 0.02% 0.05% 0.08% 0.32% 0.65% 0.95% 1.38% 98.62% 

Median - - - 0.02% 0.13% 0.18% 0.30% 99.70% 

Average - - - - 0.03% 0.07% 0.13% 99.87% 

Matcher H 

Quartile3 - - - - 0.03% 0.08% 0.12% 99.88% 

Max - - - - - 0.02% 0.03% 99.97% 

Min 0.48% 4.28% 6.33% 8.68% 11.87% 15.95% 21.05% 78.95% 

Quartile1 0.02% 0.05% 0.22% 0.47% 0.68% 1.23% 1.80% 98.20% 

Median - - 0.03% 0.10% 0.17% 0.28% 0.43% 99.57% 

Average - - 0.03% 0.07% 0.13% 0.22% 0.37% 99.63% 

Quartile3 - - - - 0.08% 0.10% 0.17% 99.83% 

2 (Right Index) 

Matcher I 

Max - - - - - - 0.02% 99.98% 

Table 5: Summary of Distribution of matcher scores, right index fingers 

 

 Summary of Cumulative Distribution, Left Index 

Finger Matcher Type Hard to match Easy to 

match 

 FAR=1 FAR≥10-1 FAR≥10-2 FAR≥10-3 FAR≥10-4 FAR≥10-5 FAR≥10-6 FAR<10-6

Min 5.05% 5.68% 6.40% 8.98% 11.97% 15.80% 20.17% 79.83% 

Quartile1 0.05% 0.12% 0.15% 0.33% 0.58% 0.88% 1.42% 98.58% 

Median - - - 0.05% 0.17% 0.23% 0.27% 99.73% 

Average - - - - - 0.05% 0.10% 99.90% 

Matcher H 

Quartile3 - - - - 0.02% 0.07% 0.08% 99.92% 

Max - - - - - - - 100.00% 

Min 0.72% 4.00% 6.28% 9.30% 12.77% 17.28% 23.03% 76.97% 

Quartile1 0.02% 0.10% 0.32% 0.57% 0.82% 1.38% 2.45% 97.55% 

Median - - 0.02% 0.13% 0.22% 0.38% 0.55% 99.45% 

Average - - - 0.05% 0.10% 0.27% 0.52% 99.48% 

Quartile3 - - - 0.02% 0.05% 0.08% 0.13% 99.87% 

7 (Left Index) 

Matcher I 

Max - - - - - - - 100.00% 

Table 6: Summary of Distribution of matcher scores, left index fingers 

The confidence intervals for the summary numbers highlighted above are 

detailed in Table 7.23 The highest and lowest observed numbers of subjects 

among the two matchers and two hands are included. 

 

23 Confidence intervals for unobserved events were calculated using the intervals for a single 

instance as a bound. 

13 SEPTEMBER 2005 17/24 
GOATS 

 

Number of 

subjects Confidence Intervals (95%) 

 Low High Low High From To 

Always hard to match 0 0 0.02% ± 0.03% 0.02% ± 0.03% 0.00% 0.05% 

Usually hard to match 0 2 0.02% ± 0.03% 0.03% ± 0.05% 0.00% 0.08% 

Hard to match 1/4 of the time 4 18 0.07% ± 0.07% 0.30% ± 0.14% 0.00% 0.44% 

 

Always easy to match 4618 4856 76.97% ± 1.07% 80.93% ± 0.99% 75.90% 81.93% 

Usually easy to match 5967 5984 99.45% ± 0.19% 99.73% ± 0.13% 99.26% 99.86% 

Easy to match 3/4 of the time 5990 5995 99.83% ± 0.10% 99.92% ± 0.07% 99.73% 99.99% 

 

(out of 6,000 

subjects, two 

matchers, right and 

left index fingers) 

Table 7: Summary of results with confidence intervals 

When Doddington introduced the concept of Goats, he defined them “as 

those speakers who are particularly difficult to recognize.” [pg 1] He then 

determined the existence of Goats using analyses of variance (F-test and 

Kruskal-Wallis Test). The subtle distinction here is that he defined Goats 

in absolute terms (difficult to recognize), but conducted the test in relative 

terms (determining if some of the subjects were more difficult than others 

to recognize). In the field of speaker recognition, this is probably not a 

meaningful distinction. However, with fingerprints, the accuracy level is 

high enough that some subjects can be more difficult to recognize than 

others (in relative terms), but still easy to recognize (in absolute terms). 

There are certainly individuals whose fingers are harder to match than 

others. This can be shown through analyses of variance, or more simply 

through the results in Figure 2, which shows that the median score and 

range of scores are clearly dependent on subject. 

5 Image Quality Values 

This study defines Goats as individuals who are difficult to match in 

terms of matcher scores. A different study could define Goats as 

individuals with poor-quality fingerprints, in terms of image quality 

metrics (IQMs) rather than through matcher scores. IQMs are practical to 

use operationally, whereas matcher scores are generally only available for 

after-the-fact evaluation. 

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GOATS 

Table 8 shows the overall distribution of the NIST Fingerprint Image 

Quality (NFIQ) values24 for the Multi-Instance Subset of POE. NFIQ 

defines values of 4 or 5 as poor or very poor quality. 

NFIQ 

Right 

Index 

Left 

Index 

1 28.6% 33.8% 

2 42.3% 37.8% 

3 26.3% 25.4% 

4 1.7% 1.6% 

5 1.1% 1.4% 

Table 8: Distribution of image quality as measured using NFIQ 

The poor image quality values (NFIQ 4/5) were not distributed evenly 

across subjects. Table 9 shows the percentage of subjects having 

fingerprints with poor image quality values (for the 6,000 individuals with 

ten samples of fingerprints from each finger). For example, for 0.1% of the 

subjects, all ten of their right index fingerprints were poor quality. 

# of 

NFIQ4/5 Right Index Left Index 

None 0 85.6% 85.6% 84.9% 84.9% 

1 8.6% 9.1% 

2 2.8% 2.9% 

3 1.2% 1.2% Some 

4 0.8% 

13.3% 

0.8% 

13.9% 

5 0.5% 0.5% 

6 0.2% 0.2% 

7 0.2% 0.3% 

8 0.1% 0.2% 

Most 

9 0.1% 

1.1% 

0.1% 

1.2% 

All 10 0.1% 0.1% 0.1% 0.1% 

Table 9: Prevalence of multiple poor-quality fingerprints 

These results are far from random: if NFIQ values from Table 8 were 

distributed with no relation to subject, about 74% would have no NFIQ4/5 

fingerprints25, only 0.001% would have five out of ten NFIQ4/5 

fingerprints, and only 6*10-16 would have ten out of ten NFIQ4/5 

fingerprints. The results show that that image quality as measured by 

 

24 NFIQ is a standard, publicly-available method of measuring fingerprint image quality, 

described at ftp://sequoyah.nist.gov/pub/nist_internal_reports/ir_7151/ir_7151.pdf ; the software 

(export-controlled) is available at http://fingerprint.nist.gov/NFIS/. 

25 74%: for each finger (averaging left and right), 97.1% of fingerprints are NFIQ<4; 0 out of 10 

fingerprints with NFIQ4/5 = 0.97110≈74% 

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GOATS 

NFIQ is not randomly distributed among subjects. Instead, NFIQ4/5 

fingerprints are concentrated in a small group of subjects: a majority of the 

NFIQ4/5 fingerprints occur in 3.3% of subjects. 

Note that the matchers used are capable of matching even poor quality 

fingerprints at relatively high scores. This explains the differences 

between the NFIQ results and the matcher score results. Less accurate 

matchers might show a greater degree of correspondence to the NFIQ 

results, with the result that a study using such matchers would measure a 

larger proportion of goats in the population. 

6 Correspondence between Fingers 

For subjects with poor-quality fingers, it is important to know whether 

poor-quality fingers on one hand are correlated with poor-quality fingers 

on the other hand. 

Table 10 shows the number of poor-quality fingerprints per subject, as 

determined by NFIQ, counting both left and right index fingers. In other 

words, 2% of the 6,000 subjects had from 6 to 10 poor-quality fingerprints, 

out of 20 (10 left and 10 right index fingers), and for 0.6% of subjects a 

majority of fingerprints from both hands were poor quality. 

Multi-instance POE subset 

# of fingerprints per subject with NFIQ≥4

(out of 10 left and 10 right index fingers) 

0 78.0% 

1-5 19.5% 

6-10 2.0% 

11-15 0.5% 

16-20 0.1% 

Table 10: Number of poor-quality fingerprints per subject (10 left and 10 right index 

fingers) 

Table 11 shows how matcher scores (in terms of FAR) correspond for 

fingerprints collected at the same time. For example, only 0.07%-0.08% of 

all sets of right and left index fingerprints were worse than 10-2 for both 

fingerprints. 99.5%-99.7% of subjects had at least one finger that was easy 

to match. 

Note that conditional probabilities that can be drawn from these results: 

• The overall probability of a hard to match left index finger is about 

0.7% (0.65% for Matcher H, or 0.73% for Matcher I). 

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GOATS 

• If the right index finger is hard to match, the probability the left index 

finger collected at the same time is hard to match jumps to 13% 

(12.9%26 for Matcher H, and 13.1% for Matcher I). 

Summary of corresponding FAR distributions for fingerprints collected at 

one time 

Matcher H 

 Left Index 

 > 10-2 10-3 to 10-6 < 10-6

> 10-2 0.07% 0.04% 0.40% 

10-3 to 10-6 0.05% 0.16% 1.38% 

Right index 

< 10-6 0.54% 1.14% 96.24% 

Matcher I 

 Left Index 

 > 10-2 10-3 to 10-6 < 10-6

> 10-2 0.08% 0.08% 0.46% 

10-3 to 10-6 0.07% 0.22% 1.72% 

Right 

index 

< 10-6 0.58% 1.32% 95.47% 

Table 11: Correspondence between fingers 

7 Correspondence between Matchers 

The matchers used had similar levels of matching accuracy, but did not 

always return equivalent results. Table 12 shows the proportions of 

individual scores that were outside the hard/easy to match thresholds for 

each matcher separately and together. 

Distribution of Individual Scores 

 Matcher H Matcher I Both 

Hard to match FAR >=10-2 0.6% 0.7% 0.4% 

Easy to match FAR <10-6 98.0% 97.5% 97.0% 

Table 12: Correspondence between matchers 

Table 13 shows the distribution of the differences in FAR between the two 

matchers, over all individual scores. For example, the 6 row means that 

the log of the FAR differed by 6, such as would occur if one matcher had a 

FAR of 10-7 and the other had a FAR of 10-1. Note that there were cases in 

which one matcher returned a FAR of 1 (100) when the other returned a 

FAR of 10-7. 

 

26 12.9% = 0.07% / (0.07% + 0.04% + 0.40%) 

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Distribution of Individual Scores 

Difference 

between 

log(FARH) and 

log(FARI) 

0 97.26% 

1 1.41% 

2 0.73% 

3 0.35% 

4 0.16% 

5 0.06% 

6 0.02% 

7 0.01% 

Table 13: Difference between log(False accept rates) for matchers H and I 

8 Conclusions 

1 The results clearly show that the proportion of individuals who 

had consistently hard to match fingerprints is smaller than 0.05% in the 

US-VISIT population. 

The study used a definition of “hard to match” as a matcher score 

corresponding to a False Accept Rate of 10-2 (1%) or worse, and a 

definition of “easy to match” as a matcher score corresponding to a False 

Accept Rate of 10-6 (0.0001%) or better. 

• None of the 6,000 subjects had fingers that were always hard to match 

• Less than 0.05% of the subjects had fingers that were hard to match the 

majority of the time 

• No more than 0.2% of the subjects had fingers that were hard to match 

even a quarter of the time 

2 Most individuals were consistently easy to match. 

Most of the US-VISIT population can be readily matched even at a high 

score threshold. 

• For 77% to 81% of subjects, every fingerprint comparison had matcher 

scores better than a False Accept Rate of 10-6 (0.0001%). 

• For more than 98% of the subjects, three-fourths of fingerprint 

comparisons were easy to match. 

• For more than 99.5% of the subjects, the majority of the fingerprint 

comparisons were easy to match. 

• Every one of the 6,000 subjects had at least one fingerprint comparison 

that was easy to match. 

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GOATS 

3 Fingerprints that are hard to match cannot generally be attributed 

to intrinsic characteristics of a person’s fingers. 

Each finger used in the study had a range of performance: none was 

consistently difficult to match, and more than 99.9% were easy to match in 

some cases. A hard to match fingerprint, therefore, is indicative of 

problems with that specific fingerprint image, and does not mean another 

fingerprint from the same finger would be hard to match. 

4 Poor quality fingerprints on one hand are correlated with poor 

quality fingerprints collected at the same time from the other hand. 

Only 0.7% of subjects had hard to match left index fingers. However, for 

subjects with hard to match right fingers, 13% of subjects had hard to 

match left index fingers. 

Note: These results should be applied to systems outside US-VISIT 

with caution. 

The population in US-VISIT is to some extent a cross-section of the 

world’s population, and therefore it is tempting to state that these results 

are generally applicable. The following cautions should be noted: 

• The proportion of hard to match cases is correlated to the accuracy of 

the matchers used. Less accurate matchers cannot be expected to have 

the same results. 

• US-VISIT has well-defined quality control procedures for fingerprint 

collection. Datasets with less rigorous quality control procedures, or 

collected on less accurate capture devices, will not yield the same 

results. 

• Different subject populations will not yield the same results. In 

particular, populations that have a greater proportion of manual 

laborers or elderly can be expected to have a greater proportion of 

hard to match fingerprints. 

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GOATS 

9 References 

Campbell Campbell; Speaker Recognition: A Tutorial; Proceedings of the IEEE, Vol. 

85, No. 9, September 1997. 

http://www.ee.columbia.edu/~patricia/papers/tutorials/tutorial.pdf 

Doddington Doddington, et al; Sheep, Goats, Lambs And Wolves: A Statistical Analysis 

of Speaker Performance in the NIST 1998 Speaker Recognition Evaluation; 

http://www.nist.gov/speech/publications/papersrc/icslp_98.pdf

FpVTE C. Wilson, et al; Fingerprint Vendor Technology Evaluation 2003, 

NISTIR 7123. June 2004. http://fpvte.nist.gov/ 

GAO GAO; “Border Security: Challenges in Implementing Border 

Technology,” Statement of Nancy Kingsbury, Managing Director 

Applied Research and Methods, Testimony Before the Subcommittee 

on Terrorism, Technology, and Homeland Security and Subcommittee 

on Border Security, Immigration, and Citizenship, Committee on the 

Judiciary, United States Senate; March 12, 2003. 

http://www.gao.gov/new.items/d03546t.pdf 

IQS R.A. Hicklin, et al; Implications of the IDENT/IAFIS Image Quality Study 

for Visa Fingerprint Processing, October 2002. 

http://www.mitretek.org/publications/biometrics/NIST-IQS.pdf 

NFIQ E. Tabassi, et al; Fingerprint Image Quality NIST IR 7151, August 2004. 

ftp://sequoyah.nist.gov/pub/nist_internal_reports/ir_7151/ir_7151.pdf 

NFIS C. Watson, et al; NIST Fingerprint Image Software. 

http://www.itl.nist.gov/iad/894.03/databases/defs/nist_nfis.html 

NIST2002 NIST; Summary of NIST Standards for Biometric Accuracy, Tamper 

Resistance, and Interoperability, November 13 2002. 

ftp://sequoyah.nist.gov/pub/nist_internal_reports/NISTAPP_Nov02.pdf

SDK C. Watson, et al; NIST Fingerprint SDK (Software Development Kit) 

Testing, NISTIR 7119. June 2004. http://fingerprint.nist.gov/SDK/ 

 

 

 

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