Articles and Papers

Sasquatch: Size, Scaling, and Statistics

Wolf H. Fahrenbach

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Measurements and estimates on Sasquatch dimensions, collected over the last 40 years in the Western U.S and Canada, were subjected to statistical analysis and extrapolation by scaling laws appropriate to primates and mammals. The study has yielded average population values for foot length and width, scaling factors of foot length to height, values for weight, plantar pressure, walking and running gait, speed, and a tentative growth curve as a function of time for the female of the species. The results suggest a substantial population with traits different from those of other higher primates and man.

Introduction

Over the last half century several thousand eyewitness reports of Sasquatch (also known as Bigfoot) sightings, footprints, and other circumstantial evidence have accumulated (Bord and Bord, 1982; Deery et al. 1997; Green, 1978, 1980a, b, c; Perez, 1988). Although Green (1978, 1980c) has collated his collected observations in synoptic fashion, the numerical values contained in the sources have not been explored statistically. A sufficiently large sample size, as we have for many measurements, has the advantage of supporting through such treatment either an origin from a living population of animals or, conversely, exposing a set of fictitiously generated values.

Any editing method for these data invariably involves a value judgement by the investigator, who gauges the credibility of eyewitnesses by assorted criteria that are apt to vary from person to person, are often arbitrary, and will always be fallible. Therefore, I am using here all the available measurements at the risk of increased statistical noise. Excluded are only reports with preternatural content. Many data sets suffer from inherently large systematic error sources that will be mentioned and must be contended with. A systematic confounding variable in the entire set is the lumping of all ages and the two sexes, the latter having been reported to be dimorphic in body size and other attributes. Values derived from the Patterson movie of 1967 do not carry any special weight other than the chest circumference, for which it is the only source.

I am operating under the premise that the Sasquatch is a living primate rather than an elaborate figment of the imagination. Therefore, I have availed myself of various pertinent allometric scaling formulae for mammals in general and primates in particular, that permit a more rational extrapolation to different physical aspects of the species than pure guesswork allows. The principle of allometric scaling consists of fitting a straight line to a logarithmically transformed, bivariate data set, generally derived from many different related species, according to the formula

Y = a * Xb

where Y = some specific aspect of the animal under investigation, be it a morphological, ecological or physiological variable;

a = the allometric coefficient, a constant which defines the intercept on the Y axis, i.e., the position of the line;

X = some measure of body size, generally weight; and

b = allometric exponent or scaling factor, which defines the slope of the line.

With the data on hand and a combination of statistics and judicious extrapolation, I am providing a numerical framework for discussing the Sasquatch. Such guidelines can and should subsequently be modified by additional data, but will resist extravagant claims or wild speculation unless they are buttressed by substantial new data and not just isolated anecdotal reports. The statistical approach will serve to blunt the impact of included spurious, duplicate or erroneous data. Readers who wish to delve deeper into the subject of allometry, including the risks and pitfalls of interand intraspecific scaling, will find details in such sources as Calder (1984), Jungers (1985a), Martin (1984), Martin and Harvey (1985), McMahon and Bonner (1973) and West et al. (1997).

I wish to emphasize that this publication constitutes personal research and has in no way been aided or financially supported by the academic institutions with which I am or have been affiliated.

Methods

Most of the data were collected by Green (1968, 1978, 1980 a, b, c) of Harrison Hot Springs, British Columbia, Canada, over the past 40 years. All the data originate from the Western States of the USA (Alaska, Washington, Oregon, California, Idaho, Nevada, Montana, Utah, Wyoming, Colorado, New Mexico) and the Western Provinces of Canada (British Columbia and Alberta). They have been further supplemented by some published values (Napier, 1972; Hewkin, 1987), by the records of the North American Science Institute as collected by the Bigfoot Research Project under the direction of Peter Byrne, by a small personal collection, and by a few details visible and measurable in the Patterson movie (Bayanov et al., 1984; Glickman, personal communication; Glickman, 1997; Hunter and Dahinden, 1993; Krantz, 1992; Perez, 1992; Sprague and Krantz, 1979). Statistical calculations and graphing were performed with Statworks and Kaleidagraph on a Macintosh computer.

Enlarged prints of Patterson film frames referred to in a subsequent section are commercially available from Progressive Research, Dept. 291, 720 Sixth Street, New Westminster, British Columbia, Canada V3L 3C5.

Results and discussion

Foot Length

Footprints are the standard stock in trade of Sasquatch research, and their sometimes inhuman length assures almost immediate measurement, even by first time witnesses. Such measurements or estimates benefit from the fact that they are made in the cold light of day, often with a ruler and generally removed in time from the adrenalin-induced jitters experienced after most direct encounters. On soft ground, slide-in of the foot might elongate the heel somewhat, although it thereby also points it. Snow prints always incur the criticism of possible enlargement due to melting except in a thin layer of fresh snow. This criticism is apparently not based on experimentation with snow footprints and may be groundless. Conversely, expert+ly collected walking and running prints, laid down by the same animal in a thin layer of soft mud overlying clay hardpan, showed no slippage whatsoever (Heryford et al., 1982). In all cases, the flat Sasquatch footprint corresponds to a human foot outline rather than a human walking print, in which the arch may not touch a hard surface. Comparison of prints in a Sasquatch trackway show a common tendency of the toes to be curled, thereby shortening the measured foot somewhat. Repetitive measurement of some individuals are undoubtedly and inevitably included, since their common identity cannot be ruled out under most circumstances.

Fig. 1

Fig. 1 — Histogram of Sasquatch footprint lengths (N = 706), binned by 2 inches ( 5.1 cm). Statistics are contained in the text

Descriptive statistics of the collected footprint lengths (Fig. 1) are as follows:

Both mean and median have changed little with addition of data over the past years. The standard deviation implies that 99.73% (? 3 SD) of the footprints of the population are going to fall between 6.3" and 24.9" (16.0 and 63.2 cm). The distribution has a tail at either end and a sharp median, giving the curve a kurtosis (the peakedness or flatness of a statistical distribution) slightly above unity, i.e., more peaked than a normal distribution. This aspect is not supportive of a significant sexual dimorphism, as has been proposed for the Russian Wildman (Sapunov, 1988), in which a bimodal distribution depresses the kurtosis below unity. At most it can be speculated that at the median of footprint size, the sexual dimorphism does not exceed 2" (5 cm) in foot length, or roughly a foot (30 cm) in body height. Reproductively mature females (as judged by the presence of an infant; see below under Growth) range in foot length from 13" to 19" (33 to 48 cm), as collected to date. Hence, the largest prints are most probably from males, also supported by eyewitness reports of such animals being more facially hirsute and devoid of breasts. Hence, the largest height difference between the sexes might amount to 24" (60 cm).

The slight skewness of the curve (asymmetry of a statistical distribution) to the left of the mean might be attributable to the contribution of juveniles smaller than the population mean and their attrition before adulthood. The normal distribution overall argues compellingly against any alternative hypothesis to the existence of the Sasquatch as a cryptic species, in that production of fictitious data over 40 years by hundreds of people independently of each other would have generated a distribution with many peaks (Sapunov, 1988). A further factor that supports the authenticity of the data is the fact, that foot length, foot width, heel width and gait are interrelated in a logical and cohesive fashion, a congruence not plausible by pure chance.

As a telling comparison, Napier's collection (Napier, 1972) can be taken by itself. Its 59 footprints have a mean length of 15.5" (39.4 cm), a median of 16" (40.6 cm), and a standard deviation of 2.99" (7.59 cm). Thus, the mean of his collection deviates by merely 2 millimetres from the larger population mean.

For comparison, the American adult male foot has a mean length of 10.4" (26.5 cm; N=672) and the female 9.5" (24 cm; N = 225) (Robinson, 1990). The maximum human foot length recorded, 18.5" (47 cm), belonged to a pituitary giant (McMahon and Bonner, 1983) and clearly represents a pathological state.

Many of the data points represent a single measurement out of a trackway that might have extended over many yards or in some cases over several miles, where the ground and expertize of the investigator allowed uninterrupted tracking. Undoubtedly, only a fraction of the population of any species is ever represented by recorded footprints. Given the Sasquatch with a life expectancy of around 40 years (see below) and a montane, wet environment not conducive to the preservation of footprints, this collection of 706 prints over 40 years years speaks of a substantial population, probably in the "low thousands," as speculated by Krantz (1992).

Ball Width and Width Index

One of the characteristics of Sasquatch footprints that sets them apart from their human counterparts, aside from length, is the disproportionate width at the ball of the foot (Fig. 2), a ratio that is reminiscent of the foot of a human infant. The width is subject to more alteration during walking than the length due to lateral expansion in different substrata, but no allowance for this error source can be made. Descriptive statistics of the collected footprint widths are as follows:

Fig. 2

Fig. 2 — Histogram of Sasquatch ball width distribution (N = 410). Statistics are contained in the text

This width can be represented directly in relation to foot length (Fig. 3), but a more common display, favored by the shoe manufacturing industry, is the ratio of width divided by length, called the width index, a dimensionless number that reduces two variables to one ratio. If these values (0.46 for the mean foot size) are plotted against foot length (Fig. 4), the calculated regression line shows a minimal decrease in the ratio, i.e., the width increases as the 0.83 power of length (R = 0.705). This means that the width increases slightly more slowly than the length. The scatter of the data is such that this regression line is primarily included to serve as comparison to the change in the human foot. This identical tendency has been studied in human feet over a range of 6" - 12" (15.2 - 30.5 cm) (adult men and women; N = 897) (Robinson, 1990), where, however, the progressive narrowing of the foot with increasing length is much more pronounced and more tightly documented (Fig. 3, lower line). Almost the entire set of graphed Sasquatch footprints has a greater width index than average human feet do.

Fig. 3

Fig.3 — Scattergram of width of Sasquatch footprints (N = 410) plotted against foot length. The computed regression line indicates that the foot width increases as the 0.83 power of foot length, i.e. the width does not track the length isometrically, but lags slightly

It is obvious from the scatter of the data that enormous individual variations exist, partly by dint of embedded presumptive sexual dimorphism. Although sufficient data are not available, the feet of females may be narrower than those of males. The Patterson female has a width index of 0.41, comparable to that of human infants (0.43; Roche and Malina, 1983). Similar individual and sex-linked variations can also be found among people.

Fig. 4

Fig. 4 — Scattergram of the preceding data (N = 410) converted to width index (width/foot length) and plotted against foot length. The short regression line refers to combined male and female human data (N = 897) from Robinson, 1990. Both human and Sasquatch feet get proportionately narrower with increasing length, but Sasquatch feet remain close to a 0.5 width index.

Heel Width and Width Index

Heel width statistics were anticipated with particular interest, since Krantz (1992) speculated that the width of the heel would have a direct, possibly predictive, relationship to weight. He adduces the observation that the width of the talus represents a stable proportion of the human heel width and is a function of the bearing strength of the pertinent joint cartilage. At first sight, the heel width histogram mirrors (Fig. 5) that of the foot lengths rather closely, though being lower in numbers. The widest Sasquatch heels challenge one's credulity unless one has seen the proportion of the heel to the size of the whole foot.

Fig. 5

Fig.5 — Histogram of Sasquatch heel width distribution (N = 117)

Descriptive statistics of the collected heel widths are as follows:

As is the case with the ball of the foot, the heel does not grow isometrically with the length of the foot but lags behind (Fig. 6), as the human heel does. The Sasquatch appears to rely less on the heel plant in walking, but rather bears more of its weight on the broad anterior part of the foot, distal to the metatarsal hinge (Meldrum, personal communication) or, for that matter, more evenly distributed over the entire sole in the absence of an arch. Placement of the Sasquatch foot on a suitable substratum has been observed to produce a slapping sound, implying a foot placement that is not congruent with a heel plant and a subsequent forward rolling of the foot, as occurs in the human foot with its rigid arch. In an expertly documented track of footprints (Heryford, 1982), the footprint changed from a normal shape during calm walking to a round footprint, i.e., the anterior half of the foot, during running (step length changing from 4' to 9' (122 to 274 cm), in which the heel never touched the ground. The scatter of the heel width data argues against using these values in weight estimates.

Fig. 6

Fig. 6 — Scattergram of heel width index (heel width/foot length) plotted against foot length (N = 117). The regression line shows a proportional narrowing of the heel with increasing foot length.

From: Cryptozoology Vol. 13: 47 - 75

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