The Probability of Forgeries: Reflections on a Statistical Analysis
The past few years have witnessed intense interest in inscriptions that have originated in the antiquities market. More than a few cover articles in Biblical Archaeology Review have been devoted to the topic, and dozens of pages of the journal have been generated to treat these inscriptions. These inscriptions have also found a place in peer-reviewed journals and other scholarly publications.  Other print media have followed suit, and the interest and publicity reached a climax at the very end of 2004 with the coverage of a reputed forgery conspiracy by international news organizations. 
While it is impossible to know all the reasons behind this interest, there are several reasons that are not hard to understand: many of the inscriptions mention well-known biblical figures; there are romantic stories surrounding the discovery of these inscriptions; and there are even controversies and conspiracy theories. These are things that journalists and publishers love. All of these factors have resulted in much publicity and an intense interest in whether or not these inscriptions are authentic.
For one of the authors of this essay (Vaughn), this interest reached a crescendo shortly after the discovery of the so-called James Ossuary. Soon after its discovery, several people called Vaughn and asked him what he thought. He soon received photographs and more details via e-mail. There were calls from reporters as well as colleagues at other schools. He shied away from the reporters, but he told his colleagues that he was, in general, skeptical. His immediate reason for skepticism was that the inscription violated his TGTBT rule. What does TGTBT mean? Quite simply "too good to be true."
Why the TGTBT Rule is Not Arbitrary
Several colleagues asked Vaughn if his TGTBT rule was arbitrary, and this led Vaughn to explain why he developed this rule long before the James Ossuary was discovered. The TGTBT rule was developed as a way to help him as an epigrapher exercise caution and not fall into the temptation to "create" readings that were not supported by the data, as explained below.
When Vaughn was first being trained as an epigrapher and palaeographer in the early 1990s, he studied new techniques for photographic documentation and study of inscriptions with Bruce Zuckerman, Ken Zuckerman, and Marilyn Lundberg of West Semitic Research. During this time, B. Zuckerman shared some advice for working on inscriptions that had been given to him by Moshe Goshen Gottstein. Gottstein stressed that all epigraphers should have a set of rules that they followed while reading and deciphering Semitic inscriptions. Further, they should be clear and honest about their rules, and they should acknowledge when they break their rules. Only then will other scholars be able to evaluate their work and findings.
With this advice in mind, the following are a summary of Vaughn's "rules":
1. Start with the letters that are unambiguous and fill in as much as possible with some degree of certainty. Do not make restorations or conjectures until later in the process.
2. Ancient inscriptions were meant to make sense. So, try to reconstruct inscriptions in the most sensible manner possible without wild reconstructions. The simplest explanation is to be preferred.
3. Be willing to trust your feelings for a reading or an inscription—this is not arbitrary, but rather a recognition that an epigrapher must develop both an eye and feel for inscriptions.
4. Related to rule #2, readings should be consistent with other inscriptions. If the readings are not consistent with other inscriptions, there should be a good reason. This is where Vaughn goes back to his first two principles. He is willing to read an inscription as unique if the letters clearly indicate this reading or if the unique reading is required for the inscription to make sense. However, he does not prefer unique readings unless he has no other choice. Likewise, he does not trust his feeling if the reading is unique and he has no other choice.
5. Another rule to help place constraints on his desire to make sense of inscriptions is the TGTBT (too good to be true) rule. The TGTBT rule places constraints around this feeling for deciphering inscriptions: if something is "too good to be true," then the epigrapher should be skeptical unless there is compelling evidence to authenticate the reading. In other words, the epigrapher should avoid sexy decipherments unless they can be proven: the epigrapher should not play to the crowd, as it were.
6. The epigrapher should be honest with others if one of these rules is violated. Once again, this does not mean that a rule cannot be violated, but the epigrapher should be honest about his or her method and biases in order that others can evaluate the work. 
A Desire to Scientifically Test the TBTBT Rule
The above set of rules explains why Vaughn (along with some other epigraphers) was by definition a skeptic when many of the alleged forgeries were first brought to light. Yet, even though these rules were developed in an effort to be careful, one might question whether this skepticism is really necessary. It is at this point that Vaughn had a conversation with a colleague who is a statistician, Carolyn Pillers Dobler. Vaughn and Dobler discussed whether it would be possible to look objectively at various traits on seals and bullae in order to see if they were from the same group. They thought that the traits of objects from controlled excavations and from the antiquities market should be similar if both came from the same larger group; that is, from inscriptions that were authentic. Therefore, they undertook a statistical study to see if there were significant quantities of forgeries. They reasoned that if there were significant quantities of forgeries that had not been identified as such, then the TGTBT Rule should be taken even more seriously.
Vaughn and Dobler thus looked at Hebrew seals and seal impressions and studied a variety of traits to see if they could find statistically significant differences between seals and seal impressions from known and unknown provenance. They were amazed that such striking differences were found. They were actually shocked that they found as much evidence for the forging of Hebrew bullae as for the forging of Hebrew seals.
Their assumption going into the study was that it was more likely that Hebrew seals had been forged, but that there would not be a large number of Hebrew bullae that were forgeries.  Their reasoning was that it would be harder to fake a bulla than a seal and that it would not be profitable to fake a bulla. Although they do not follow the antiquities trade, they had heard that Hebrew seals drew large sums of money while bullae were much cheaper. The assumption was that the difficulty involved in faking a bulla combined with this economic factor would mean that bullae were safer.
It turned out that Vaughn and Dobler were mistaken. While that statistical study cannot be rehearsed in detail here, a few of the findings are summarized below. One of the traits studied was the type of register dividers on bullae:A register divider is something that divides the registers of writing on a bullae or seal. For example, as seen here, if a seal has writing on two lines (called registers), these top and bottom registers are typically divided from each other by some device. We note that the most common type of register divider for bullae is a straight line or lines. For bullae of known provenance, this type of divider was found 77% of the time (44 out of 57 items). However, there are a significant number of times (18%; 10 out of 57 bullae) where the registers in the bullae of known provenance were divided by "something else."  It is striking that while 18% of bullae of known provenance had register dividers of "something else," only 4% of bullae of unknown provenance were divided by "something else." From a statistical standpoint, these differences between the known and unknown groups are quite significant, and the chance that they would occur at random is less than 3 in 10,000. In other words, it seems that there is less than a 3 in 10,000 chance that the two groups (known and unknown) come from the same larger group. These probabilities would suggest that a significant number of the bullae of unknown provenance came from a different larger group (that is, they are forgeries).
The probability was even smaller when we looked specifically at the register divider classified above as "something else." Nine out of 57 (16%) bullae of known provenance were divided by a lotus bud, whereas only 6 out of 204 bullae (3%) of unknown provenance had a lotus bud. Naturally one asks why a sample that is four times the size of the bullae of known provenance would have fewer lotus bud dividers and only 3% compared to 16%. The odds of this distribution happening randomly are less than 2.3 in 10,000. Once again, these probabilities suggest that a large number of the "unknown" group come from a different larger group and are probably forgeries.
Why might these differences occur? One can only hypothesize, but Vaughn and Dobler have a good suggestion. If someone wanted to fake a bulla, she or he would want to make the bulla realistic and similar to other known bullae. Since most bullae have register dividers that are "lines" rather than a lotus bud, it seems more likely that the vast majority of faked bullae would have lines as register dividers rather than "something else." Surely at least a few of the bullae of unknown provenance are authentic, so this would probably account for some of those with the lotus bud dividers. Such a scenario cannot be proven, but it is logical.
What can be known is that there is only a 2.3 out of 10,000 chance that this phenomenon would happen randomly. These statistics point to the strong probability that a large number of the bullae of unknown provenance are forgeries. It should also be added that these statistics went against the initial conclusion that most of the bullae of unknown provenance would turn out to be authentic because it was more difficult to fake a bulla than a seal.
A Significant Difference in Actual Seals
Out of twenty-eight seals of known provenance, nine of them have some type of iconography and five of them (18%) have an ankh symbol as part of their iconography. Since only nine seals  of known provenance contain any type of iconography, we note that 56% of these seals with iconography have an ankh symbol. We notice that the percentages are drastically smaller with the seals of unknown provenance. Only eight of 495 (2%) seals of unknown provenance have the ankh symbol. The probability of this happening at random (if both the provenance seals and non-provenance seals come from the same larger group) is less than one in 10,000! Thus, this is a very strong indicator that the seals of known and unknown provenance come from different larger groups, and these data suggest the presence of a significant number of forgeries in the group of "unknown" seals.
Once again, Vaughn and Dobler hypothesize as to why this is the case. The following table summarizes the type of iconography that is found:
Notice that the seals of unknown provenance contain much more interesting iconography, but there are examples of many types of iconography on seals of known provenance. The iconography from seals of unknown provenance is well known from ancient Near Eastern art and cylinder seals. Much of this iconography is just not found on Hebrew seals with inscriptions. Vaughn and Dobler thus postulate that someone who wanted to fake a seal would create a piece of art that would be pleasing to the eye and would be more attractive to those associated with the antiquities trade.
Size of the Seals
The size of the seals was also studied. What was found was that seals of unknown provenance were almost all very close to the mean and the median in terms of length and width. This is what one would expect with seals and bullae that might be faked. If the seal or bulla was a fake, it would probably be constructed to be about the same size as most known seals or bullae. However, there was much more variation in the size of bullae and seals of known provenance. The only difference was that the correlation between length and width was much stronger. In other words, those of known provenance may have a greater length, but the width increased in proportion to the greater length. Those of unknown provenance were closer to the mean and median. Once again, this is what one would expect if large numbers of the unknown group were forgeries.
The differences in size were even greater when the depth of the seal was taken into account. Seals of known provenance increased the depth of the seal in proportion to an increase in length or width. There was much variation, but the correlation stayed almost the same. On the other hand, seals of unknown provenance did not proportionally increase the depth of a seal with an increase in length and width.
One can speculate why these differences might occur. It seems reasonable to assume that a forger would know about the approximate correlation between length and width, but such a person might not be aware of the needed correlation in terms of depth. Thus, seals of known provenance exhibit the expected correlation while those of unknown provenance do not. Once again, it seems that many seals are forgeries.
Conclusion: the Viewpoint of an Epigrapher
The ability to analyze more precisely the corpus of known seals and bullae will facilitate the attempts to fake inscriptions. The advent of computer technology in the last twenty years makes it even easier. A potential forger does not need to be one of three or four leading Aramaic scholars in the world to be able to find a rare syntactical form.  That person needs only to own a computer with a database of all the Aramaic texts and spend some time doing a few searches to come up with a form that will stump all but the top experts.
So what is the conclusion from these data? Vaughn has studied dozens of other Hebrew inscriptions (beyond seals and seal impressions), and he has studied more than a thousand seals and seal impressions. He has deciphered about twenty-five seals or other inscriptions that were previously considered unreadable, and he most recently corroborated with a team of scholars to provide crucial new decipherments to the silver plaques from Ketef Hinnom.  Vaughn has a good eye for inscriptions and palaeography, and he is probably able to pick out diagnostic features for dating of Hebrew inscriptions as quickly as almost anyone else. However, he honestly and humbly states that he can be fooled.
The statistical study presented in this essay suggests that other experts can also be fooled. Such an observation seems self-evident, but it runs against the popular method of authenticating Hebrew inscriptions. The popular magazine, Biblical Archaeology Review, has tended of late to support the authenticity of illicit inscriptions by enlisting the opinions of scholars and collectors who assert that these inscriptions are real. Little or no empirical evidence has been given. For example, in the most recent issue of BAR, the editor (presumably Hershel Shanks) provides a biography of Robert Deutsch (one of the antiquities dealers who is accused) and states that "he scoffs at young scholars who pontificate about forgeries without ever having handled these objects."  These ad hominem jibes are easy to throw into the discussion, but they do little to further scholarly debate.
The statistical study presented in this essay indicates that even the experts can be fooled. As emphasized previously, it is not simply a matter of having experience in examining inscriptions. One of the authors of this essay (Vaughn) has examined personally almost every bulla of known provenance as well as dozens of bullae of unknown provenance. He has visited museums and collections around the world and concentrated on items that are known as authentic because they come from excavations. This experience is important, but it is not fool-proof. Even the "experts" must utilize other methods to make sure that they are not fooled by would-be forgers.
Vaughn acknowledges that others have better eyes than his, but he would suggest that they too can be stumped—we are all only human. All that epigraphers can say without more sophisticated testing is that this inscription is consistent with everything that they have seen. In the end, it is just an opinion, and one that cannot be proven. The study presented here shows that one should be extremely cautious in considering seals and seal impressions that originate from the antiquities market. While this statistical study cannot state with certainty which items are authentic and which are not, it does indicate a very high probability that many of these inscriptions are indeed forgeries. As pointed out at the beginning of this essay, this statistical study was completed long before the current forgery scandal was known. The current situation and the indictments that have been brought forward would only seem to reinforce the findings presented here.
Andrew G. Vaughn, Gustavus Adolphus College, email@example.com
Carolyn Pillers Dobler, Gustavus Adolphus College, firstname.lastname@example.org
Notes: 1. Many academic journals such as Bulletin of the American Schools of Oriental Research do not consider articles that present an unpublished inscription that originated on the antiquities market.
2. It should be noted that this statistical study was completed before any of the news of the alleged forgery scandal were known. The statistical part of this essay is an abbreviated version of a longer, more technical article that will appear in the forthcoming festschrift for Amihai Mazar. (Andrew G. Vaughn and Carolyn Pillers Dobler, "A Provenance Study of Hebrew Seals and Seal Impressions—A Statistical Analysis," forthcoming essay in I Will Tell Secret Things from Long Ago (Abiah Chidot Menei-Kedem—Ps.78:2b): Archaeological and Historical Studies in Honor of Amihai Mazar on the Occasion of His Sixtieth Birthday, ed. by A. Maeir and P. de Miroschedji [Winona Lake, Ind.: Eisenbrauns, in press]). The other parts of the present essay are a reflection by Vaughn on the challenges of examining inscriptions in general. The statistical research for that article was completed over three years ago. It is quite gratifying that recent criminal investigations seem to support our statistical study, but it must be emphasized that the present study was not prompted by the current scandal.
3. A nice example in point is the Mesha Stele—an inscription that is "too good to be true" but almost certainly "true."
4. Vaughn even stated in a book review published in JBL and RBL that the authenticity of bullae was much more certain than that of seals because the impressed objects in fired clay would be difficult to fake. This statistical study and the current forgery would suggest that he was wrong. See Andrew G. Vaughn, Review of Robert Deutsch, Messages from the Past—Hebrew Bullae from the Time of Isaiah through the First Temple in JBL 121 (2002) 339-43; and Andrew G. Vaughn, Review of Robert Deutsch and André Lemaire, Biblical Personal Seals in the Shlomo Moussaieff Collection in JBL 121 (2002) 339-43. Both reviews were also published in RBL (http://www.bookreviews.org).
5. It should be noted that the numbers do not add up to 100% because some bullae do not have any register dividers.
6. One notes from the accompanying chart that the types of iconography add up to fourteen, whereas only nine seals actually have iconography. The reason for this difference is that some seals have multiple types of iconography on the same seal. There are nine seals with iconography and some of these nine seals have more than one type of figure.
7. We are referring to the rare syntactical Aramaic form that is found in the James Ossuary. For an analysis of the Aramaic, see Edward M. Cook, "Remarks on the Aramaic of the James Ossuary," http://www.bibleinterp.com/articles/Cook_remarks.htm (November 2003).
8. Gabriel Barkay, Marilyn Lundberg, Andrew G. Vaughn, and Bruce Zuckerman, "The Amulets From Ketef Hinnom—A New Edition and Evaluation." Bulletin of American Schools of Oriental Research 334 (2004) 41-71.
9. Hershel Shanks, "Update: Finds or Fakes," BAR 31:2 (2005): 58-69; p. 60 cited here.
Citation: Carolyn Pillers Dobler , Andrew G. Vaughn, " The Probability of Forgeries: Reflections on a Statistical Analysis," SBL Forum , n.p. [cited March 2005]. Online:http://sbl-site.org/Article.aspx?ArticleID=372