I am a Bayesian epistemologist. And in line with the independent findings of the philosopher of history Aviezer Tucker, I developed and applied under peer review a way to model historical reasoning with Bayes’ Theorem (method, in Proving History; application, in On the Historicity of Jesus), because that allows us to see the actual logic and premises of historical arguments, making them easier to vet and verify or correct—rather than simply using vague declarations of intuition that can’t be vetted or even diagrammed in any logic, a procedure historians have usually foolishly and unproductively relied on, a folly whose consequences were extensively demonstrated by David Hackett Fischer in his witty survey of the matter in Historians’ Fallacies.

The simplest form of the Bayesian equation to use for this purpose is the Odds Form, in which the odds on any claim being true equal the prior odds times the likelihood ratio, which is the relative odds of the evidence being as it is. This is the form I use in my peer reviewed work On the Historicity of Jesus. I’ve been asked a few times to do a walk-through of how the math works there. So I will accomplish that here. This is actually covered across the book as well, as there are many aspects to account for, and I assume there that readers haven’t been exposed to probability theory before. But what’s needed now is something simpler and more direct. For all the many details, you still have to go into the book to get those, along with the footnoted citations of evidence and scholarship that form their basis. Here we’ll just strip all that away and generalize to the basics, of pretty much just the math (which is really, just, the logic), so you can see what is mechanically going on.

I have written up helpful articles on the mathematics involved here several times before. For example, you might benefit from reading one or all of the following:

• Advice on Probabilistic Reasoning
• What Is Bayes’ Theorem & How Do You Use It?
• A Test of Bayesian History: Efraim Wallach on Old Testament Studies
• How to Correctly Employ Bayesian Probabilities (Jesus Edition)
• Kamil Gregor on the Historicity of Jesus

Now to the task at hand…

Doing the Math

One tool you can use along with this more direct and simplified summary is the Bayesian Calculator made available in the CHRESTUS app (works in iOS and Android). That calculator allows you to input the prior odds, and then the evidentiary odds for every item of evidence you want to isolate, assess, and include—because you can create an entry for each and assign relative odds to it. It also allows you to calculate upper and lower error margins at the same time. The calculator will then do all the math for you, including converting the final odds to a probability.

But if you are going to do the arithmetic yourself, you need to know how to convert odds to probabilities, and vice versa. If you say something has a 1 in 3 chance of happening, that’s a probability. It translates into decimal notation as 33% (a 1 divided by a 3). To convert this into odds, you have to break it out into its parts: a 1 in 3 chance, means 1 to 2 odds. The 1 and 2 sum to 3, so “1 to 2” means the same thing as “1 in 3” (because you have 1 chance compared to 2, which means there’s 1 chance out of a total of 3: because 1 + 2 = 3). Thus “1 in 3” or “33%” will be represented in an odds-based equation by 1/2. This is crucial to grasp, so you know what’s going on here. Then, to convert it back, you do the same math in reverse: for 1 to 2 odds, rather than divide 1 by 2, you divide 1 by 3, because it’s 1 out of a total of 1 + 2 = 3 chances, not 1 out of a total of 2 chances (likewise 3 to 4, or 3/4, becomes 3 in 7 and thus 3 divided by 7, and so on). So when you see “odds are 1 to 2,” you know that means “the probability is 33%,” because 1/(1 + 2) is 1/3 and thus 0.33[…]. A 1/2 odds is thus not a 50% probability; it’s a 33% probability. 

You may grasp this the more easily when we spell out the actual total probability: a 1/2 odds means the same thing as 33.3%/66.7% (rounding). Because 33.3 + 66.7 sums to 100% and thus accounts for the entire probability-space. And since 66.7, which means 66.6[…], is twice 33.3[…], this is represented in the odds form as 1/2. Thus, 33/67 is 1/2. So a 33% chance Jesus existed is here the 1, leaving us with the 2 as a 67% chance Jesus didn’t exist, twice that 33%.

You also need to know the difference between actual and relative odds. Actual odds are as just explained, and that appears two places in the Odds Form of Bayes’ Theorem: the prior odds, and the posterior (or final) odds. Relative odds appear in the only other term in that equation: the evidential odds, or “likelihood ratio.” Relative odds are what you get when comparing two independent probabilities. For example, if you are faced with a fork in the road, and there is an 80% chance of getting lost if you turn left but a 100% chance of getting lost if you turn right, the relative odds between those two choices is 80/100 or 4/5. From relative odds you cannot calculate the probabilities; you only know their ratio. For example, a relative odds of 4/5 could result from either that 80/100, or from a competely different pair of probabilities—like, say 20/25. In that case, there would be a 20% chance of getting lost going left and a 25% chance of getting lost going right. Yet that produces the same relative odds as the 80% and 100% do, signifying the difference in likelihood is effectively the same in those two cases. 

Note that relative odds are often a lot easier to estimate or know. For example, you don’t need to know what the probabilities are, if you can work out that, whatever they are, you are twice as likely to get lost going left as going right; as then the relative odds are always going to be 2/1, no matter what the actual probabilities are (whether 20%/25% or 80%/100% or 8%/10% and so on). This is why the likelihood ratio in Bayes’ Theorem is so useful a tool.

Margins of Error

Another thing you’ll need to get a handle on is this: any credible evaluation of the probability of something must acknowledge one’s lack of precise knowledge or certainty. In subjects such as this you can’t know any probability to even a percentile, much less multiple decimal places. There will always be some margin of error you have to accept, which will be represented by the farthest extremes on either end you can believe at all reasonable. For example, if you are ballparking your chances of winning a hand at poker, and aren’t a card shark or mathematician, you might still have enough information and savvy to know your odds of winning that hand can’t be lower than, say, 20%, nor can they be higher than, say, 67%. That then is your margin of error: you don’t know what the probability of success is, other than that it is “somewhere” in between 20% (a 1 in 5 chance) and 67% (a 2 in 3 chance). The “20%” is your lower bound; the “67%” is your upper bound. And a margin like that (of 47 percentiles, almost half a complete probability range) is rather large; it signifies high uncertainty and imprecision.

There is more that can be said about that, such as regarding the role of and difference between this, which can be referred to as a “confidence interval,” and a “confidence level,” which is, separately, how certain you are that the probability falls somewhere in that window. But if you want all that detail, you should consult Proving History, in which I lay out all the mechanics of probability that relate to this (for example, “confidence interval” is in the index, as also “margin of error”). For the present purposes, all you need is this: if you estimate probabilities as much against a claim as you can believe at all reasonable to accept, that will build the lower bound of your margin of error; then if you estimate probabilities as much in favor of a claim as you can believe at all reasonable to accept, that will build the upper bound of your margin of error. In each case, if you reject probabilities you think would not be reasonable (being too unreasonably high, or too unreasonably low), then the resulting conclusion (the resulting range of probabilities encompassing your margin of error, like the “20-to-67%” example above) will logically, necessarily, be the only reasonable range for you. Because then, any probabilities outside that range would require you to accept something you recognize as simply unreasonable. This way you avoid having to work out any precise confidence level; since “reasonably confident” estimates will all commute to a “reasonably confident” conclusion regardless.

This is how you can find out what you must believe, given your own personal assessments. You can then test whether your assessments are objectively reasonable by various techniques (such as I lay out in Proving History generally and On the Historicity of Jesus specifically). I’ll mention some of those here as we proceed. But keep in mind, you must always choose either or both margins of error to asses and discuss. You can’t just calculate one probability and declare that “the” probability. That would be to disguise or ignore your uncertainties, which can only leave you vulnerable to all manner of fallacies and errors (many of which as discussed in my survey of Kamil Grefgor’s error-prone critique of all this, for example).

With that in mind, and to again keep things as simple as possible, I shall here on out only be discussing my upper bound in OHJ: the highest probability Jesus really existed that I can find at all reasonable to believe.

Ramifying the Hypotheses

The easiest approach is binary: compare two hypotheses, which exhaust all—or nearly all—of the available probability-space. 

Thus, we shouldn’t “burden” historicity with being overly ambitious or complicated. Most “lists” of what we supposedly can “know” about the historical Jesus actually reduce the probability Jesus existed, if you “require” those lists to be all true for Jesus to have existed. For example, that Jesus was specifically baptized by John the Baptist. There are actually independent reasons to doubt that (which are well represented in the peer reviewed literature yet generally just dogmatically ignored, because Jesus historians have a serious methodology problem), but set that aside for a moment. It is a matter of logically necessary fact that P(Jesus) > P(Jesus*), where “Jesus*” means “Jesus existed and was baptized by John the Baptist.” I won’t burden you with the formal proof. Just be aware, any time you “add” things, it always reduces the probability of the collection, compared to a less ambitious version of your theory—in this case, “Jesus existed and either he was or was not baptized by John the Baptist.” That’s far easier to prove than trying to tack more and more on to what you think is “required” for “Jesus existed.” So don’t tack anything on—if you can help it.

The thesis you want to test should be the most probable any can be. So, only assert as hypothetically required the least possible details. Hence “minimal historicity” means the absolute mininum, such that if you remove any one thing from the definition of “Jesus existed,” it is simply no longer the case that Jesus existed. I survey what this minimum looks like (it’s a lot more minimal than you think) in OHJ (Ch. 2). The same needs to be done for “minimal mythicism.” But in that case, there are far more logically possible causal explanations than have any plausibility, so we have to logically account for those; but we won’t have to mathematically account for them. For example, “twelve disciples hallucinated an entire ministry of Jesus for a whole year” and “the Roman government back-fabricated the entire New Testament after the Jewish War to simultaneously make fun of and pacify the Jews” and even “a cabal of fringe Jews decided to make a one-for-one copy of Horus to worship, for…reasons, and named it Jesus” and “all ancient texts and artifacts were invented by a monk named George in 987 A.D.” are all “logically” possible, but have vanishingly small prior probabilities—even collectively they occupy less than a tenth of a percentile. And we are rounding to whole percentiles, with a margin of error in the tens of percentiles, so a “tenth” of a percentile is literally, mathematically, invisible in any math we then do. Therefore we can simply ignore all these alternatives, exactly as we do the “Jesus was a supernatural incarnated cosmic archangel whose body was manufactured inside Mary’s womb by magic…” etc. Even collectively, all supernatural Jesuses have a vanishingly small prior, and so on the historicity side of the equation, “supernatural” Jesus can also be ignored in the math. We will never even consider it.

The end result is a near perfect division of all one hundred percentiles of the prior probability space between “Jesus existed” and “Jesus didn’t exist.” The latter will remain solely the only causal account of the evidence that doesn’t have a vanishingly small prior. In other words, what is the least we can propose that would explain the evidence without a historical Jesus, without adding anything that is absurdly improbable right out of the gate. The answer to that is a stripped down (and thus a minimalized) version of the Doherty thesis: Jesus was originally believed to have undergone a cosmic drama only known through revelation and scripture, and was turned into a historical person a relative lifetime later, and then that new version politically eclipsed the old. I survey what this minimal mythicism looks like (it’s also a lot more minimal than you think) in OHJ (Ch. 3). 

I then provide all the background evidence that establishes that this actually, indeed, requires no absurd assumptions, unlike all those other “theories” (in Chs. 4 and 5). For example, savior gods whose lives were originally imagined as cosmic or mythic, and known only by revelation or fable, yet who were historicized in later biographies, were not unusual, but a dime a dozen. In fact, this was a particular fad at exactly the time Christianity arose. And this included examples immensely popular in provinces directly adjacent to Judea and heavily populated by Jews who maintained influence and made regular pilgrimmages there—such as Osiris, whom Plutarch tells us was taught among insiders to have become incarnate in outer space either on or below the moon, where he is killed by the Egyptian version of Satan, only to rise from the dead three days later in a new more glorious body, and ascend to heaven in power, to grant salvation to those baptized in his name. But to outsiders, it was taught in the equivalent of “Gospels” for Osiris that he was a real historical pharaoh whose incarnation, death, and resurrection occurred on Earth, in Earth history. This exactly matches the Doherty thesis. That it was fully realized already for one god (and more or less for many others as well), disproves any contention that it was improbable. It’s obviously the most likely way Jesus was developed if he didn’t exist. No other “theory” of his not existing has such massive a proof of concept in existing background evidece. So that’s our minimal mythicism.

These therefore are the two hypotheses we are comparing; and we can mathematically act as if they divide the entire space of possibilities. So now we can return to the math.

The Prior Odds

The basic equation is, quite simply, prior odds times evidential odds. So we have to start with the prior odds. In the case of Jesus, that means answering one simple question: in the set of all people of that era most similar to Jesus in relevant characteristics, how typically do they turn out to be historical, rather than mythical? This is a straightforward question about a frequency. You have to avoid the disingenuous or foolish error of looking at the wrong set of of people, as also the unproductive error of looking at too small a set. You need a set large enough to get some usable frequency-range from, but small enough to more accurately fit Jesus, because if you don’t do the latter you are violating a fundamental rule of epistemic logic: you cannot ignore information you have. If you know Jesus belongs to a narrower reference class, you cannot ignore that. You have to take it into account. Likewise for the former error: if you look at too narrow a class, so narrow you can extract no frequency information from it, you miss the forest for the trees, which is the same mistake—ignoring information you have.

I have already covered all this on all its own terms in Jesus and the Problem of the Fraudulent Reference Class. But for the present, you just need to know two things: 

• First, the prior probability is not the posterior (or final) probability. A lot of people “freak out” when you find that someone has a low prior probability of having really existed. Because they don’t understand that that is not “the” probability of their having existed. Evidence can turn everything around. Alexander the Great might have been found to have a low prior probability of being a real person, given how extensively mythologized he was (that isn’t exactly the case, but let’s suppose it is). But the evidence he existed is so vast and overwhelming it completely reverses and utterly drowns any low prior he might have started with. So starting with a low prior probability does not spell doom. It just means someone looks a lot like a mythical person, at first glance and in context, so you have to check if evidence indicates they are not such a person but just a historical person heavily mythologized.
• Second, you should know how to get different results, if such we should. In actual reality, most people (including Alexander) don’t belong to such a heavily mythologized reference class. I have already discussed this point with regard to Hannibal and Spartacus: military generals who fought wars in a literately documented place and time tend to have existed, no matter how mythologized they also get. So we should expect that usually to be the case. This is not so for worshiped savior heroes who only appear in history in sacred biographies. People who appear only in heavily mythologized contexts and whose existence is fundamentally of religious rather than mundane political importance tend not to have existed (think, Moses, Osiris, Hercules, Romulus). And Jesus belongs to that set. Alexander the Great does not. He was a worshiped savior hero, and was heavily mythologized, but he first appears in, and is predominately found in, mundane political history, unlike Jesus. The physical and textual evidence of his existence is also overwhelming; but here we are only talking about his prior probability, which is a function of what usually happens with characters “like” him.

The best proxy I found to evaluate the frequency of historicity for figures like Jesus was the Rank-Raglan set, properly ramified. This is because it is the most clearly defined, and thus narrowest set (belonging to it by accident is statistically too improbable to credit) that contains the most members, enough to get at least a rough idea of a frequency of historicity from (no other sets so clearly and narrowly defined contain as many as 16 members). But we needn’t rely solely on that. Jesus belongs to more mythologized sets of people than anyone else in antiquity. In fact, he appears to be one of the most mythologized figures of the era. Whereas he belongs to no mundane sets capable of overriding that assessment. For example, unlike Alexander, he does not first appear in ordinary political speeches, memoirs, documents, and histories, and he was not a prominent political actor. Indeed, Jesus plays no significant role in the political history of Judea as recorded by Josephus (or by anyone else). And that’s the case even if we count the Testimonium Flavianum (even though we shouldn’t), which never ties anything about Jesus into any of the surrounding causal-political narrative—his existence makes no difference to the political or military course of events in Judea. He is solely a religious founder, a worshiped savior hero. And those people tend not to exist; unlike military leaders or major political actors (or even minor functionaries), and the like.

In other words, what did people back then usually make up? People like Jesus. Not people like Alexander, Spartacus, Herod Antipas, etc. (See my whole chapter on how we determine the historicity of these and several other people back then, and why we lack for Jesus what we have for them, in Jesus from Outer Space). So we have to start with more suspicion about Jesus than we do with Alexander et al. This is represented in the logic of argument with a lower prior probability. As in fact it has to be. It would be dishonest to act like Jesus was “just the same” as all those other people. He’s not. He’s actually far more like a very different group of people, ranging from Osiris and Romulus to Hercules and Moses. And in that group of people, historicity is actually rare—not typical. In formal terms, if you put everyone Jesus is most like in a hat and drew one of them at random, the probability they’d be a real person has to be the same. You can’t “special plead” Jesus into having any different odds than that—except with specific evidence, which is what we get to next. It therefore cannot affect this frequency. 

Putting Jesus in the correct reference class, I find the upper bound (the highest frequency one can at all reasonably believe) to be a 1 in 3 chance Jesus existed. Because in no way can more than 1 in 3 people in that set (of heavily mythologized savior heroes) have likely existed for real. If you check the list and the evidence pertaining, no honest person can disagree with that. There just is no credible evidence more than that many ever existed. This is, still, prior to considering any evidence that Jesus might be an exception to this. So it is not yet the probability Jesus existed. It’s just the prior probability. So if you want to get a different prior, you have to prove—and prove with empirical facts, not just gut “feelings” or unevidenced assertions—that Jesus belongs to a reference class whose members exist at a higher frequency than that. But you still can’t ignore classes he already also belongs to. You cannot ignore information you have—that is a defining feature of apologetics, not legitimate historical reasoning.

Hence I discuss this in OHJ (Ch. 6.5, “The Alternative Class Objection”). The point there is that you can’t, for example, just say Jesus belongs to the Josephan Christs class (and he does: messiahs, hence Christs, portraying themselves as a new Joshua, which is “Jesus” in Greco-Latin transliteration) and “therefore” has the same prior probability of existing as they do, because we also know he belongs to the heavily mythologized and worshiped savior hero class, and they do not have the same prior probability of existing. We don’t know the frequency of Josephan Christs who are also heavily mythologized and worshiped savior heroes who really existed, so we can extract no information about the prior probability for Jesus from that class. And between the two classes apart, Jesus more squarely belongs to the myth-heavy class than the other. We also can’t speak of modern reference classes of religious founders, because that’s the wrong context; back then, religious founders were more typically mythical than they are today.

So in OHJ, I come to the maximum prior probability for Jesus, like any other heavily mythologized savior hero, of 1 in 3, which of course translates into a probability of 33%. It also translates to an odds of 1 to 2, or 1/2 (since, again, 1 + 2 = 3, hence “1 in 3” means “1 to 2”). In other words, the set of all such persons is 1 part historical and 2 parts not. Thus at best 1 out of every 3 such people is historical. Which means at least 2 out of every 3 such figures turns out to be mythical, and only historicized later. And this is not a “guess.” It’s an observed frequency in the data; in fact, well above the observed frequency: which is why there is no reasonable way to get those prior odds higher. And those other heroes were also, indeed, all historicized: every single mythical hero in antiquity was “marketed” as a real person who existed in history, even when there is no reason to believe they ever did. So there is nothing unusual about Jesus being so—to the contrary, that would be typical. 

And that is what must be represented in the math.

Evidential Odds

So, we can’t get to a prior probability that Jesus existed any higher than 1 in 3. Which when stated as odds equals 1 to 2: for every one such person who really existed, there were at least two such people who didn’t. Can we change that with evidence proving Jesus is one of the exceptions to that rule? To answer that question, you first have to determine what the evidence actually is. More often than not, “evidence” for the historicity of Jesus is bogus; it’s simply made up (see Historicity Big and Small: How Historians Try to Rescue Jesus and How to Successfully Argue Jesus Existed (or Anything Else in the World), or for the most egregious examples, 41 Reasons We’re, Like, Totes Sure Jesus Existed!). For example, no one named Thallus wrote about Jesus in the first century. That simply never happened. No such evidence exists.

So we have to nail down what evidence really does exist. When you go looking, you’ll typically find, almost none does. And that’s the real problem here. Jesus is the exact opposite of Alexander the Great, for whose historicity the evidence is extraordinary; for Jesus, it’s virtually nil. But in OHJ I did my best to be as charitable as reasonably possible to the case for historicity. There are, overall, four categories of evidence to consider: the evidence outside the Bible (“extra-biblical” evidence); the book of Acts (purportedly the first-ever history of early Christianity); the Gospels; and the Epistles. I thus assign a whole chapter to each in OHJ (chapters 8, 9, 10, and 11 respectively).

Once you have isolated what real evidence exists, the question you then need to ask is: how likely is all that evidence on either explanation? Because it is the ratio of those two probabilities that makes the “likelihood ratio,” the evidential odds, the next term in the equation. You can do this all together, or you can break out each item of evidence and assess it independently. But if you do that, you have to take into account the probabilistic fact that some evidence is not formally “independent,” but rather forms a dependent probability. For example, the book of Acts was written by the same author as the Gospel of Luke, who was expanding on the Gospels of Mark and Matthew (or Q, if you still believe that sort of thing; or both). Thus the probability of references to a historical Jesus in Acts is dependent on the probability of references to a historical Jesus in the Gospels. This means it is not an independent probability, and thus can’t corroborate the Gospels. If P(Acts|Gospels) = 1, regardless of whether Jesus existed or not, then Acts can never afford any evidence Jesus existed. There would have to be something in it that you can confirm was independent of the Gospels (on the importance of independent evidence in history, see OHJ, Ch. 7.1-2). 

To put it another way, the odds that the author of “Luke” would throw references to a historical Jesus into Acts even if Jesus never existed is already 100% once you’ve calculated (and thus accounted for) the probability that the author of “Luke” would throw references to a historical Jesus into his Gospel. As a depenent probability, P(Acts|G&~h), where G is “Luke’s Gospel” and ~h is “Jesus didn’t exist,” will simply be 1 (100%). It needn’t have been; you can have partial dependence (e.g. the probability of drawing a red card at poker goes down the more red cards have already been drawn, but doesn’t drop to zero in any typical game). But in this case, we fully expect an author who has already decided to add historifying details in one book to add them in its sequel. So this all then collapses to the question of how likely it is that Luke would insert historifying details into his works in the first place, which you will have accounted for with P(Gospels|~h). One thing you can never do (as it violates basic logic) is “double dip,” i.e. count the same evidence twice. The probability Luke would “historify” Jesus will already have been accounted for in P(Gospels), so you can’t count it “again” in P(Acts). Unless, again, there is something in Acts that can’t be explained this way or isn’t expected on this causal sequence of Luke composing a historifying Gospel and then flavoring Acts to match.

With these principles in place, you can then decide how to break down and assess likelihood ratios for all the evidence, given the two competing hypotheses laid out above.

Extra-Biblical Evidence

In OHJ I survey all of this, and all the possibilities regarding it, and come to the conclusion that none of it increases the probability Jesus existed, and some of it even decreases it. In fact the probability of most of it, as we have it now, is just as likely whether Jesus existed or not. That decades after the Gospels circulated, various authors would start using or quoting them as sources, even embellishing them (dozens of more Gospels exploded onto the scene in the second century, just as pagans started taking notice of the movement and its literature as well), is 100% expected either way. For example, if Jesus didn’t exist and was first “invented” into historical form by the Gospels, the probability that this invention would leak into later texts and accounts is 100% guaranteed. Thus, none of those leaks can corroborate the Gospels on this point. But the same is true if the Gospels preserve some kernel of a real man. So the likelihood ratio on all that kind of evidence is simply 1/1, which is just 1, and anything multiplied by 1 remains unchanged. So this evidence has no effect. It does not evince Jesus existed; nor does it evince he didn’t.

There are many ins and outs to this point. I cover them all in OHJ (Ch. 8). For example, historicists will insist there should be some evidence still surviving of the original form of Christianity or that second century authors should have known the Gospels made everything up. Neither assumption is actually valid (there is no reason to expect historicist Christians would preserve any mythicist work; nor any way authors a century later and thousands of miles away could possibly know or even find out the truth of whether Jesus existed in any sense). But neither do they work. Because we do have some surviving evidence of early Jesus mythicism, and of some second century observers doubting Jesus existed. So the claim that we don’t is false (remember what I said about historians continuing to assert as evidence for Jesus stuff that doesn’t actually exist?).

In any event, to change this outcome, we need either of two things: something outside the Bible that is unlikely to exist unless Jesus really existed; or something outside the Bible that is unlikely to exist unless Jesus never existed. Either would shift the probability one way or the other, in the proportion to their weight. For example, mere evidence of second century mythicist Christians does not do this, because for all we know they could be an evolution from a historicist sect, and not the other way around. As either, by itself, is equally likely, there is nothing any more unlikely about that on either theory. It therefore doesn’t have any effect—it doesn’t even increase the probability Jesus didn’t exist. Whereas evidence of this that could date to the first century, might have some effect, as that’s getting pretty close to the origins of the religion. Conversely, if we could uncover something we could verify was written before the Jewish War (which started in the 60s A.D.) that discussed Jesus more in the fashion of a personal memoir rather than mythic fables (like someone’s letter discussing their conversations with the people who met Jesus in life), this would be very unlikely unless Jesus existed, so its likelihood ratio would heavily favor historicity. 

For instance, if that hypothetical recovered letter was only just barely mundane and clear and unsuspicious enough to be even as little as five times more likely to exist if Jesus existed than if he didn’t, then (all else being equal) our starting prior odds of 1 to 2 (that “1 in 3” probability) becomes a final odds of 1/2 x 5/1 = 5/2 which leaves us with about a 71% chance Jesus existed (5/(5+2) = 5/7 = 0.714-etc.), so we will have gone from “probably didn’t” exist to “probably did exist” on just a single piece of minimal evidence. That’s how easily Jesus could be rescued. In reality, most evidence we have for other figures is vastly better than that, generating likelihood ratios of tens or even hundreds, in some cases thousands or millions, to one in relative odds. The evidence for Jesus is never that good. (It’s arguably not even weakly good. But that’s a function of the “lower bound” on my margin of error and I’m not discussing that today.)

Conversely, if we recovered a lost letter by someone of that period reporting on what Christians were then going around teaching, and it was explicitly the Doherty thesis, this would be extremely improbable unless Jesus actually, in fact, didn’t exist. If it were mundane and clear and unsuspicious enough, it could easily be a hundred times more likely to exist if the Doherty thesis really was what Christianity began with, than if there was ever any real Jesus. This would collapse even the upper bound on our margin of error from 1 in 3, hence “1 to 2,” to a dismal 1/2 x 1/100 = 1/200, or barely half a percent chance Jesus existed at best (assuming all else being the same at this point).

The truth is, the state of evidence is so poor and vague and compromised, we have no smoking guns like this, for either theory (that Jesus existed, or that he didn’t). That’s why the engine of Bayes’ Theorem is needed to assess what our highest likelihood for Jesus existing can be on such a dismal and difficult state of evidence; whereas we have no need of running any numbers for most anyone else, where the evidence is usually so good we can tell at a glance their posterior probability will end up as near to 100% as makes all odds (e.g. Hannibal), or as near enough to or below 50% as to leave us with no high confidence they existed (e.g. Pythagoras).

In the end, even if you were being generous to historicity, the relative odds of almost all the extrabiblical evidence being the way it is are the same whether Jesus existed or not. Which is largely due to the heavily compromised state of that evidence (as documented and explained in OHJ, Chs. 7.7, 8.3-4, 8.12). So if we updated the prior at this point, all we would get is 1/2 x 1/1 = 1/2. Which is the same 33% chance that Jesus existed that we started with. 

However, I did find some of the extrabiblical evidence counts against historicity. Just not very much. The itemized things I found weighing slightly contrary to historicity are:

• The fact that two Christian traditions existed dating the life of Jesus a hundred years apart and in different political contexts. This is not quite expected if Jesus really existed, but it is the sort of thing we can expect for someone who didn’t exist. I score the relative odds of this at 4 to 5, meaning if there is a 100% chance of something like this happening to a non-existent man, then there is an 80% chance of it still happening even to a real one; thus only slightly less likely to happen. Which is being very generous to historicity.
• The silences of 1 Clement, which are frankly quite odd, for reasons explained in OHJ (Ch. 8.5). I score this the same: 80% chance we’d still see this oddity even if Jesus existed; while it’s 100% expected if he didn’t; a 4/5 relative odds. Again, very generous to historicity.
• The unusual content of an apocryphal “Acts of James” found in Hegesippus, which is slightly harder to explain (being slightly less expected) if Jesus existed, than if he didn’t. This I score at almost nil, or 9/10, meaning there is a full 90% chance Hegesippus would still tell that story this way even if Jesus existed, compared to a 100% chance if Jesus didn’t, two probabilities so close to each other as to have little overall effect.
• And finally, the combined effect of material in Ignatius [and Irenaeus and Justin] and the Ascension of Isaiah that overlap and corroborate each other, indicating the existence of an early competing view of Jesus as a celestial being only witnessed by demons and angels (as detailed in OHJ, Chs. 3.1 and 8.6). This I rate again at 4/5 relative odds.

Notably, that last weighting of evidence means I am counting the effect of the Ascension of Isaiah at almost nil—less than half [in fact, closer to a quarter] of the 4/5 relative odds gets us close to 9/10 relative odds again [or rather, 95/100]. Its impact only rises to an 80% chance of this evidence still existing if Jesus did when combined with the material in Ignatius [and Irenaeus, and Justin]. Whereas by itself, it would barely rate as [95/100 or a 95%] chance this evidence would exist if Jesus did, which is not very much different from saying it’s 100% expected and thus not evidence really of anything. [Note the bracketed items above are corrections to the original edition of this article; I overlooked the role of Irenaeus and Justin and thus even overestimated the impact of the Ascension of Isaiah.]

The significance of these little clues is in their cumulative effect. Each one is not very weighty (every one has a good chance of looking that way even on historicity, and only slightly less a chance than on mythicism). But all of them together produces a likelihood ratio of 4/5 x 4/5 x 9/10 x 4/5 = 576/1250. If we update our prior probability of 1/2 we get 1/2 x 576/1250 = 576/2500, which gets us a probability of about 19% (= 576/(576+2500) = 576/3076 = 0.187-etc.). Which is just over half where we started, at 33%. Notably, there is no extra-biblical evidence that looks peculiar the other way around—we have plenty that looks odd unless Jesus was mythical, but nothing that looks odd unless Jesus was historical. That has an effect, the very effect we are seeing here.

The Book of Acts

In OHJ (Ch. 9) I survey some really strange things about the narrative in Acts, which are hard to explain if Jesus existed; things that are simply not expected if he existed. Which logically entails that those features are less probable if he existed than if he didn’t. I lay out a table at the end of that chapter itemizing those things, and showing what math then follows. I also cover in Ch. 12.2 a full discussion of what happens mathematically if you come to a different conclusion about this feature of Acts, and what it actually takes, empirically, to justify coming to such a different conclusion. I there use that as an example for readers to adapt to any other case in the book, whether material in the Gospels, in the Epistles, or outside the Bible, and likewise whether it’s new evidence I don’t evaluate, or new evaluations of the evidence I do. So if you want guidance on that, you really should read that section.

In Acts the two general oddities I find and weigh are the unusual omissions in Paul’s trial speeches, and the mysterious vanishing acts in the overall narrative. The first of those consists of the fact that in every trial that Acts relates a speech from Paul in there is no recently executed Jesus (a practical impossibility at such trials), only a gospel learned from scripture and revelation. See OHJ (Ch. 9.4) for all the details as to why this is not an expected outcome if Jesus really existed, whereas it is if Luke is drawing on material originating from a church that had no knowledge of such a Jesus. In the end, I still estimate this as very, very weak evidence: only 9 to 10 relative odds; as in, if this oddity is 100% expected on mythicism (and it is, once allowed to leak through in extant texts like this), then it is still 90% expected even if Jesus really existed. That’s quite generous to historicity; it’s claiming this oddity is almost entirely expected anyway—when we know it’s hardly so expected as that.

The second of those two oddities consists of all of Jesus’s family, including his mother and father and all his brothers, and all persons peculiarly involved in the Jesus story in Luke’s Gospel, from Joseph of Arimathea and Mary Magdalene to Pontius Pilate, simply vanishing from history as soon as Acts begins its public history of the movement (in Acts 2). What’s most peculiar about the case of Pilate, since otherwise we at least know from other evidence he did exist, is that it is extremely difficult to explain how he would never be involved in any subsequent legal events, given that a vanishing body (or even an executed convict being claimed still alive and giving orders, even if the body remained accounted for) should have warranted vehement concern from Pilate and initiated an extensive criminal investigation and even the scapegoating of Jesus’s closest followers. Yet none of this happens.

In essence, very little of the church’s history in Acts from its first public day (beginning with Acts 2) makes much sense unless there was no historical Jesus the empire had recently killed to be concerned about, but only a being met in visions, as Acts on many occasions implies. It would appear that whatever account of the church the author of Acts was working from was not first told by anyone aware of a historical Jesus crucified by Pilate (or any earthly authority). Yes, maybe this is just an odd fluke of what stories got told or transmitted or glossed over or omitted; so we can’t say this is only explicable if Jesus didn’t exist. But what we can say, as a matter of objective fact, is that this is still not what we would expect, so it cannot be “100% expected” if Jesus existed—whereas it is 100% expected if he didn’t (once we cancel out coefficients of contingency relating to the random chance of evidence like this surviving, which is the same on either theory). I estimated the relative odds here at 4/5, which means it could not possibly be more than 80% likely all these vanishing acts would occur in the earliest church history if Jesus existed. That’s quite generous to historicity; it’s claiming this oddity is again almost entirely expected (when we know it isn’t even at all expected), yet certainly less expected than the previous oddity—which I generously gave a 90% rather than an 80% chance of appearing. And there really is no way to argue these probabilities up further.

Overall, in Acts I find that apart from those two odd things, there is no content that is unexpected on either theory (that Jesus existed, or that he didn’t). That Acts wouldn’t give us much new detail is 100% expected on historicity, because Acts isn’t about Jesus. That Acts would repeat details already affirmed in Luke (or Luke’s sources) is 100% expected on mythicism, because you already expect an author committed to doing that, to keep doing it. The only thing weird here is that he didn’t consistently keep doing that, which isn’t as explicable on historicity as it is on mythicism. Otherwise, for example, Luke moves the suicide of Judas from his source Matthew, to Acts, and alters the story fantastically to suit Luke’s agenda; but there is nothing about that that is any more likely if Jesus existed, nor anything about his doing that that’s any more likely if Jesus didn’t exist. It makes no difference either way. Likewise with Luke including repetitions of Gospel material in his death-oration for Stephen (see OHJ, Ch. 9.5).

So the only evidence in Acts that makes any difference, is its strange omissions. Which generate an at-best likelihood of 9/10 x 4/5 = 36/50, which normed to “percents” is equivalent to 72/100. In other words, best chance, there is a 72% chance Acts would look even this weird way if Jesus existed; but a 100% chance it would look this way if he didn’t—because we already know he was being historicized by this author and many of his sources, so the fact that Acts is somewhat historicizing, but adds nothing new to that information, is fully expected whether Jesus existed or not. Whereas these strange omissions are not “fully” expected if Jesus existed. Which leaves us with a warranted suspicion; which must have a weight in our calculation, however small.

So if we update our prior again, starting with our previous update of 576/2500, it goes down even a little more, not up. We get 576/2500 x 36/50 = 20,736/125,000 odds, which entails a probability of 20,736/(20,736 + 125,000), or 20,736/145,736, which gets us to about a 14% chance Jesus existed. Down from the 19% we just landed at, and now below half the 33% we started with. Acts made the case for Jesus worse. But only a little.

The Gospels

I already extracted relevant information from the Gospels in generating the prior probability: they make Jesus look so enormously mythical, so much more like mythical but historicized heroes, that we have to start with the assumption that more likely that’s what he is. But as I lay out in OHJ (Ch. 10), nothing else in the Gospels makes any further difference. There is nothing in the Gospels, for example, that is unlikely unless Jesus existed—everything in them is as expected to have been invented if he didn’t exist, as to have been reported if he did. I survey this point pericope-by-pericope across all four Gospels. There just isn’t anything in there that’s unexpected. Yes, historians have tried to claim there is; but none of those claims actually hold up. They are either factually false, or fallacious (their conclusions do not follow even from what is asserted), as I thoroughly show (and with abundant peer reviewed scholarship concurring) in Proving History (Ch. 5).

There is also nothing in the Gospels that is only likely if Jesus didn’t exist. Apart from that one single fact of how mythologized they make Jesus be (and thus what reference class of like heroes he most resembles), all of what’s in the Gospels, even the obviously made-up stuff, is just as expected even if Jesus existed. In other words, once you get past a certain point, adding more mythical stuff to someone no longer has any additional effect on the probability they are mythical. They are already maximally mythologized. Thus, having a hundred bogus stories about a guy, doesn’t make him any more likely to be mythical than if you had fifty. (See my discussion of this point in my discussion of the Covington review of OHJ.)

Therefore, since we already let the Gospels set the prior, and we cannot double-dip, we can’t count the effect of the Gospels twice. Whereas what’s left to consider, simply has no effect: it’s as likely to be generated whether Jesus existed or not. So when we move to update our prior again, we get 20,736/125,000 x 1/1 = 20,736/125,000. Still 14%. No change.   

The Epistles

The Epistles (of Paul and a few others) found in the New Testament are of course the only battleground left. These have two general features pertinent to this debate: first is their extremely unusual silences regarding a historical Jesus, which even includes oddly exclusionary statements implying the only way anyone ever heard from Jesus was by revelation and hidden messages in scripture (such as Romans 10:12-15 and 16:25-26); and second are the few ambiguous passages historians try to leverage into evidence that Jesus was, nevertheless, a real guy. 

The combination of these two things (there are many unexpected silences and omissions; and what possible mentions there may be are weirdly ambiguous) does leave the Epistles less likely if Jesus existed than if neither of these two things were the case. As in, they are not quite what we expect to have. They are weird. And weird means unusual. And unusual means infrequent. And infrequent means improbable. Whereas we entirely expect the Epistles to look this odd way if Jesus didn’t exist (as then, we expect only letters that were ambiguous enough to support historicity would be selected for preservation later by the prevailing historicist Church). So there is no honest way to get the odds to be particularly high here. They must be lower for historicity than a more expected set of letters would be. This is a logically necessary fact, and thus unavoidable.

For example, if these letters were rife with arguments over and discussions of people who met Jesus and what they related, and things Jesus endured or experienced when alive, or unambiguous discussions of his family affairs, and so on—for instance, if we had letters about Jesus, that were like Pliny the Younger’s or Cicero’s letters about their near contemporaries, such as Pliny being asked and writing about the heroism of his father decades after his death, or Cicero relating the actions and fate of Pompey—then the probability they’d have such content and still Jesus didn’t exist would be extraordinarily low. Indeed I’d put the relative odds in such a case well into the millions to one—or if I were to be as skeptical as at all possible, no less than hundreds to one (let’s say, at least 200 to 1). Which would vastly overwhelm our now updated prior of 20,736/125,000 to 20,736/125,000 x 200/1 = 4,147,200/125,000, or more than 33 to 1 in favor, for a probability that Jesus existed of 4,147,200/4,272,200 (from 4,147,200/(4,147,200 + 125,000)), which is over 97%. So you can see why a prior probability of 2 to 1 against is weak tea, indeed quite inconsequential, when you have real evidence for someone’s existence.

But this is not what we have for Jesus. The letters of Paul are nowhere near that good as evidence; and this must logically necessarily be represented in the math. You can’t admit the letters of Paul are vastly less impactful as evidence than what I just described, yet then count them as being exactly as impactful as I just described. That would be fundamentally incoherent. If you don’t have an amazing piece of evidence, the probability of something must then be lower, by exactly as much as it would be higher if you did have that evidence. This is a logically necessary fact; it cannot be avoided by any trick. 

To work out what all this means in mathematical terms, I broke the Epistles down into several items of content, and some I found made no difference. For example, Jesus’s sayings are never reported to have come from a living man, but if any method of hearing them is ever mentioned, it’s hearing him communicate them in mystical revelations or through the ancient prophets (OHJ, Ch. 11.6). Which is exactly what we expect on mythicism. But this is still possible on historicity, although it requires a lot of uncomfortable assumptions for the historicist. You basically have to admit Jesus never said anything while alive that anyone had reason to ever note that he did—that is, maybe some of the sayings reported did come from his ministry and not later revelations, and just no one made note of that, as weird as that would be. Nevertheles, as I am only testing minimal historicity, which does not require (and thus does not predict) any ministry when alive worth mentioning or specifying as such, never mentioning any sayings as coming from the man before he died is just as expected if he existed as if he didn’t. This odd outcome in that case is then equally expected either way. So I scored it as having no effect, hence 1/1, and thus just 1. I did the same with Paul’s discussion of the Eucharist, as he says he got that by revelation (directly “from the Lord”: see OHJ, Ch. 11.7), which is as likely whether Jesus existed or not, and thus we can’t tell whether Jesus existed or not just from that information.

But a few other items I scored differently. Some I even scored as weighing in favor of historicity. Some I scored as weighing against. The ones I counted against were:

• Epistles not by Paul that were still weirdly silent on there being a real Jesus, like James, Jude, and 1 Peter (OHJ, Ch. 11.3). This really makes no sense if there was a recent glorified man named Jesus they all hung around with and were inspired by and even persecuted for and named to authority by (even less if any of these guys were his biological family; and arguably even less still if these letters are forgeries, as then it’s hard to explain why forgers would miss this opportunity to create such evidence, as we see the forger of 2 Peter did: see OHJ, Ch. 8.12). In any event, I counted this collective silence only at 4/5 relative odds—meaning, again, I allowed an 80% chance these letters would look like this even if Jesus did exist after all (while, again, it’s 100% expected if he didn’t). Which is, again, generous.
• All the hymns and creeds Paul declares as being “the gospel,” or some version or component of it (as well as those found across Hebrews and Colossians), not one of which ever mention Jesus being alive on Earth, ever met by anyone while alive, or even “preaching the gospel” anywhere. They instead all assume Jesus was encountered, and the gospel learned, after his death, in mystical revelations, and confirmed in ancient scriptures. This is most strange indeed. Yet I scored it barely worse, at 3/5 relative odds. That means if we 100% expect to see this if Jesus didn’t exist (and we do), then we’d only expect this on historicity 60% of the time. That’s still better than half a chance, so I’m still being generous to historicity here. I’m actually saying it’s weird, but that “more likely than not” this is still what Christians would generate as their hymns and creeds even if Jesus existed.
• And the additional absence of anything significant ever done by Jesus when alive—as in, nothing anyone ever had occasion to mention, discuss, be curious or argue about, or use as an edifying or instructive example—all despite Paul writing over 20,000 words on the subject of Jesus and his teachings and intentions and accomplishments and their importance.

As I wrote in OHJ (Ch. 11.8): 

It’s remotely possible Jesus never said anything that was ever deemed relevant or interesting. But it’s not possible that he never did anything that was ever deemed relevant or interesting. And even if you think that’s possible, it can’t be possible that he neither did nor said anything relevant or interesting.

So, we have to weigh this fairly. We expect a lot more to be discussed in these letters, and yet don’t find it. We already accounted for the unusual absence of historical facts about his pre-mortem preaching, and the absence of any in the gospel creeds declared of him; now we must also weigh the unusual absence of mentions of his even ever doing anything while alive (other than getting killed—and that indeed for reasons we again are never told about so as to situate them in Earth history). I scored this silence at 3/4. In other words, if we 100% expect this for a non-existent man (and we do), then it’s only 75% likely we’d have the same weird silence for a real historical man. Note again this is very generous. I’m practically declaring this an entirely reasonable and likely thing to find in these letters. All I am saying instead is that it’s not as much so, as it would be on the alternative. I am thus not even saying this is improbable. I’m actually saying it’s a probable outcome on historicity. But what I am also saying is that, nevertheless, we still must slightly more expect this if Jesus didn’t exist. It’s honestly hard to argue with that. And again, this has to be represented mathematically. You can’t “skip over” it.

So let’s pause and update our prior again. We left our most recently updated odds at 20,736/125,000, entailing a probability Jesus existed of only 14%. Now if we add this evidence it will of course drop even more: 20,736/125,000 x 4/5 x 3/5 x 3/4 = 746,496/12,500,000, which produces a probability of 746,496/(746,496 + 12,500,000) = 746,496/13,246,496 = 0.056-etc. or less than 6%. It’s not looking good. 

But wait. That’s all I counted against. I then allowed three pieces of evidence to weigh in favor of Jesus really existing:

• Paul says Jesus was “made out of a woman” (sic)
• Paul says Jesus was “made from the semen of David” (sic)
• Paul says he knew some “Brothers of the Lord” (sic)

Each of these is really awkwardly ambiguous—way more ambiguous than we have any right to expect. I explain why, and all the required minutiae, in OHJ (Chs. 11.9 and 11.10). These sound a lot like the sort of cosmographical things one would say of a celestially incarnated Jesus. In the first case Paul outright says he is speaking allegorically (Yes, Galatians 4 Is Allegorical); in the second case he appears merely to be affirming a realization of scripture in some esoteric way that they knew God could have effected directly (for instance, Paul conspicuously does not say Jesus “descended” from David, nor explains how he knows any of this, nor names his father, or any other normally expected detail); and in the third case, Paul only mentions knowing one kind of brother of the Lord: the adopted sons of God; in other words, baptized Christians. Paul never shows any knowledge of a need to make clear he means different kinds of Brothers of the Lord in different places, some biological, others cultic. So these are actually really not good evidence for historicity; fully considered, they actually argue against it. Because we’d expect much clearer data than this if there were a real Jesus behind any of it.

Nevertheless, I stretch my credulity as far as I possibly can, and actually assign these as evidence for, not against, historicity. I weigh each one of these three details as being twice as likely to be found in the letters of Paul if Jesus existed, than if he didn’t. The net effect is 2/1 x 2/1 x 2/1 = 8/1: this evidence, collectively, is eight times more likely if Jesus existed, than if he didn’t. That’s pretty good. What happens then when we make our final update to the probability Jesus existed? Our most recently updated odds of 746,496/12,500,000 x 8/1 = 5,971,968/12,500,000 gives us quite a boost. We now have a probability Jesus existed of 5,971,968/(5,971,968 + 12,500,000) = 5,971,968/18,471,968 = 0.323-etc., or over a 32% chance Jesus existed.

What could we do to increase this? Not much. We have such good explanations and even expectations of even these three items of evidence on mythicism that already saying they are each twice as likely on historicity is quite a stretch. And there is no other evidence to account.

Consider:

• Paul’s discourse on mothers he outright says is allegory; so we can’t really assert that he is “definitely,” out of the blue and for no discernible reason, referring to a real mother in this one line. The vocabulary and rhetorical context suggest he does not mean that—even if he knew Jesus was a real man with a real mother, he isn’t likely discussing that here. That Paul would say this in such a context is already 100% expected on mythicism. So it can’t really be “more” expected on historicity.
• Paul’s line about Jesus receiving a body manufactured from the seed of David clearly derives from the Nathan prophecy, which we 100% expect the first Christians to have connected to even a cosmic Christ, because any Christ had to fulfill that prophecy regardless. So we already know, with 100% certainty, that they would have done so. It is therefore not a surprise to see it here done. There is no evidence that Paul means ordinary biological inheritance through a long genealogy. He thus could mean whatever any cosmic Christ worshipers needed it to mean.
• And Paul outright tells us all baptized Christians are Brothers of the Lord, and the actual grammar and rhetorical context of the only two times he uses this full pleonastic phrase is exactly the way we expect him to if that’s all he means there. So these passages are already 100% expected on mythicsim, given our background knowledge of what Paul elsewhere says about becoming Brothers of the Lord. There is no evidence Paul ever even heard of a distinct category of “biological” brothers of the Lord; and he never says he is referring to such a category in either of the passages concerned. So we cannot simply “assume” he was. 

Thus, saying these three lines are “unexpected” on mythicism isn’t even true. Saying they are each twice as expected (and thus collectively eight times as expected) if Jesus really historically existed is therefore pushing the limits already of what we can reasonably imagine possible. So there really isn’t any room to move here; there’s no reasonable way to push these numbers higher. What we really need is some unambiguous evidence; not this weirdly vague shit. A plain statement of Jesus’s family history from Paul, for example, would fully flip the probability Jesus really existed well above 50% and thus well back into “probable” territory. Likewise if we could prove the entire extant text of 1 Thessalonians 2:14-16 was authentically written by Paul, i.e. if all the extensive evidence rendering that vanishingly improbable didn’t exist (see There Is No Logically Sound Case Against Interpolation in 1 Thessalonians 2). Or if someone’s memoirs about Jesus had preceded the sacred fables in the Gospels. Or if we had anything like we have for any other historical person discussed in ancient letters. But we just don’t have anything like that. And you really need to ask why—not rhetorically (it’s no use inventing armchair assumptions to explain all this away; that actually won’t work); but sincerely. Because any answer you give might entail assertions for which you actually have no evidence. And what business do we have doing that?

Conclusion

In the end, if we clump together and dismiss all measured features of the evidence that ended up having no effect and drop all that (since 1/1 x 1/1 x 1/1 … etc. = 1, and anything multiplied by 1 doesn’t change), our final equation would look like the following (and this is shown in tabular form at the end of each chapter in OHJ assessing each category of evidence, i.e. Chs. 8.13, 9.7, 10.8, and 11.11; and the results of each chapter are tabulated in Ch. 12.1):

• P[1/2] x X[(4/5 x 4/5 x 4/5 x 9/10)] x A[9/10 x 4/5] x G[(1/1)] x E^con[4/5 x 3/5 x 3/4] x E^pro[2/1 x 2/1 x 2/1] = 5,971,968/12,500,000

Which, as just noted, gives us a probability of historicity of 5,971,968/(5,971,968 + 12,500,000) = 5,971,968/18,471,968 = 0.323-etc. = just over 32%. (Here “P” means Prior Odds, “X” means Extra-Biblical Evidence, “A” means Acts, “G” means the Gospels, “E^con” means evidence in the Epistles measured against historicity, and “E^pro” means evidence in the Epistles measured for historicity.)

So, for example, if we kept the same prior and dropped all other evidence except the Epistles we’d have:

• P[1/2] x E^con[4/5 x 3/5 x 3/4] x E^pro[2/1 x 2/1 x 2/1] = 384/200

For a probability of historicity of 384/(384 + 200) = 384/584 = 0.6575-etc., which is just under 66%. So the oddities in the extra-biblical evidence and the book of Acts do make a crucial difference. But so did the biased assumption that those three references in Paul have such an outsize effect as evidence for historicity (after all, just take out E^pro and see what happens). And this would still only be the upper bound of the margin of error—the lower bound would likely still fall below 50% (you can trace that math in OHJ; it’s the other column on every table), so even in this hypothetical case (where we “don’t have” all those odd things in Acts and those other first and second century texts suggesting an early mythicism) we still would not “know” the probability Jesus existed was above 50%, since all we’d know is that it fell somewhere between that and the lower bound—whatever you calculated that to be (if it ended up different from mine). And even this upper bound of “66%” would still be closer to 50% than to 100% and thus still signify a warranted agnosticism as to Jesus’s historicity, not confidence in it. 

But we do have that evidence. So we can’t drop it like this anyway. Moreover, we can’t “ignore” our margins of error. And all we just mentioned was the upper bound of those margins. Always when forming estimates of the prior and relative odds for the lower bound of your magin of error, you are epistemicaly obligated to stretch your reasoning in the other direction: in each case, you must ask how far against the assumption of historicity can you reasonably allow, rather than (as I have done here) the other way around. For example, that 1 in 3 persons as mythologized as Jesus really existed approaches the unreasonably optimistic; the evidence suggests that, actually, fewer than 1 in 15 did. So the lower bound prior is definitely going to sink the expected odds of his historicity. Likewise all the evidential odds, as each likelihood ratio there cannot be generous to historicuty anymore, but instead as generous to mythicism as you can reasonably imagine—as generous to mythicism, in fact, as we have been to historicity, when generating the upper bound of our margin of error. That’s the only honest way to calculate and thus account for your uncertainties and thereby control for any possible biases that may be governing your intuitions.

Again, all the details of this you have to get from On the Historicity of Jesus. All I have done here is summarize. But in the end, this is how the math in there works out, leaving us with almost a 33% chance Jesus existed—at best. Because that’s with remarkably generous evaluations of the evidence, giving historicity every possible fair turn, assigning it remarkably high odds in every case of producing or matching the evidence we have, even despite how frequently unusual that evidential turnout was. To get a different result, you have to present good, true, empirical reasons to up the prior probability that comparable savior heroes existed (like Osiris or Hercules or Aesop or Moses) and/or to give historicity a higher chance at producing all this weird evidence (and thus upping the likelihood ratios), and/or present some evidence (something overlooked here?) that is significantly more likely if Jesus existed than if he didn’t (something like we have for all the other historical personages we are sure existed, from Hannibal to Pilate, as I document in Jesus from Outer Space). 

All I found was that there just isn’t anything like that for Jesus. Nor can I argue the prior or any of these likelihoods should be higher; they are honestly already unreasonably high. What good reason can you have to raise them? That’s the question you have to answer—not avoid.