The Calculation of a Miracle: The Persian Gulf War, 1991

On January 17, 1991, a coalition of armed forces from 34 countries led by the United States started operation Desert Storm to liberate recently-conquered Kuwait from Iraq. Iraq began its retaliation the next day. Over a period of several weeks, 39 modified Scud B (Al Hussein) missiles were fired at Israel, with 14 exploding in highly-populated residential areas of Tel Aviv and Haifa. (The remainder of the Scuds were either duds, or landed in the wilderness, in the Mediterranean, or were intercepted by U.S. Patriot anti-missile missiles.) Two Israelis were directly killed by these Scuds, and 11 were seriously injured.

In 1993, a scientific paper written by Fetter, Lewis, and Gronlund, entitled “Why Were Scud Casualties So Low?” was published in the prestigious British scientific journal Nature.[1] An expanded and more detailed version of the paper appeared a few months later.[2] The low casualty rate had attracted professional scientific interest. The paper uses a standard mathematical formula to predict the number of casualties expected in a missile attack. The formula is an extrapolation from past missile attacks and takes into account three parameters that modify the extrapolation: a) the size of the warhead, b) the population density, and c) whether there was warning of the attack.

The extrapolation used by the Fetter et al paper was based on casualty statistics from thousands of V1 and hundreds of V2 rocket attacks on London during World War II. The V1 “buzz bombs” gave warning of their approach, while the V2 rockets did not. On average in London, each V2 rocket caused about twice as many casualties as did a V1 rocket.

As a test of the accuracy of the extrapolation, the formula was first applied to the 125 modified Scud B missiles that exploded in Teheran, Iran between February 29, 1988 and April 4, 1988 during the “war of the cities” between Iran and Iraq. The Scuds gave no warning of their approach, so the extrapolation was based only on the casualty rates from the V2 rockets in London. Reports indicate that, on average, between 9.2 and 16 people in Teheran were killed per Scud. Taking into account the difference in warhead size between the V2 and the Scud, as well as the difference between the population density of London and Teheran, the formula predicts an average of 14.4 deaths per Scud in Teheran. This prediction is accurate, since 14.4 is between 9.2 and 16. Similarly, the predicted number of seriously injured per Scud in Teheran, 35.1, is close to the observed value of approximately 32 per Scud. The Fetter et al paper notes that the accuracy of the prediction is obtained in spite of the differences in construction between structures in London and Teheran. London homes are built with brick; buildings in Teheran are built with reinforced concrete, as are buildings in Tel Aviv and Haifa.

The Israel Anomaly

Having established that the extrapolation formula works well, and that the difference in construction between brick and reinforced concrete structures does not adversely affect the accuracy of the extrapolation, the Fetter et al paper applies the formula to the case of the Scud attacks on Tel Aviv and Haifa. The missiles used against Iran and Israel were the same. Noting that the Israelis had warning of incoming Scuds from shared American satellite tracking data, and accounting for differences in population density, the formula predicts that the 14 scuds that exploded in residential areas of Tel Aviv and Haifa should have resulted in a total of 21 deaths and 61 seriously injured.[3] This is significantly more than the two deaths and 11 serious injuries that occurred. The paper notes that the total number of casualties caused by all 14 Scud impacts in Israel is less than the average number of casualties caused by a single missile explosion in London or Teheran.”[4] How does one explain such an incredible discrepancy?

The Fetter et al papers offer several possible explanations.[5] First, there is the inaccuracy of the Scuds and the fact that some of them were duds. However, this has no relevance at all to the extrapolation, which is based solely on the number of actual explosions (14) in residential areas and not on the number of missiles launched (39).

The second possibility offered to explain the small number of casualties in Israel is that Israeli structures are made of reinforced concrete while the buildings in London are made of brick. This difference is, however, irrelevant since the extrapolation worked well for Teheran, where the buildings are constructed with reinforced concrete, just as in Tel Aviv and Haifa.[6] Furthermore, the number of residential buildings and apartments destroyed in Tel Aviv and Haifa was exactly as expected based on the London experience. The final answer given is sheer luck! The Israelis were just very lucky![7]

Is It Luck?

During the Persian Gulf War, a handful of Scuds exploded in Riyadh and Dhahran Saudi Arabia. Twenty-nine people were killed.[8]

On January 18, 1991, a Scud exploded in the densely populated Ezra district of Tel Aviv. No one was seriously injured or killed.[9] Was this luck?

On April 4, 1985, a Scud exploded in Bakhtaran and another in Hamadan, Iran. The former killed 25 people; the latter killed 11.[10]

On January 19, 1991, another Scud exploded in the densely populated Ezra district of Tel Aviv, just 300 meters from the Scud impact of the previous day. This time a bomb shelter was demolished. Unlike other shelters, this one was empty, and once again, no one was seriously injured or killed.[11] “Lucky” again?

On October 27, 1982, a Scud exploded in Dezful, Iran. Twenty-one people were killed and 100 wounded.[12]

On February 9, 1991, a Scud exploded in the middle of a road in Ramat Gan, Tel Aviv. Walls of buildings on both sides of the road collapsed, but there were no serious injuries or deaths.[13] Again, “lucky”?

On May 11, 1994, a Scud exploded in Sana’a, Yemen killing 25 people. Another one exploded there on May 24^th killing 13 people.[14]

On February 12, 1991, a Scud exploded between two private homes in Tel Aviv. Several people were buried under the rubble of the collapsed homes. Seven or eight people suffered minor injuries, but there were no serious injuries and no deaths.[15] Luck?

On May 22, 1994, a Scud exploded in Aden, Yemen. Six people were killed.[16]

On February 19, 2013, three Scuds exploded in Aleppo and one in Tal Rifaat, Syria. One hundred-forty-one people were killed.[17] Another Scud exploded on March 29 in Hretaan, Syria. Twenty people were killed.[18]

On October 21, 1999, two Scuds exploded in Grozny, Chechnya. One killed 27 people, and the other killed 17.[19]

On April 20, 1991, two unmodified Scud-B rockets exploded in a crowded market place in Asadabad, Afghanistan. Three-hundred people were killed.[20] This, too, is consistent with the formula, once one takes into account the larger warhead of the unmodified Scud B and the likely population density range of a crowded market place.

The Fetter et al paper in Nature indicates that there is anecdotal evidence that “luck” was an important factor in keeping the casualties so low in Israel. The paper goes on to say that casualties were “remarkably low” even when missiles hit occupied buildings which sustained heavy damage. Two examples are given where missiles destroyed multi-story buildings. In each case only one person was killed.[21]

In Tel Aviv, a total of 28 buildings, containing 118 apartments, were destroyed, and 2,493 apartments were heavily damaged. In Haifa, 1,700 apartments were seriously damaged. Lewis et al remark that the number of apartments in Tel Aviv that were destroyed or seriously damaged agrees with the formula’s prediction.[22] Yet, only two people were killed and 11 seriously injured in Israel! Apparently, the occupied buildings are not protected; only the people in them! Who could control this? Why is it that all the casualties from Scuds in other countries conform to the extrapolation from London, but not the ones from Israel? Why is it that the total number of casualties from all 14 Scuds that exploded in Tel Aviv and Haifa is less than the casualties from a single Scud exploding anywhere else? Can it truly be accounted for by luck?

The Mathematics of Luck

There is a way of evaluating if an unlikely event can reasonably be attributed to luck. We need to calculate the probability of the event occurring by chance and see if it is very small. If the probability is “too small,” then it becomes unreasonable to attribute the event to luck. “Too small” is usually defined in the technical scientific and medical literature as no larger than 0.05 (that is, 1/20); occasionally as no larger than 0.01 (1/100). In the field of high energy physics, “too small” was defined as 0.000000287 (1/3,484,320) for the Nobel Prize-winning discovery of the Higgs boson (an elementary particle discovered in July, 2012). This is one of the most stringent definitions of “too small” in any of the sciences.

The Fetter et al papers do not calculate the probability of expecting 21 deaths and observing only 2, or of expecting 61 serious injuries and observing 11 by chance, but we can: The probability of observing two deaths (or less) by chance, (i.e., luck) is 0.000000184 (1/5,434,783). This is considerably smaller than the stringent definition used in confirming the discovery of the Higgs boson! The probability of the dearth of serious injuries happening by chance is 0.00000000000000426. That is, approximately one in 234 trillion! This is over 67 million times as significant as the stringent definition of “too small” in the example of the Higgs boson given above. We can thus reject the possibility of the small number of deaths and serious injuries happening by chance (that is, luck) with absolute certainty.

The Fetter et al paper makes note of the fact that between four and eight Patriot anti-missile missiles used by Israel missed their targets and exploded in residential areas of Tel Aviv and Haifa. The paper does not take this into account when calculating expected casualty rates.[23] The Patriot missile carries a much smaller warhead than the modified Scud B – only 90 kg.  Nevertheless, the warhead is three times the size of the warhead of a Katyusha rocket and is thus a significant destructive force: Katyusha rockets have been used since World War II by many countries to affect damaging bombardment of enemy forces and structures. They terrorized German troops during World War II. Taking the explosions of four Patriots into account, the expected number of deaths in Israel rises from 21 to 24.2. The expected number of serious injuries rises from 61 to 70.4. The respective probabilities are now 0.00000000982 or 1/101,832,994 and 0.00000000000000000166, or about 1 in six hundred thousand trillion. The latter is less likely than someone flipping an unbiased coin 59 times and getting all heads! In real life, this does not happen. Even if the casualty rate from Scuds during the Persian Gulf War were the only scientific evidence for G-d’s intervention on behalf of the people in Israel, it would suffice. The probability of these casualties being so low just by chance or luck is so small as to be well beyond the requirement for acceptance by any scientific journal.

The Persian Gulf War ended on February 28, 1991. That day was Purim. Did the war end on that date to let us know that it was not coincidence just as the Persian Jews were saved from a similar fate approximately 2,400 years ago? As frum Jews, we know that this was not a coincidence. G-d sends us messages; we just have to be open to receiving them. However, for those intellectuals who require hard evidence before drawing any conclusions, we have provided evidence that meets the highest scientific standards.

This article is excerpted and adapted from The Cosmic Puzzle by Harold Gans, Feldheim, 2020.