A significant amount of discussion on this sub relates to how probable or coincidental the events and circumstantial evidence described in the PCA against Kohberger are. Stated simply - was Kohberger just very, very unlucky and at the centre of a series of unfortunate coincidences which have implicated him? This post attempts to quantify the probability of the events/ evidence arising innocently by chance and will try to estimate a probability based, as far as possible, on available objective data for each piece of evidence. Some subjective estimates are required and these are made conservatively i.e. erring on the side of innocent coincidence.

To calculate an overall probability, event probabilities are multiplied assuming each is independent, not impacting on each other i.e. we are dealing with a series of "ANDS" - e.g. what is the probability Kohberger's DNA got on the sheath AND that a car matching his was outside the house at 4.00am. This is analogous to calculating the probability of rolling a six on a die : 1 in 6, but the chance of rolling two sixes on two dice thrown sequentially is [1 in 6] x [1 in 6] = 1 in 36.

These are of course estimates and are presented as a basis for discussion/ challenge and comment.

The probability to be estimated is that:

1. Kohberger, through innocent contact, got his DNA on a sheath which was found under a victim
2. AND a car of the same make, model and color as Kohberger's car and which was also missing a front license plate was driving repeatedly around the murder scene and parked there for 15 minutes at the time of the murders
3. AND Kohberger's phone moved synchronously with the suspect car over a 40 mile rural route from south of Moscow at 4.48am back to the area of Pullman of his apartment
4. AND that Kohberger matches the physical description of the suspect seen in the house

Taking each of these in turn:

1. Kohberger innocently got DNA on a sheath that was found under a victim: the most innocent scenario is DNA transfer through a brief contact, such as handling someone's sheath in a social setting or in a store, or even through indirect transfer such as shaking hands with someone who then handled the sheath. This marginal "touch/ transfer" scenario very likely introduces a time limitation - a trace quantity of DNA in a monolayer of skin cells would likely degrade in c 5-10 days. The question then, if indeed it is innocent "touch/ transfer" DNA, is not whether Kohberger ever touched the sheath but whether he touched the sheath in a time period very close to the murders. An estimate here is imprecise as we don't know if Kohberger frequently shopped for knives and handled them in stores without buying - however a key limiter is that the KaBar USMC sheath he touched then finds its way to the murder scene. Estimate: 1 in 1000

2. Car of same make, model, color at scene: What percentage of cars are White Hyundai Elantras? Based on annual sales for 2021, Hyundai Elantras were 0.87% of USA car sales. (127,360 sold out of 14,718,973 total).

25.8% of cars in USA are white, so White Hyundai Elantras (WHE) are 0.22% of all cars.

41% of cars are from states that do not require a front license plate (based on population share of those states).so: ***0.09% of cars are white Hyundai Elantras with no front license plate.*

What percentage of cars are driving around at 4.00am - here I will take a conservative 2% estimate of cars*.*So we may expect 0.002% of cars to be WHE driven at 4.00am*.*In terms of being at location at King Road, again will assign a very conservative 10% chance, not factoring in the inherent improbability of driving past the house 4 times, parking and leaving at speed*.\

So:* ***0.0002% chance of a WHE with no front plate at 4.00am at King Road by random chance, 1 in 5,000.*[Sources of all car data with links are listed at bottom of post. By not reducing the incidence of WHE as a % of all cars to just 2011 to 2015 models the estimated prevalence of WHE's is significantly increased, so conservatively erring on the side of innocent chance]

1. Kohberger's phone moves synchronously with the suspect car from near Blain ID at 4.48am back to the area of Pullman of his apartment. The innocent scenario is that Kohberger is driving around Blaine and happens to follow, very closely, another WHE with no front plate back to the area of his apartment in Pullman 40 miles away, and both cars start this journey by driving in the opposite direction of the destination for the first c 15 miles before reversing course. Using the probability of a WHE with no front plate being at a specific spot, in a very rural, isolated area at 4.48am at 1 in 5,000 as in (2) above and the chance of another WHE driving to the area of Pullman where Kohberger lives at 1 in 100, gives:1 in 5000 to in 1 in 500,000 chance of Kohberger's phone driving synchronously and closely behind the suspect car (which is another WHE). We will use the higher probability to be conservative.

2. Kohberger matches the eyewitness physical description: of 5'10" or taller, not very muscular, athletic build. As it is difficult to quantify "athletic build" here we will simply (i) exclude 60% of adult males who are overweight (per CDC), this is a conservative usage, actual figure is over 70% overweight and obese/ morbidly obese (ii) exclude males who cannot fit by age, disability (over 65, under 15) 36%.So: 25.6% of men would fit by age and not being overweight, 1 in 4.

Calculating overall probability of innocent coincidences explaining Kohberger incrimination:

[Kohberger innocently left DNA on sheath that was left at scene, 1 in 1000] AND [Car of same make, model, color and no front plate at scene, 1 in 5000] AND [Kohberger's phone moves with suspect car from near Blaine to Pullman, 1 in 5000] and [Kohberger matches the physical description, 1 in 4]

[1 in 1000] x [1 in 5000] x [1 in 5000] x [1 in 4] = 1 in 100,000,000,000; 1 in 100 billion

This is obviously in some part based on subjective estimate. But even using fairly conservative estimates set out above the chance of these coincidences all occurring seems very, very remote. Even changing some of the estimates to increase the estimated "innocent" probability by a factor of 10 or even 100 (e.g. chance of a WHE with no front plate being at the scene at 4.00am is 1 in 500 not 1 in 5000) still gives a 1 in 1 billion to 1 in 100 million chance of all these coincidences occurring sequentially and by innocent chance. Clearly it is questionable whether simply multiplying these probabilities as independent events is the right statistical treatment, and no one could credibly claim an accurate estimate given uncertainties, but just as an exercise this at least roughly dimensions and illustrates some of the events/ evidence probabilities by examining statistics related to them.

TL/DR : Multiplying probabilities of innocent explanations of evidence documented against Kohberger gives a 1 in 100 million chance of these all arising by chance

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Links to referenced statistics:

Car sales for 2021 year total: https://www.goodcarbadcar.net/2022-us-vehicle-sales-figures-by-model/

20 Most Popular car types by sales: https://www.newsweek.com/most-popular-car-models-america-2020-1579462

Car colors in USA: https://www.forbes.com/sites/jimgorzelany/2022/10/04/heres-why-the-most-popular-car-colors-are-also-the-dullest/

Population USA states with no front plate 137,100,000 is 41% of population: https://en.wikipedia.org/wiki/Vehicle_license_plates_of_the_United_States

USA population demographics : https://www.statista.com/statistics/241488/population-of-the-us-by-sex-and-age/

USA population by age: https://en.wikipedia.org/wiki/Demographics_of_the_United_States

Overweight/ obesity stats in USA - NIH https://www.niddk.nih.gov/health-information/health-statistics/overweight-obesity

Overweight, obesity stats USA CDC https://www.cdc.gov/obesity/data/adult.html