22 Death Threat Confessions: Simple Statistical Analysis Proves They Are 100% Real

Death Threats
The murderers sent Dr. Egan 22 coded death threats via emails and letters after they killed his mother, 84-year-old Leah Egan.
The FBI counterintelligence agents that are part of their crime ring like to document their crimes and mock their victims in coded messages.
The messages came from MIT/DOJ-FBI (7), Lam Research (12), and Analog Devices (3).

Statistical Analysis
Their best defense against the charge of sending death threats is to simply say, “We did not send any death threats. The patterns in the letters and emails are random and happened by chance.”
How do we prove these messages are not random, but instead were purposefully coded to be death threats?
A simple statistical analysis anyone can do…

Simple Statistics
There is an old saying: “Once is coincidence, twice is suspicious, and three times is enemy action.”
We can easily calculate the probability that a set of unusual events one after the other is real or random.
The area of statistics used here is referred to by various names: the coin toss test, the probability version of Pascal’s Triangle, or the Binomial Theorem.
Anyone can do the calculations with a cheap calculator or Excel or Google sheets.

The Old Saying
Let’s use the old saying above as the starting point.
Treat each event as a coin toss with 50% chance of heads (real) and 50% of tails (random).
For one unusual event, if we get a tail, we have 50% random. A plain old coin toss. We can say nothing one way or the other because we have data from only one coin toss.

For two unusual events, that is two coin tosses with two tails in a row. The chance of both being random is 50%*50% = 25%. Suspicious. The chance that this is real is 100% - 25% = 75%.
For three unusual events, three tails in a row, the chance of all three being random is 50%*50%*50% = 12.5%. Enemy action. In that case, the chance of all three being real is 100% - 12.5% = 87.5%.

Enemy Action
The standard cutoff in scientific research and in the courts is a 5% chance of randomness.
Although the chance of all three events being random is 12.5%, which is higher than the traditional cutoff of 5%, if the risk is high, e.g., death or injury or defeat on the battlefield, you should be cautious now, instead of waiting for more proof.
Insurance companies do this, calculating risk = chance of event * magnitude of loss if it happens.

5 Unusual Events are not Random
If we continue, the chance getting four tails on a row is 50%*50%*50%*50% = 6.25%. The chance of all four being real is 100%-6.25% = 93.75%.
It only takes five unusual events, five tails in a row, to get below the cutoff for statistical significance of 5%.
50%*50%*50%*50%*50% = 3.125%. The chance of all five being real is 100%-3.125% = 96.875%.

22 Unusual Events
If 22 unusual events happen, getting 22 tails in a row, the chance that it happened randomly is 0.000024%.
The probability that the death threats are real is 100% (99.999976%)