Degrees of Probability

People’s dominant mode of thinking about the major issues of the world is often binary: ‘black or white’, ‘this-or-that’, ‘either-or’. However, this dualistic opposite approach is grossly reductionist and ineffective in a world with various shades of gray (or palette of colors). Our language is unhelpful, when we thoughtlessly default to using vague terms for ideas that require finer degrees of nuance. For example, people frequently use the word “possible”, to denote everything from that which is very likely–say, chance of rain, to something that is highly unlikely, say winning the lottery. Since “possible” means greater than 0%, both are technically “possible”, though one is substantially more probable than the other.

This frequent lack of specificity in colloquial language causes widespread misunderstanding . What does it mean to be “successful”; who is considered “rich”; what does “maybe” mean? Unless the purpose is to be intentionally ambiguous or misleading, we can do better with our wording.

To this end, I propose the following scales. They go into deeper shades of meaning, while still retaining common English descriptors. I think these help strike a balance of getting a clearer level of understanding without getting overly saddled with semantics. I bet–I mean it’s “virtually certain”–if we are more thoughtful with using these qualifiers for our language, we will find we have a lot more common ground on confounding issues, and will reduce talking over and around each other.

Levels of Confidence Scale
Description Salient Example Degree of Certainty Level Order Approximation
absolutely certain 100.00% 9 > Fifth order (5-sigma)
(colloquially) certain physical law ~ 100% (99.99%) 8 Fourth order (4-sigma)
virtually certain man-made law ~ 99% (98 – 99.9%) 7 Third order (3-sigma)
highly probable (almost/ nearly certain) rule ~ 95% (90 – 97%) 6 Second order (2-sigma)
probable/ likely hunch; theory ~ 75% (65 – 85%) 5 First order (1-sigma)
even chance/ 50-50 observation, random opinion, hypothesis
~ 50% (40 – 60%) 4 Average
probably not/ unlikely uninformed opinion ~ 25% (15 – 35%) 3
highly improbable/ remote ~ 5% (2 – 10%) 2
virtually impossible ~ 1% (0.01 – 2%) 1
categorically impossible 0.00% 0

Notes:

  • Nothing really should be at Level 9. Since humans are not omniscient, this level is for all purposes unattainable.
  • Physics uses 5-sigma confidence intervals. Unless we’re in the realm of physics, or speaking hyperbole, not much else should be at Level 8 either.
  • While we overuse Levels 9, 8, and 0, common discourse really resides between Level 1 7.
  • Since science treats everything as a testable hypothesis, by definition there is no Level 0; and with few exemptions (e.g. physics), no Level 1 “fact”. Nothing is 100.00% knowable truth.  We merely approach it with new knowledge and discoveries.
  • I rank a single, random person’s opinion at level 5. If the person is well-informed and unbiased, it’s level 4 for me. A veritable expert’s opinion would be level 3. Conversely if the person is  uninformed and intelligent, it falls to level 6 or 7.
  • Some pervasive mis-estimations I see:
    • In terms of investments:
      • Being successful long-term at day-trading is Level 7. I think most people who do it believe it is Level 4.
    • The base rate for a long-term marriage is Level 4; for a “happy” marriage is Level 2 or 3. Those who do get married ignore the former, are unaware of the later, or simply believe, naturally, that their own case is unique.
    • Stepping out of a casino as a winner is Level 2. Most gamblers who go in believe it is Level 5.
    • Starting a successful new business (still operational after 5 years) is typically Level 1 or 2. Optimistic entrepreneurs believe it is at least Level 3 or above.
Levels of Wealth Scale
Investment Time Horizons Scale
Length of Time Term Salient Examples
1 day – 2 weeks Ultra Short-Term trading: high frequency traders, day trader, market maker
1 – 6 months Short-Term speculating: trend followers, technical trader, short seller, retail/ recreational investor, stock manipulator, get rich quick schemes
1 – 3 years Medium-Term typical external manager performance evaluation period: mutual funds, hedge funds, individual hobbyist investor
5 – 12 years Long-Term market cycle (once or twice): company insiders, value investors, financial advisor, pension funds
15 – 30 years Ultra Long-Term generation: retirement, family office, sovereign wealth fund