Scenario analysis was a recurrent exercise during my college days studying finance. The point was to produce a single theoretical value based on weighing the probability of a variety of scenarios.

A simple exercise would go something like this: There is a 25% chance that Spacely's Sprockets will generate 2011 annual income of \$25 billion, a 50% chance it will produce 2011 annual income of \$20 billion, and a 25% chance it will generate 2011 annual revenue of \$15 billion. Therefore, I expect Spacely's Sprockets' 2011 annual income to post at \$20 billion.

If I were feeling particularly studious, the probabilities would be derived by correlating its past income to sundry balance sheet and income statement markers, economic indicators, and past market conditions.

Truth is, I usually only felt particularly studious when I thought I was being watched. If I thought I wasn't, which was often the case near the end of a hectic semester, I would simply fabricate the inputs and manufacture relationships to arrive at the probabilities.

Unsure sure things
Today, I'm unsure if my diligent technique was anymore insightful than my lazy one, since both techniques involved plugging in numbers with a whole lot of uncertainty behind them to arrive at probabilities.

We are all familiar with probabilities, particularly as they relate to games of chance: You roll a die and you have a 1-in-6 chance of any one of six numbers showing.

But there is a big "but" involved here. You can only ensure the die is fair if you toss it a very large number of times. Betting along the way, believing the die is fair before you're sure it is, can be an expensive revelation.

Tossing a die can be replicated a large number of times. Such events reliably lend themselves to probability calculations.

The same can't be said for events such as investing. It's silly to state that Warren Buffett (through Berkshire Hathaway (NYSE: BRK-B)) invests in stocks he believes have a high probability of success. Who doesn't? And what's a high probability anyway -- a 55%, 75%, 95% chance of success? In hindsight, Coca-Cola (NYSE: KO), American Express (NYSE: AXP), and General Electric (NYSE: GE) preferred turned out to have a high probability of success for Buffett. USG (NYSE: USG), I'm not so sure.

Value is always at risk
In short, investors are attempting to quantify the unquantifiable when they attach concrete probabilities to investing outcomes. Sure, math is useful at dissecting the investing past and even the present, but it won't provide reliable probabilities for the future.

Reason being, any probability attached to a social science -- such as economics and investing -- will be distorted by observer bias and structural limitations. No example is more glaring than the futility of value-at-risk (VaR) analysis.

If an analyst estimates that his investment portfolio has a one-day 5% VaR of \$1 million, he believes there is 5% probability that the portfolio will fall in value by more than \$1 million over a one-day period, assuming markets are normal, or rather replicate his historical reference.

But there is no such thing as normal in investing. If the period over which volatility is measured is stable, VaR will understate the real risks, something many financial stock investors learned painfully over the past couple of years. To quote Goldman Sachs (NYSE: GS) CFO David Viniar from 2007, "We are seeing things that were 25-standard deviation moves, several days in a row." If anyone had a VaR model that captured that risk, let me know.

It's belaboring the obvious to state that I think a stock's probability of success is higher than its probability of failure when I buy, or vice versa when I sell. But neither I nor anyone else has any idea what that probability is, which is why it's ridiculous to slap a figure to that probability. I'm 100% sure of that.

For more Foolishness:

Fool contributor Stephen Mauzy, CFA, owns General Electric. He's the author of the upcoming book Wealth Portfolio. American Express, Coca-Cola, Berkshire Hathaway, and USG are Motley Fool Inside Value picks. Berkshire Hathaway is a Motley Fool Stock Advisor pick. Coca-Cola is a Motley Fool Income Investor selection. The Fool owns shares of Berkshire Hathaway and has a disclosure policy.