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How to Assign Probabilities

The weakest part of many scenario analyses is the probability assignment. Investors often use default distributions (33/33/33, 25/50/25) without thinking, or adjust probabilities reactively based on recent news rather than genuine conviction. Yet probability assignment is where your actual research compounds into better decisions. A careful probability distribution based on thorough research, anchored in conviction, and regularly updated with new information, can meaningfully improve returns over time.

Quick Definition​

Probability assignment is the process of allocating likelihood weights to each scenario (bear, base, bull) such that they sum to 100% and reflect your genuine conviction about which outcome is most likely. Probabilities should be grounded in research, anchored to testable assumptions, and revised as new information arrives. A distribution like 20/50/30 (bear/base/bull) is not arbitrary—it encodes your view that the base case is twice as likely as either extreme, with a slight bias toward optimism.

Key Takeaways​

  • Probabilities must sum to 100% and reflect your actual conviction, not defaults or fear of overconfidence.
  • Start by assigning probability to your highest-conviction scenario first, then distribute remaining weight to other scenarios based on how different you believe them to be.
  • Common distributions reflect different conviction levels: 50/35/15 signals strong base case conviction; 30/40/30 signals high uncertainty.
  • Base case probability is typically 40–60% in most analyses, reflecting the center of gravity for conviction without claiming false certainty.
  • Update probabilities quarterly at minimum, or when major business developments occur; stale probabilities lead to stale valuations.
  • Test your probability distributions against your own historical track record; if your stated probabilities don't match realized outcomes, you're systematically biased.
  • The market's implied probability distribution (backed out from current price) offers a useful reality check for your own probabilities.

Why Probability Assignment Matters​

Three analysts build identical DCF models with identical assumptions. Their base cases are all worth $50 per share. Yet one assigns 25/50/25 probabilities, another uses 35/40/25, and the third uses 40/35/25. Their expected values are:

  • Analyst 1: (Bear×0.25) + (Base×0.50) + (Bull×0.25) = weighted toward base
  • Analyst 2: (Bear×0.35) + (Base×0.40) + (Bull×0.25) = pessimistic bias
  • Analyst 3: (Bear×0.40) + (Base×0.35) + (Bull×0.25) = conservative

Same scenarios, different probability weights, different decisions. The probability distribution encodes your actual conviction in a way that scenarios alone cannot. This is why assigning thoughtful probabilities matters—it's where subjectivity turns into actionable insight.

According to research by the Yale School of Management on forecast calibration, investors who explicitly assign probabilities and track their accuracy over time improve forecast calibration and long-term returns compared to those who rely on intuition alone.

Framework 1: The Conviction-First Approach​

The most honest way to assign probabilities is to anchor on your highest-conviction scenario first.

Step 1: Identify Your Highest-Conviction Scenario​

Ask yourself: Based on my research, which scenario am I most confident will unfold?

For most investments, this is the base case. But not always. If a company has strong momentum and clear catalysts, the bull case might be your highest conviction. If risks are genuine and under-appreciated, the bear case might be most likely.

Be honest. This is not where you hedge or express false humility. If you've studied the company thoroughly and believe 12% growth is sustainable, you genuinely believe in the base case. Assign it high probability.

Step 2: Assign the Core Probability​

What's your confidence level in this scenario? Some frameworks:

  • 70%+ = Very high conviction (you've done deep research, assumptions are grounded, risks are understood and unlikely)
  • 55–70% = Strong conviction (good research, reasonable assumptions, but meaningful uncertainty remains)
  • 40–55% = Moderate conviction (you have a view, but significant alternatives are plausible)
  • 25–40% = Low conviction (you're unsure; this scenario is one of several equally plausible paths)

Most analyses land in the 45–60% range for the highest-conviction scenario, reflecting realistic confidence in your central estimate.

Step 3: Distribute Remaining Probability​

Once you've assigned probability to your core scenario, distribute the remaining probability to other scenarios based on how different you believe they are.

Example:

You assign 55% to base case. You have 45% remaining probability to distribute between bear and bull.

  • Bull case represents "the company executes well and captures upside from a clear catalyst" (e.g., new product launch, market expansion). You believe this is plausible and 60% as likely as base case. Assign 45% × 0.60 / (0.60 + 0.40) = 27% to bull.
  • Bear case represents "competition intensifies, growth slows, margins compress." You believe this is plausible but less likely than bull. Assign 45% × 0.40 / (0.60 + 0.40) = 18% to bear.

Distribution: 18% bear / 55% base / 27% bull

This distribution reflects your conviction: base case is most likely (55%), bull case is plausible but lower probability (27%), bear case is a hedge (18%).

Why This Works​

This approach doesn't require you to assign probabilities from scratch. Instead, it anchors on your genuine highest-conviction scenario, then distributes remaining probability proportionally based on relative likelihood. It's more honest than defaults and more grounded than arbitrary allocation.

Framework 2: The Relative Likelihood Approach​

Another approach is to explicitly rate each scenario's likelihood relative to the others.

Step 1: Rate Each Scenario​

On a scale of 1–10, how likely do you believe each scenario is?

  • Bear case: 6 (plausible but not as likely as others)
  • Base case: 9 (most likely, but not certain)
  • Bull case: 7 (plausible, clear catalysts)

These are relative ratings, not probabilities yet.

Step 2: Normalize to Probabilities​

Sum the ratings: 6 + 9 + 7 = 22

Divide each rating by the total:

  • Bear: 6 / 22 = 27%
  • Base: 9 / 22 = 41%
  • Bull: 7 / 22 = 32%

Distribution: 27% bear / 41% base / 32% bull

This distribution reflects your assessment: base case is most likely (41%), but bull case is nearly as plausible (32%), with bear case as a meaningful downside hedge (27%).

Calibration Check​

Does this distribution feel right given your conviction? If it feels too pessimistic (too much bear), adjust the ratings (lower the bear case rating). If it feels too optimistic, adjust upward. The numerical normalization is a starting point; your intuition is the final calibration.

Common Probability Distributions and What They Signal​

Different distributions encode different conviction levels:

50/30/20 (Base/Bull/Bear)​

Signal: Strong conviction in base case; bull case is plausible but requires favorable conditions; bear case is a tail risk.

Usage: Applies when you've done thorough research, assumptions feel solid, and downside risks are understood but unlikely. Common for mature, stable businesses where the trajectory is relatively clear.

Example: A utilities company with stable cash flows and regulated returns. Base case assumes steady-state operation; bull case assumes favorable regulatory shifts; bear case assumes regulatory headwinds. 50/30/20 reflects confidence in the base.

40/40/20 (Base/Bull/Bear) or (Bull/Base/Bear)​

Signal: High conviction in two scenarios (base and bull are nearly equally likely); downside is hedged but less likely.

Usage: Applies when tailwinds are clear and execution seems likely, but you're not fully confident in the most optimistic outcome. Base and bull are close calls.

Example: A software company with strong product-market fit and clear expansion catalysts. Both the "steady execution" (base) and "successful market expansion" (bull) are plausible. 40/40/20 reflects this near-equivalence.

25/50/25 (Bear/Base/Bull)​

Signal: High uncertainty; bear and bull cases are balanced mirrors around the base case. You're genuinely unsure which way the company evolves.

Usage: Applies to situations with genuine, material uncertainty—early-stage companies, turnarounds, businesses in structural transition, or situations where binary outcomes are plausible.

Example: A biotech company with a pending FDA decision. If approved, bull case (30% probability); if rejected, bear case (20% probability); if approved with restrictions, base case (50% probability). High uncertainty justifies balanced distribution.

30/50/20 (Bear/Base/Bull)​

Signal: Downside risks are meaningful; base case is most likely; limited upside catalyst.

Usage: Applies to mature or challenged businesses where downside is more salient than upside, or businesses facing structural headwinds.

Example: A traditional publishing company. Multiple paths lead to steady decline (bear case); base case assumes some digital transition and modest stabilization; bull case assumes successful digital pivot. 30/50/20 reflects asymmetric downside risk.

10/70/20 (Bear/Base/Bull)​

Signal: Extreme conviction in base case; bear case is a tail risk; bull case is unlikely though possible.

Usage: Rarely appropriate. This distribution signals very high confidence, and humans are notoriously overconfident. Use sparingly, only when you have deep conviction and substantial research backing.

Example: A company with proven business model, stable competitive position, and clear visibility to 10-year cash flows (rare). 10/70/20 might apply, but should trigger skepticism about whether you're overconfident.

Building a Probability Distribution From Research​

Here's a systematic approach to setting probabilities grounded in research rather than intuition:

Step 1: Define the Scenario Assumptions​

What are the key assumptions that differ between scenarios? Common distinctions:

  • Revenue growth (e.g., bear 8%, base 12%, bull 18%)
  • Operating margin (e.g., bear 22%, base 32%, bull 36%)
  • Competitive position (e.g., bear loses share, base stable, bull gains share)

Step 2: Research Historical Precedent​

For each key assumption, what's the historical outcome?

Example: Revenue growth assumption

  • Company's 5-year historical average: 11%
  • Analyst consensus estimate: 12%
  • Company's own guidance: 12–14%
  • Industry growth rate: 9%

Your bear case (8% growth) is below company average, suggesting material slowdown—plausible but not baseline. Your base case (12% growth) aligns with consensus and guidance—reasonable. Your bull case (18% growth) is significantly above history but consistent with company claims about market expansion—ambitious but not absurd.

Step 3: Assess Credibility in the Market​

What are credible people saying about this stock's trajectory?

  • Do analysts predict significant upside or downside?
  • Are short-sellers articulating bear case risks? (If yes, bear case is plausible and credible.)
  • Are long-focused investors predicting upside catalysts? (If yes, bull case is plausible.)
  • Is consensus narrow and bullish, or scattered? (Narrow suggests low uncertainty; scattered suggests high uncertainty.)

If multiple credible analysts have bull case thesis, your bull case probability should reflect this. If a credible short-seller has articulated a bear thesis, your bear case is grounded in real market opinion, not unique pessimism.

Step 4: Assign Conviction Probability Based on Research Strength​

Frame your probability assignment around the depth of your research:

  • Spent 2–4 hours researching? Probably deserve 40–50% conviction in base case; hedge with broader distributions (35/40/25 or 30/45/25).
  • Spent 10–20 hours, read all filings and calls, talked to industry experts? Can justify 50–60% conviction in base case; tighter distribution (20/55/25).
  • Spent 40+ hours, deep dive into competitive dynamics, management track record, customer interviews? Can justify 55–65% conviction; narrow distribution (15/60/25).

The depth of research should correlate with confidence in the base case (higher research → higher base case probability).

Testing Probability Assignments Against Outcomes​

The best way to improve probability assignment is to track whether your stated probabilities match realized outcomes over time.

Calibration Exercise​

Keep a record of 10–20 past investments with stated probability distributions. Then assess:

Did the base cases you assigned 50% probability occur roughly 50% of the time? Or did they occur more frequently (suggesting you're too pessimistic in your probability spreads) or less frequently (suggesting overconfidence)?

Example calibration check:

Over 10 past investments:

  • You assigned base case 50% probability 7 times. Actual base case occurred 5 times. (50% assigned → 50% observed = well-calibrated)
  • You assigned base case 60% probability 3 times. Actual base case occurred 3 times. (60% assigned → 100% observed = underconfident in base case; could justify higher probability next time)

If your historical record shows patterns (e.g., you always assign too much probability to bear case, or you're overconfident in bull case catalysts), adjust future distributions accordingly.

Updating Probabilities Over Time​

Initial probabilities are a starting point. As new information arrives, update them.

When to Update Probabilities​

  • Quarterly earnings: Assess whether actual results support your base case assumptions. If results are stronger, increase base case and bull case probability; decrease bear case.
  • Major competitive developments: A competitor launches a disruptive product? Increase bear case probability.
  • Management changes: New CEO with strong execution track record? Increase bull case probability.
  • Macro shifts: Economic slowdown appears likely? Increase bear case probability.
  • Earnings guidance changes: Company raises full-year guidance? Increase base and bull case probability.

Example: Probability Evolution​

January 2024 (Initial analysis)

  • Bear 20% / Base 50% / Bull 30%
  • Expected value: $50

April 2024 (After Q1 earnings better than expected)

  • Bear 15% / Base 45% / Bull 40%
  • Expected value: $55 (higher base case value + shifted probability toward bull)

July 2024 (Competitor launches aggressive product, commentary suggests pricing pressure)

  • Bear 25% / Base 50% / Bull 25%
  • Expected value: $48 (revert to lower conviction as risk has become apparent)

October 2024 (Company wins major contract)

  • Bear 15% / Base 40% / Bull 45%
  • Expected value: $60 (high conviction in bull case as catalyst has materialized)

This evolution is healthy. You're updating conviction as new information arrives. Stale probabilities (unchanged for 12+ months while business conditions shift) are a red flag.

Using the Market's Implied Probability Distribution​

An underutilized technique is backing out the market's implied probability distribution from the current stock price.

How It Works​

If you've valued the stock at:

  • Bear case: $25
  • Base case: $50
  • Bull case: $80

And the stock trades at $45, you can solve for what probability distribution the market is implying:

($25 × P_bear) + ($50 × P_base) + ($80 × P_bull) = $45

(With P_bear + P_base + P_bull = 100%)

This is a system of equations. Solving it reveals the market's implicit conviction.

Interpretation​

If the market is implying:

  • Bear 45% / Base 35% / Bull 20%

But you've assessed:

  • Bear 15% / Base 50% / Bull 35%

The market is pricing in significantly more downside than your analysis suggests. This divergence is signal. Either:

  1. The market is being irrationally pessimistic (opportunity to buy if you trust your research)
  2. The market sees risks you've missed (red flag; reconsider your base case)
  3. The market is pricing in a scenario you haven't modeled (time to expand your framework)

This comparative analysis sharpens your thinking and forces discipline.

Probability Distribution Visualization​

Common Mistakes​

1. Using default probabilities without thinking. "I'll do 25/50/25 because it's balanced." If you've researched thoroughly, your probabilities shouldn't be default. They should reflect your conviction.

2. Probability anchoring to recent events. Stock rallied 50% in the past month? Don't automatically shift all probability to bull case. Update probabilities based on changed fundamentals, not price momentum.

3. Confusing confidence with probability. You're 80% confident in your bear case assumptions (high confidence you've identified real risks). But that doesn't mean bear case is 80% likely—it means you're confident in the risk analysis. These are different.

4. Static probabilities in changing business. You assigned 25% to bear case in 2024. The company has executed flawlessly, competition has faded, margins have expanded. Update to 10% in 2025. Stale probabilities make for stale valuations.

5. Probabilities that don't add to 100%. Obvious, but happens. Use a calculator. 19% + 55% + 28% = 102%. Fix it.

6. No narrative backing for probability choices. "I chose 50% for base case because it's the most likely outcome" is vague. Better: "Research suggests 12% growth is sustainable based on historical average (11%), management guidance (12–14%), and market growth (9%). Consensus agrees. I assign 50% to base case (12% growth) and hedge with 25% bear case (8% growth, reflects competitive risk) and 25% bull case (18% growth, reflects market expansion catalysts)."

7. Overweighting base case. Beginner investors often assign 70%+ to base case, hedging only 15% each to extremes. This is usually overconfident. 50/35/15 or 50/30/20 is more realistic for most analyses.

FAQ​

Q: How often should I update probabilities?

Quarterly at minimum (with earnings). More frequently if major business developments occur (competitive launch, management change, macro shift). Don't update mechanically every day or with every price move.

Q: Should I show probability distributions to the company's management?

Carefully. A probability-weighted valuation report is standard analyst practice. If your bear case is negative, management might see it as pessimistic. Use good judgment. For buy-side analysis, probability distributions are normal practice.

Q: What if I genuinely can't decide between scenarios?

That's called high uncertainty, and it's honest. A 30/40/30 or 25/50/25 distribution reflects genuine uncertainty. Better to be transparent about uncertainty than to force false conviction.

Q: Can I have a 65% probability in bear case?

Yes, if you genuinely believe downside is most likely. A company in structural decline might have 60/25/15 (bear/base/bull). The label doesn't matter; what matters is that your distribution reflects conviction.

Q: How do I handle a scenario I assign <5% probability?

If a scenario is <5% likely, consider removing it from formal analysis. Include it only if it's a genuine tail risk you want to acknowledge (e.g., bankruptcy, black swan event). Most analysis is cleaner with three scenarios of material probability.

Q: Should I adjust probabilities for risk tolerance or portfolio constraints?

No. Probabilities should reflect your genuine assessment of likelihood, independent of portfolio factors. If you can only take on bear case 15% risk, that's a portfolio decision, not a probability reassignment.

Summary​

Probability assignment is where discipline turns into edge. Rather than using defaults or anchoring to recent price movements, a thoughtful probability distribution is grounded in research depth, calibrated against historical precedent, and regularly updated as new information arrives. Start with your highest-conviction scenario and assign it meaningful probability (40–65% for most analyses). Distribute remaining probability based on relative likelihood of other scenarios. Test your distributions against historical outcomes; if bear cases you assigned 20% probability occur 40% of the time, you're systematically underweighting downside. Track the market's implied probability distribution; divergence from your own often signals opportunity or risk worth investigating. Over time, this discipline compounds—well-calibrated probability assignments lead to better decisions, more accurate expected values, and edge over investors who rely on intuition or defaults.

Next​

Continue to Expected Value in Valuation to learn how probability-weighted values drive investment decisions and how to interpret the results.