Weighted geometric mean: how weights shape a decision score
The essentials in 30 seconds
- A weighted geometric mean multiplies each rating raised to its weight, with the weights adding up to 1.
- Ratings of 0.8, 0.6 and 0.4 give 0.639 with weights of 0.5, 0.3 and 0.2, and 0.519 when the weights are reversed.
- The same 0.1 gain on the weakest rating adds 0.029 under a weight of 0.2 and 0.061 under a weight of 0.5.
- EQOS Asia keeps its weighting coefficients proprietary, under NDA (EQOS Asia method page, as of October 2026).
Not every dimension of a decision matters equally, and a weighted geometric mean puts that fact into the arithmetic. This guide shows how weights enter the formula, how they change a score in a 3-dimension example, and how to set and record them. It continues the comparison of geometric vs arithmetic mean in a decision score, as of October 2026.
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What does a weighted geometric mean measure in a decision?
A weighted geometric mean raises each rating to a power called its weight, then multiplies the results. The weights are positive numbers that add up to 1. A dimension with a weight of 0.5 counts for half of the exponent budget, and a dimension with a weight of 0.1 counts for a tenth. The result is a single number on the same 0 to 1 scale as the ratings.
When every weight equals 1 divided by the number of dimensions, the formula returns the ordinary geometric mean. Weights therefore refine the method and keep its main property: a low rating still pulls the score down. The weights decide how strongly each dimension takes part in the final figure, so they deserve as much care as the ratings themselves.
How do you compute a weighted geometric mean, step by step?
Four steps give the result. Write the ratings from 0 to 1 and the weights, checking that the weights add up to 1. Raise each rating to the power of its weight. Multiply the powers together. Read the product, which is already the weighted geometric mean, with no further root to take. A spreadsheet needs one formula per dimension and one multiplication.
Weights given as points out of 100 convert easily: divide each by 100 before computing. Rounding at the end, and not at each step, keeps the figure steady. A reviewer who has the ratings, the weights and the sources can reproduce the number exactly, which is the standard a decision score should meet. The figure lists the steps.
How do weights change a weighted geometric mean for a decision?
Take three illustrative dimensions rated 0.8, 0.6 and 0.4. With equal weights, the geometric mean is 0.577. Give the first dimension a weight of 0.5, the second 0.3 and the third 0.2, and the score rises to 0.639, because the strongest rating now carries the most weight. These figures are illustrations, not EQOS Asia results.
Reverse the weights, so that the weakest rating of 0.4 carries 0.5 and the strongest carries 0.2. The score falls to 0.519. The three ratings are identical in all three cases, and the score moves by 0.120 between the highest and the lowest. The table shows the three results, and the lesson is that weights express a view of what matters.
How should you choose the weights for a weighted decision score?
Ask each decision maker to distribute 100 points across the dimensions alone, then average the results and divide by 100. Large gaps between people reveal a disagreement about strategy, and settling it before rating anything saves a later argument about the total. Write the weights down before looking at any rating, so the weights do not drift toward a preferred answer.
Anchor each weight in a reason. A dimension may weigh more because a lender checks it, because a regulator requires it, or because it has delayed past projects. A one-line reason next to each weight turns an opinion into a record. Review the weights once a year, or when the decision context changes, and keep the earlier versions.
Why does the weight of a weak dimension decide how much a fix pays?
A fix pays most where a weak rating carries a high weight. Return to the example with ratings of 0.8, 0.6 and 0.4. Under weights of 0.5, 0.3 and 0.2, raising the weakest rating from 0.4 to 0.5 lifts the score from 0.639 to 0.668, a gain of 0.029. Under weights of 0.2, 0.3 and 0.5, the same fix lifts it from 0.519 to 0.580, a gain of 0.061.
The result guides the lever plan. A team that knows which weak dimension carries a large weight can put its first effort there and expect the largest movement in the score. A weak dimension with a small weight can wait. This is the same logic as a sensitivity analysis, applied to the weights and ratings together.
How does EQOS Asia treat the weights of its decision engine?
EQOS Asia states that each dimension is raised to its weighting, which makes the score a geometric product and not a simple average (EQOS Asia case study pages, as of October 2026). The weighting coefficients of the Codex Universalis are proprietary, and the documentation is available under NDA on request (EQOS Asia method page, as of October 2026).
The public simulator offers a hands-on view. Its Expert mode activates fine-tuning of weights, manual module selection and temporal modulation, and its Target button shows the result of activating the top 3 levers, the 3 dimensions that weigh the most (EQOS Asia simulator page, as of October 2026). The calibration coefficients stay computed server-side.
How do you record the weights of a decision score for review?
Keep a one-page weight sheet with five columns: dimension, weight, reason, owner and date. The sum of the weights sits at the bottom and reads 1. A reviewer who joins later can see why a dimension carries its weight, who proposed it, and when it changed. The sheet also makes it simple to rerun the score under alternative weights.
A full EQOS Asia analysis documents its method in an interactive report with a 30/60/90 day lever plan (EQOS Asia method page, as of October 2026). To discuss weights for your own case, a 30-minute pre-diagnostic by video, scheduled in Singapore time (SGT), is available at no commitment, and the pricing page lists the tiers that follow (EQOS Asia contact and pricing pages, as of October 2026).
Frequently asked questions
What is a weighted geometric mean?
It is a geometric mean in which each rating is raised to a weight before the results are multiplied. The weights are positive and add up to 1. Heavier weights make a dimension count more, and a low rating still pulls the whole score down.
Do the weights in a weighted geometric mean need to add up to 1?
Yes. With weights that add up to 1, the product needs no extra root, and the result stays on the same 0 to 1 scale as the ratings. If you set weights as points out of 100, divide each by 100 before computing.
How do weights change the ranking of options?
They can reverse it. In the worked example, the same ratings of 0.8, 0.6 and 0.4 give 0.639 under one weight set and 0.519 under the reversed set. Running two or three reasonable weight sets shows whether a ranking is stable.
Can I see EQOS Asia weights?
The weighting coefficients of the Codex Universalis are proprietary, and the documentation is available under NDA on request. The simulator Expert mode lets you fine-tune weights in a public demo (EQOS Asia method and simulator pages, as of October 2026).
Test your knowledge
1. What do the weights of a weighted geometric mean add up to?
- 10
- 100
- 1
Show the answer
1.
2. What does each rating get raised to?
- Its weight
- The number of dimensions
- Zero
Show the answer
Its weight.
3. Which score do ratings of 0.8, 0.6 and 0.4 give with weights of 0.5, 0.3 and 0.2?
- 0.577
- 0.639
- 0.519
Show the answer
0.639.
4. Where does a fix to the weakest rating pay most?
- Under a low weight
- Under equal ratings
- Under a high weight
Show the answer
Under a high weight.
5. What does EQOS Asia keep proprietary?
- The 9 dimension names
- The weighting coefficients
- The 0.618 cut
Show the answer
The weighting coefficients.
About the author
Stéphane Jambu
President, EQOS Forecast Asia
Stéphane Jambu leads EQOS Forecast Asia and works as a consultant in e-commerce, search visibility, and AI. LinkedIn profile
Sources: EQOS Asia method page (eqos-asia.com/method.html), simulator page (eqos-asia.com/simulator.html), pricing page (eqos-asia.com/pricing.html), contact page (eqos-asia.com/contact.html), WeWork case study (eqos-asia.com/case-studies/wework.html), consulted on 22 October 2026. Page updated on 22 October 2026.