Resource estimation explained: from a simple average to a weighted average
Resource estimation predicts a value, such as grade, at a location that has not been sampled, by taking a weighted average of the samples that have been.
Every common estimation method, from inverse distance weighting to kriging, makes its estimate in the same way: multiply each sample value by a weight and add the results, where the weights add up to one. If the samples stay the same, the only difference between methods is how the weights are chosen. This guide, part 1 of 4, builds that idea from a plain average, with one short formula and no other maths.
A simple analogy: estimating adult height
Say a baby has just been born and you want to estimate how tall it will be as an adult. You cannot know, so you estimate. A natural way is to measure existing adults and take the average. For six adults measured at 171, 168, 170, 200, 190 and 155 cm, the total is 1,054 cm, the average is 1,054 / 6 = 175.7 cm, and so every new child is estimated at about 176 cm.
You can do exactly the same with assay values: add all the assays and divide by the number of samples, and you have a grade estimate. It is the simplest estimate there is.
Why a plain average is not enough
The average ignores what you already know. If the six adults come from two countries, three from the Netherlands (171, 200, 190 cm) and three from Türkiye (168, 170, 155 cm), then a baby born in the Netherlands is better estimated from the Dutch measurements alone: 561 / 3 = 187 cm. A baby born in Türkiye gets 494 / 3 = 164.7 cm.
In geology the same thing happens: a sample close to the block you are estimating tells you more than a sample far away. But throwing half the samples away is wasteful, and it fails for a baby born somewhere with no measurements at all, such as Belgium or Austria.
The weighted average
The fix is to give every measurement a weighting factor (WF) instead of a simple keep-or-discard choice. Multiply each value by its WF, add the results, and divide by the sum of the WFs. Setting the Turkish weights to 0 and the Dutch weights to 1 gives the same 187 cm as before, but the same recipe now works with any weights between 0 and 1.
Weighted average = sum of (value × weight) ÷ sum of weights. This is the basis of most geostatistical methods.
Inverse distance weighting (IDW)
In inverse distance weighting, the weight is based on distance: 1 divided by the distance. Belgium is about 200 km from the Netherlands and about 2,500 km from Türkiye, so Dutch measurements get a weight of 1/200 = 0.005 and Turkish ones 1/2,500 = 0.0004. The weighted average is then 185.3 cm, a little shorter than a Dutch baby and taller than a Turkish one, which matches intuition.
In short form the estimate is e = Σ ω × v, where v are the sample values and ω the weights, normalised so that they add up to 1. You can use the distance itself, its square or its cube as the basis for the weights, and the formula does not change. You could even use a sine or a polynomial. Whatever you pick, only the weights change.
Trends
The weights can also reflect direction. If a deposit has a trend, points along the trend can be given higher weights than points across it, or the data can be scaled along the trend so that distances reflect it. The formula stays the same and only the weights are adjusted. This is the idea behind anisotropy.
If the samples remain the same for different estimation methods, the estimate depends only on the choice of the weights.
Apply it
Estimate on the same model you build
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Common questions
Introduction to resource estimation FAQ
What is a weighted average in resource estimation?
It is an average in which each sample value is multiplied by a weight, and the results are added and divided by the sum of the weights. Samples that are more relevant to the location being estimated get larger weights.
What is inverse distance weighting?
Inverse distance weighting uses a weight of 1 divided by distance (or distance squared or cubed), so that nearby samples have more influence on the estimate than distant ones.
Do kriging and IDW use different samples?
Not necessarily. If both use the same samples, the only difference is how the weights are calculated: IDW from distance alone, kriging from a variogram model that also accounts for how the samples relate to each other.