How Does StoneAlgo's Cut Quality Score Work?

Diamond Dimension Details
Note: Diamond cut quality is typically discussed for round diamonds because the shape has a simpler geometric form. More complex shapes like cushion, princess, emerald, oval, etc. do not have as universally agreed upon ideals as round cut diamonds do. Our cut score is only available for round diamonds. The discussion below focuses on round cut diamonds exclusively.

Quick StoneAlgo Backstory

Back in the day, when I was first looking for a round diamond for my now wife, I had a difficult time understanding the way diamonds were priced in the online market (let alone at the jeweler). It seemed like pricing was random at times, with similar diamonds sometimes shown at wildly different prices. So, I brought in my business partner Jay to help leverage both of our backgrounds in modeling risky financial assets. Our goal was to come up with an algorithmic way to sift through millions of diamonds and produce a list of the most undervalued stones. What we realized very quickly, was that higher levels of cut quality did not necessarily cost more than lower levels. This became one of our favorite ways to maximize value, it was like a free upgrade if you found a diamond that was well priced and also had a super high cut quality.

GIA & AGS Cut Grades

Diamonds are a commodity, but diamond cutting is an art form. Two diamonds with the exact same color, clarity, carat weight, fluorescence, symmetry, and polish will perform completely differently if their cut qualities are dissimilar. At the end of the day, the GIA, AGS, and other rating agencies lump diamonds into rigid categories like Ideal or Excellent, Very Good, Good, Fair, and Poor. But why should we think there is a significant difference between the worst Excellent cut and the best Very Good cut diamond when there is hardly a difference at all? A single degree difference in pavilion angle could move an Excellent cut diamond across the boundary into Very Good territory. On the flip side, why should we think the worst Excellent cut is the same as the very best Excellent cut? If the worst Excellent cut is nearly a Very Good cut, while the best Excellent cut is far from having those credentials, wouldn’t it make sense to prefer the better Excellent cut? Furthermore, the AGS & GIA don’t agree on the same specifications for their top grades because these grading systems are man made constructs. The existing grading systems which simplify cut quality specifications into a single word were simply not good enough for nit picky diamond buyers like me. I needed something a little more refined, so I started doing some research.

The Main Angles for Cut Quality

There is no SINGLE diamond cut that is perfect. There are numerous “local maximums” on the diamond cut quality scale, and they depend on a variety of angles and measurements that balance each other out. The main dimensions required for measuring cut quality are table %, pavilion angle, crown angle, girdle thickness, and depth % (which can be solved for as a dependent variable). Most cut quality grading charts do not include girdle thickness, a major flaw since this directly affects the ideal pavilion angle required to return light back out through the top of a diamond.

AGS 0 Cut Specifications

AGS Ideal cut diamonds (AGS 0 cut grade) have an even more stringent set of parameters than GIA Excellent cut diamonds. They also differ slightly, where some AGS 0 diamonds will not be GIA Excellent and vice versa. One of our first steps in analyzing the interplay between different measurements and angles was to go through every grid produced by the AGS to get a deeper understanding of how they interpreted cut quality based on two dimensional information. The AGS has produced tons of tables that create different heat maps based on Table % that show the ideal crown and pavilion angles for their different ratings of AGS 0 – 10 (AGS 0 is the best), while assuming that the girdle thickness is fixed at 3.5%. What you can see below is that the sweet spot for crown and pavilion angles (the red zone representing AGS 0) shift and shrink considerably when the table changes from 57% to 60%. You can see all of these tables on the AGS’s website here. Our cut quality scoring system would need to naturally adjust to different parameters.

AGS Table 57 Heatmap AGS Table 60 Heatmap

Below is a simple interpretation of how the ideal crown angle and pavilion angle balance each other out at different table percentages.

Diamond Table Versus Crown and Pavilion Angle

We even took the time to convert this data into a 3D model that better showed the interplay of various table widths and angles…

AGS 3D Clamshell
Tip: view this blog on a larger screen to interact with this 3D plot

The More Math-y Tolkowsky Model

The AGS has done a ton of great work, but we needed to come up with our own model and find a way to make something more robust – something that could handle different girdle thicknesses and score over a million diamonds to determine which were the best and worst of the GIA Excellent/AGS Ideal cut diamonds. We found our foothold in an old book on the mathematics of diamond design from 1919 by Marcel Tolkowsky. Tolkowsky’s words, written nearly 100 years ago, were music to our ears.

It is a remarkable fact that, although the art of cutting a diamond has been known for more than two thousand years, it is entirely empirical, and that, though many keen contemporary minds have been directed upon the diamond, and the list of books written on that subject increases rapidly, yet nowhere can one find any mathematical work determining the best shape for that gem. The present volume's chief aim is the calculation of that shape.

Tolkowsky goes on to describe a detailed study of the optics of light performance and how this relates to the angles and overall geometry of a gem stone. He describes the importance of reflection (light bouncing off of the diamond’s exterior), refraction (light that enters the diamond and is bounced back out of the stone), and dispersion (white light breaking into a rainbow of colors aka “fire”) – all the while remaining mathematically rigorous in his approach. In the end he creates a framework that we could leverage in our own mathematical modeling and for which we are deeply grateful.

Tolkowsky Diamond Design

StoneAlgo Cut Quality Score

After studying a long list of technical and non-technical resources we were able to work out our own formula that included all of the relevant angles and measurements (including girdle thickness) to determine a fair approximation of a diamond’s cut quality. Our model is calibrated with a maximum score of 10 points (representing “perfect” diamonds) and detracts points based on how far a diamond’s geometry falls from its nearest “perfect” cousin. There are many ideal shapes for a round cut diamond, as the interplay between different table percentages, pavilion angles, girdles, and crown angles may balance each other out to produce excellent light performance for various combinations of these measures. Our cut quality grading system recognizes this fact and is incredibly robust at handling it. We believe it is the best 2D cut quality analysis tool on the market today – allowing for a quick interpretation of cut quality and light performance without the requirement of 3D light performance imaging.

After scoring over 1.1 million diamonds (as of this writing in November 2018) we ranked all of the diamonds based on their cut score and determined their percentile rank. The top 1% (99th percentile) of diamonds receive cut scores of 9.7 or higher, the top 10% are 9.4 or higher, top 25% are 9.0 or higher, and the top 50% are 8.4 or higher. We recommend searching for diamonds in the top 50% of all GIA Excellent cut diamonds because they don’t command a significant premium in the market but offer better light performance. Put slightly differently, as I interpreted this fact when searching for my own diamond, it’s like getting a free upgrade.

StoneAlgo Cut Score versus Percentile Rank

Diamond Prices and Cut Quality Scores

It is fair to say that given the choice between the best GIA Excellent cut diamond and the worst GIA Excellent cut diamond, we would all prefer the best one (all else being equal). Since this is an opinion that most rational buyers would agree on, it in turn makes sense that we should place a higher value on the best cut diamond than we do on the worst cut diamond. However, the market does not always recognize this difference and this leads to buying opportunities for the best cut quality diamonds. But sometimes the market does discount diamonds of lower cut quality, even when they are graded as GIA excellent cut. In these situations it may make sense to purchase a lower cut quality diamond as long as it still looks appealing to the eye. The lowest GIA Excellent cut quality specifications are still very good, and these diamonds should still look great to the human eye. It all comes down to what you as a buyer are looking for, and the price that the diamond commands.

A Final Note on Finding Diamonds

Like all mathematical models that seek to replicate physical objects based on limited data, the StoneAlgo Cut Quality Score is not an exact representation of a diamond's physical beauty. The data we use is two dimensional, and a diamond is a 3D object. We are forced to assume that the angles and widths are consistent in 360 degrees around the diamond, but this is often not the case. However, the StoneAlgo model is outstanding at what it does and should correlate highly with light performance (we’ve studied light performance imaging for a large population of diamonds to confirm this). The StoneAlgo Cut Quality Score is a tool, but it is not a direct replacement for your own eyes. A diamond buyer should never purchase a stone sight unseen, and this is why we exclusively show diamonds with real HD images (and light performance images when available) on StoneAlgo. We hope you find this info useful and that it gives you another powerful weapon in your search for the best diamond.