Traditionally, swordsmiths would test newly forged swords to determine their quality. If a katana failed to cut through a piece of rolled tatami omote, for instance, it usually indicated a dull or otherwise weak blade, in which case the sword was modified. Even today, swordsmiths use practice tests such as this before selling new swords. However, there are four key metrics that swordsmiths have used -- and continue to use -- for evaluating the quality of swords.
Hardness refers to the blade's ability to retain its shape under resistance. Swords produced with a hard blade don't bend or deform upon striking a target. Rather, the blade retains its original shape, indicating a high level of hardness. Hardness is important because it defines whether a blade will hold an edge. Swords with a soft blade will chip and sustain other structural blade damage upon impact, forcing the owner to resharpen it.
Some people assume that hardness and strength refer to the same characteristic, but this isn't necessarily true. Strength refers to the sword's ability to maintain its structural integrity under stresses and strains, whereas hardness refers to the sword's ability to retain shape under resistance. The two terms share similar characteristics, but strength focuses specifically on resistance to stresses and strains.
There's also flexibility, which refers to the sword's ability to flex and bend under resistance. Swords can have either a stiff or flexible blade. If a blade is flexible, it will bend under resistance, such as the striking of a target or object. If it's stiff, it won't bend bend. Even when a sword has a flexible blade, though, the blade will revert back to its original shape. This is the fundamental difference between flexibility and hardness. Swords with soft (low hardness) blade will deform permanently under resistance, whereas shape deformation is only temporary with flexible blades.
Finally, balance is a key metric that's used to evaluate a sword's quality. Balance refers to the position of a sword's balance point. Ideally, it should provide equal distribution of weight, with the point of balance being located just a few inches from the tsuba (handguard). If a sword's point of balance is too high or too low, it can be difficult to draw and use, especially during real-world combat scenarios like those frequently experienced by samurai warriors in Japan's feudal period.
Of course, traditional Japanese swords like the katana excelled in all four of these attributes. They were strong and yet still flexible with the right point of balance. Even today, swordsmiths from across the world use these same techniques to create superior quality swords.