Experienced dog breeders or buyers choose their dogs not only based on the qualities of the dog they are interested in but they also consider the qualities of their relatives. In this case, we are specifically estimating the genetic quality of a dog for hip and elbow conformation and its genetic potential to transfer its genes for good hips and elbows to its offspring. This process was optimized into a single criteria called the BLUP (best linear unbiased prediction) using data for both hip and elbow conformation simultaneously in the records.
The 'best' means the prediction is the best with regard to its having the minimum prediction error. The 'linear' means a linear function between the OFA hip and elbow score and the genetic relationships in the dog’s pedigree as far back and as widely as data is available in the public OFA database. 'Unbiased' means the prediction equals the expectation of the true breeding value. The 'prediction' is the prediction of the genetic basis underlying the OFA hip and elbow score. This genetic basis is called “breeding value”. AS THE BREEDING VALUE HAS THE SAME DIRECTION AS THE OFA SCORE, A SMALLER BREEDING VALUE BASED ON THE OFA SCORE MEANS A BETTER HIP AND/OR ELBOW GENETIC QUALITY, OR VALUE. Dogs with excellent hip and normal elbow scores were categorized as a "1", while the worst hips were categorized as "7" and worst elbows a "4".
The calculation of BLUP is a process of integration of phenotypes and pedigree information. The calculation also removed the related factors such as sex, age and time of year when the scores were measured. The details of the calculation can be found in the statistical model section of the paper here.