This is again one of the most important metric for any classification predictions problem. To understand this let’s assume we have 3 students who have some likelihood to pass this year. Following are our predictions :
A – 0.9
B – 0.5
C – 0.3
Now picture this. if we were to fetch pairs of two from these three student, how many pairs will we have? We will have 3 pairs : AB , BC, CA. Now, after the year ends we saw that A and C passed this year while B failed. No, we choose all the pairs where we will find one responder and other non-responder. How many such pairs do we have?
We have two pairs AB and BC. Now for each of the 2 pairs, the concordant pair is where the probability of responder was higher than non-responder. Whereas discordant pair is where the vice-versa holds true. In case both the probabilities were equal, we say its a tie. Let’s see what happens in our case :
AB – Concordant
BC – Discordant
Hence, we have 50% of concordant cases in this example. Concordant ratio of more than 60% is considered to be a good model. This metric generally is not used when deciding how many customer to target etc. It is primarily used to access the model’s predictive power. For decisions like how many to target are again taken by KS / Lift charts.
