The information ratio you already know divides active return by active risk. It answers a portfolio question: per unit of deviation from the benchmark, how much did the deviation earn? A factor model splits both halves of that fraction, which produces a second ratio and a much better question.
The appraisal ratio divides the selection return by the specific risk: α / σ_u. Treynor and Black named it, and it isolates the part of a manager's performance that her exposures cannot explain, measured against the risk of the part her exposures cannot explain. It is the closest thing the toolkit has to a number for skill.
Worked example: both ratios on one US fund
Put them side by side on the US fund. Its naive information ratio, quarterly and scale-free, is 1.3032, which annualises to 2.61 and would place it among the best funds anyone has measured. Its appraisal ratio is 0.0511, which annualises to 0.10 and is indistinguishable from a coin. The factor information ratio, active factor return over factor risk, is 1.7271. Nearly the whole of that spectacular record is the return to a size and value tilt held consistently through a period when size and value paid.
The reading is not that the fund is bad. A fund that holds a deliberate small-value tilt through a small-value decade has done something, and a client who wanted that tilt got it. The reading is about price and substitutability.
A tilt is available in an index fund at a low fee; selection is not available anywhere else. If the alpha is 0.28% a year with a t-statistic of 0.07 and the fee is 90 basis points, the client is paying an active fee for a passive product, and the attribution says so in a way no return series can.
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Why do two different ratios share the name information ratio?
One naming collision to disarm before it costs you an argument. The signal-construction work in the quant branch uses "information ratio" for the mean of a signal's information coefficient divided by the standard deviation of that coefficient series, which measures whether a signal's predictive power is reliable period to period. Both usages are standard and both are correct within their literature, and they share only the intuition of a mean over its own noise.
Say which one you mean, every time, because the numbers are not comparable and a committee that thinks they are will make a bad decision confidently.