A naive critic is a toxin to advanced analytics. If they don’t get the math and have a political agenda to criticize, their critical influence can set the acknowledged success of the analytics program back for many cycles. If the critic holds a position of power, even their off-hand and casual comments can result in a self-fulfilling cycle: a skeptical judgement by the executive staff slows sponsorship and funding of the work and adoption of the results , which slows the measurable business impact, which then seems to validate the criticism.
How to respond? Your executive sponsor must set the tone and defend the territory. You must be emotionally neutral but objectively rigorous in defense of the work with deliverables that novice executives can understand. You must make the critic eat their words by validating business results in any way possible (lower level managers, financial metrics, other departments). Lastly, you will be expected by the executive team to face your critic head-on.
It is in this lonely place that the Analytic Executive must stake his/her ground with key principles: 1) there is value in the data, 2) applied mathematics can extract that value, 3) the value can be proven and measured.
Most executives have been exposed to the buzz about analytics and should be open to these propositions.
Tactically, be sure there is a wide audience when presenting model results. Have your cheerleaders in the room. Wait to present results publicly until you have socialized them with stakeholders one-on-one. Ask critical questions of yourself first, from a business perspective. Don’t over promise and give fuel to the critic.