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Allow me to inform you it is. Your ratios are unrealistic even for estimating unless you really think there's 1 L6 for every 3 L5s at Google. Also we're talking about around an L8 for director:
Yet it still holds for those numbers that yes, if you can afford to reach out to them, you can afford technical staff to be in the loop. Because it's not just about the company, it's about respecting the engineer's time. Not that many people are qualified enough to be getting calls to be hired in as directors, it's not a small feat even if it's 100 hires a year. You don't want them having experiences like this if only for the image it gives off to other potential hires..
> Aside: this used to be the kind of "estimate/puzzle" question Google used to ask it's interviews, allegedly
Used to use about a decade ago? And I believe the moment you said "1:3 manager to L5 ratio" your interviewer would give you a subtle but questioning look and expect you to revise that.