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I’m an architect and I work mostly with public school districts. I strongly recommend to all my clients that they avoid wireless game/play clock systems. Regardless of claims to the contrary, the wireless signals are highly subject to RF interference. Every time I go to a stadium/field and they tell me that, once in a while during every game, the clock (game or play clock) “acts up” and seems to stop momentarily, or flicker, or go blank, and then run down a few seconds very quickly, it turns out the clocks are wireless. Every time. I tell my clients they are better off to get hard wired clocks, even if it costs a bit more. With new construction projects, the additional cost is almost negligible - only the cost to run conduit from the clock positions to the pressbox (especially if they are going to have a plastic grass field), which is something we’d virtually always include in a project, anyway, regardless if they choose to use a wireless system. That way, when they become dissatisfied with the wireless, they can easily install a hard-wired system. Yeah, a bit more difficult and additional cost to retrofit into an existing field/stadium, but worth not having the aggravation of continual clock issues.
The RFI issue is quite real. If you use crew-comm radios, you have probably heard phones ringing, static, squealing, other conversations, etc., in your ears. Those same RF signals can wreak havoc on any form of wireless transmission systems.