Back to your opening post:
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How can this be explained? Do I need a more powerful preamp?
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... and a subsequent post:
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Is is possible to know in advance what the ideal preamp gain should be? On one side we have cable loss (which is relatively straightforward to calculate). A few db on top of that should be fine, however too much would lead to overloading. How can someone figure out the sweet spot?
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The explanation has already been offered, there is more to reliable reception than signal strength. Noise, interference and multipath are all potential challenges. An amplifier has no ability to remove or correct any of these transmission impairments because they occur before the signal arrives at the amplifier. You are correct that an amplifier is able to overcome cable and splitter losses. An amplifier can also aid in the case of poor receiver noise figure if the signal going into the amplifier has sufficient noise margin and the amplifier does not distort the signal or add excessive noise.
Look at your TV Fool report... you'll see that many signals are predicted to arrive at your location at power levels as high as -21 dBm. The tuner should be able to automatically adjust it's input gain to deal with the wide range of signal levels that may be present. An amplifier offering 29 dB of gain will not be at risk of over-amplifying a signal arriving at -80 dBm... It will however cause trouble when fed a signal at -25 dBm. (The 'sweet spot' is quite broad.)
If there is a solution to reliable reception of weak, distant signals... it lies in the selection and placement of the antenna. Quit looking to an amplifier as a fix for a too small, or poorly located antenna. If reception of WUTV is of upmost priority to you, select an antenna that has maximum performance at the frequency of real channel 14. The Winegard HD7698P and the Antennas Direct XG-91 come to mind... as does the enormous Wade PB-82-BB (8 feet by 16 feet and 155 lbs... and a bunch of money). Also look at placement options that would improve the reception conditions... possibly tower mounting.