Taking into account musical memory of the notes and lyrics (though the lyrics are often on the screen), and physical ability to perform the song, about how many songs can the average karaoke singer credibly perform and make sound good?
How good is the average person’s musical memory?
I don’t know. But something I do in the car sometimes when there’s nothing on I want to listen to, is flick through all my presets and sing the crap out of whatever pops up. Just a few moments of each, on to the next, be it metal, classic country, adult contemporary, 80s…switch! I know the words to every damn thing. 
I can remember the words and melody of a whole lot of songs - if I had a lyric sheet to prompt me, the number would almost double. Unfortunately, I completely fail the “make it sound good” portion of events.
Anyone can sing any Ringo Starr song.
About 0.2.
Any number, as long as the singer knows the song. That is, the lyrics and melody. The trick to “selling” karaoke is to know the lyrics; if you spend your time on stage staring at a TV monitor, you’re doing it wrong.
Even if you need the words from the TV monitor, you can still sell it, by looking at the audience from time to time.
In my case, I know 10 or 12 songs straight off the top of my head, no lyrics needed. I know perhaps two or three dozen more that I might need a little prompting for, and the TV monitor out of the corner of my eye helps. And I can credibly perform them all.
Key (heh) is knowing what your voice is (soprano, alto, tenor, bass), and selecting songs that you can actually do with your voice. The guy who shouts “Roxxxxxx-anne” without singing the rest of the song, and the guy who tries to talk through “Sweet Caroline” just so he can get the crowd going on the “ba-ba-bas,” has no idea what he’s doing, what his voice is, or really, why he’s singing. And I won’t even begin to discuss the guy who tried to do Led Zepplin’s “Black Dog.” That was painful.
(Slight hijack)
I recently thought of the idea of assigning a value for pop singers, similar to how baseball players have a WAR (Wins Above Replacement) value. The idea of WAR for baseball players is to calculate how many extra wins they give their team over a full season compared to how many games their team would have won using a replacement-level player (an average AAA minor leaguer or free agent who is sitting by the phone waiting for a team to sign him). Players having an especially poor season can have a negative WAR, while a league MVP may have a WAR of 8 or 10.
In my scheme, the replacement singer would be an average karaoke singer. Artists who are especially bad (Vanilla Ice, etc.) are actually worse than the average amateur karaoke singer, so Vanilla Ice would have a negative WAR. IMO, Kelly Clarkson is no better or worse than the average karaoke singer, so she has a WAR of zero. (I do not like her songs.)
One of the keys to being good at karaoke is to know what version of the song they are using so you don’t need to look at the screen for the words. Most songs are abbreviated versions of the ones you hear on the radio, so even if you know the song by heart you can fuck it up by getting out of time with the version they are using. Once you trip it up, its hard to recover.
This is my problem. I remember melodies perfectly fine, but I have a terrible memory for lyrics. My one time trying Karaoke, it was a disaster.
Isn’t disaster the whole point of karaoke machines? You don’t go up because you’ll provide an entertaining performance in its own right; you go up with the expectation that it’ll be so bad that it’s entertaining.
In my experiance there are a couple of types of people who do karaoke. Ones who are prepared and know what they are doing and sound decent, if not damn good. And drunks that get up there on a dare and don’t realize just how stupid they sound or look (or both).
I’ve had people try to pressure me into going up and I flat out refuse to the point of leaving. I know how bad I sound, even when totally shit faced.
Especially since the lyrics on the screen aren’t always correct. I got up for karaoke on a vacation last month ( I had to get drunk, because I think I can’t sing, but I’m told I wasn’t terrible). I picked a not very well known song that wasn’t listed but it turned out the DJ had it. There are four versions- three are very similar, one is very different so I checked which version and fortunately, it was one of the ones I know. But every other line had a mistake in the lyrics - if I had to look at the screen for the lyrics, I would have been terrible.
Define credibly. When you’re slightly drunk, every song sounds great!
This may be distantly related to the question:
I’ve done a few “meet and greets” with Richard Thompson, who has been a very productive songwriter for over 50 years. At one session, I specifically asked him how many songs (with lyrics) he could confidently memorize for live performances, considering that he wrote the largest portion of them.
He said that it was about 100 songs. As he approached 100, he would need to go back and refresh himself regarding lyrics and/or chord progressions. He estimated that he could do five or six sets at any one time without using any references. He also admitted that he makes mistakes with lyrics more often than chords/keys.
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In my case I was neither prepared nor drunk. In my dumber dating days, a girl I was dating insisted I try it.
Oh, my friend, you must frequent some really great karaoke bars or have very little understanding of music. You may not like Kelly Clarkson’s songs or the way she sings, but the woman has talent and a great voice and would definitely have a positive WAR.