Jerome Gambit: Target f7

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I was considering a post focused on the topic of piece sacrifices on f7 - a dynamic in the Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) - when I came across the following (3-year old) discussion on reddit.

It brings to mind an early post of mine, " King of Bxf7+", from the 4th month of this blog, back in 20008.

The question can clearly be asked about the Jerome, and the responses given, likewise.

Does the "gambit" 1.e4 e5 2.Bc4 (any) 3.Bxf7 have a name? Practically why is it not as bad as it seems?

Strategy: Openings

I faced with this "gambit" sometimes. There's no way that this is a good sacrifice, but I checked the lichess database, and here is the win rate:

2....Nf6 3.Bxf7+ White 48% Black 49% (16k games)

2....Nc6 3.Bxf7+ White 48% Black 50% (23k games)

2....Bc5 3.Bxf7+ White 50% Black 46% (16k games)

2....d6 3.Bxf7+ White 53% Black 44% (8.7k games)

2....c6 3.Bxf7+ White 50% Black 47% (3k games)

2....Be7 3.Bxf7+ White 44% Black 52% (794 games, because black king is somewhat safer?)

2....c5 3.Bxf7+ White 50% Black 47% (1k games)

Even when f7 is defended by other pieces...

2....Qf6?! 3.Bxf7+ White 56% Black 42% (1k games)

2....Qe7?! 3.Bxf7+ White 50% Black 45% (230 games)

2....Nh6!?! 3.Bxf7+?? White 40% Black 58% (111 games, still not bad considering Nh6 is almost entirely for the purpose of Bxf7)

Or when black moves the f7 pawn...

2....f5 3.Bf7?? White 44% Black 54% (662 games)

2....f6?! 3.Bf7+?? White 52% Black 48% (171 games)

Or weird moves?

2....Qh4?! 3.Bxf7+ White 48% Black 50% (200 games)

2....Ke7?! 3.Bxf7 White 50% Black 50% (24 games ... probably troll games)

This can't be a coincidence. White is doing surprisingly well in this "gambit". The engine evaluation for all those positions are at least -3 (some even -4, for example the Nh6 one). The general win rate for white in all those Bxf7 openings is at least 48% (even higher), which almost makes it a viable opening. (Well, 1.e3 has a win rate of 47% for white, and I'm sure after 1.e3 white is doing at least fine) We can just compare with other openings which are about as bad: e4 f5 exf5 e6 : +3.0, Black 33%. d4 e5 dxe5 f5 : +2.4, Black 36%. e4 d5 Nf3 dxe4 Ng1 : -2.1, White 39%. These win rates are about expected. But a 48% win rate for a -3 opening? How's that possible?

So, why? This "gambit" can't be good, can it? Does it have a name? And, how to effectively punish it?

Are you sure that you are considering, in your database percentages, games of "good" players only (say with Elo > N)? Because if otherwise, and you are considering beginners games, you can more or less sacrifice any piece on the board and the result will always be 50% 

FMExperiment

Those stats aren't really good to go by since a large number of 1min bullet games usually skew the results

Wyverstein

When I first learned to at chess a local master use to play that against me as a sort of odds game. We played it until I could win a few in a row. Then he moved on to another dubious gambit until I learned that one too. Tldr I think a lot of games if they do have a high rated player might be teaching games.