I don't think it's weird to end up drawing yourself, or to use your own image as a base for a character design. What would be weird is if you actually looked exactly like that

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It depends on the game though - to have a game where you are running around being a hero, killing things etc, then some people might consider that arrogant - however if the game was more subdued, then there's no reason why you can't star yourself. My brothers ex used to ask me to put her in a game all the time. If she was fit, then I'd see the point, but she's just miserable looking, who wants a munter in their game, just so she can tell people there's a game about her. It's arrogant to think like that, arrogant and annoying

. Putting yourself in a game your making yourself is probably not arrogant at all - maybe it's like when you draw a picture of a willy on a textbook at school, we probably all draw our own, but would never actually admit to that.
The way I see it, if you decided that the character should be you, then that's very different to the character ending up looking like you. If you were to make a game like Braid, then that's the sort of thing where we expect to see similarities, whether they are advertised or not. I can imagine the lead coder of Braid to look a little bit like the player character, it just has that familiar feel to it. The character you have drawn (excellently I should add) looks like he'd be at home in a more intelligent game, like Braid, something that needs some thought.
Now for a story...
When I was in primary school we got a visit from a famous sci-fi writer whoose name escapes me, got to meet Darth Vader and Rolf Harris too, Primary school rocked in the 80's!.
Anyhoo he told us about an artist that was given the job of painting a cover for his book, but the artist kept drawing the protagonists ship as the Millenium Falcon. It was too late to change it, so the book was published with that dodgy cover - but the artist claims to have never seen Star Wars, or the Millenium Falcon before.
His resolution to that is that the artist must have seen it, but forgotten about it, then pulled it when designing the ship for the book cover. Inspiration comes from lots of places, some of which we're not even directly aware of. If you ended up making your main character look like you, then that must be who he should look like, you must want the character to be you. Can I just ask, is this a game you've been planning for a long time? - maybe even an old idea that you are reincarnating?. See whenever I think of a really old game idea, I tend to picture myself as the protagonist - maybe that's because I'd think about these ideas as a kid, and that's just how the human brain works - in our own ideas our characters don't have life yet, and to get very far in daydreaming about it, we have to flesh them out and it's easiest to use ourselves, as we are imagining being the character anyway. We probably don't think like that as adults, but kids often tell stories as if they are the protagonist.
Anyhoo, sorry to get all psycho-iatrist - I just find this stuff interesting, maybe because I'm finished work soon and it's Friday - there should be a thoughtful topic like this for every day of the week

- welcome distraction!.