Isn't this an example of the gambler's fallacy, that previous outcomes impact future outcomes?
If I remember correctly, the gambler's fallacy is for fully independent events. I think the assumption here is that the team's performance in a game will impact their next result. After a win, they get on a roll. After a loss, the coach gives them a stern talking to and they come out playing a bit harder the next night. There's some correlation between games, but I'd say it's mostly independent... I'm not a statistic…
I pitched 5 mph less due to mental effort? Well, now you don't get to throw again for 5 days. Or you walked 15 batters in a row to try and get taken out of the game. It's not going to make your night easier, you sit there till the game is finally over. No clock to run out. Just outs.