I have been studying this and here are the results I came up with using the last two weeks of each teams games.
Teams trying to win 3rd game (W3 streak) 20 of 47 won (not a big deal but some nice shots here)
Teams trying to win 4th game (W4 streak) 15 of 17 won! (nice numbers only 2 loses on teams going for their 4th straight win in the last two weeks)
Teams trying to win 5th game (W5 streak) 9-11 won! (another decent proposition. Good numbers here too.)
Basically from what I see so far. You could do well in all these categories if they continue. The numbers are small. The best way to use the teams going for win 3 is to bet against them and take the underdog, like Texas vs Oakland today as an example, KC was another example but they won. With a little common sense and smart betting this could be a shot picker.) With teams going for their 4th win in a row seems they are hot and have made it past the tough W3 and seem to move nicely on to winning 5 also. Might be something to look at. Betting a team that won the hard 3rd straight as they get their 4th and 5th in a row. I will keep an eye on this. It looks really good right now. I need to go back and get the first week of the season and add it and it needs more numbers but it is something to add to your capping, especially if you can get some type of dog method.
Teams going for W3 + pitcher's revenge angle + secondary star sytem plays which usually lose might good be a good super dog system play if they ever come together, I'll have to back track it and check it out.