Old Rajai, new success?

I'm not sure how useful this is, but if anyone was wondering what the odds were of the "Old Rajai" batting as well as he is now without having improved at all, but by just being lucky, I did some quick math.

Assuming he is a .265 batter (his career BA) then there is a 5.6% chance he would have at least 20 hits over the 57 AB's since the break.

Assuming he is a .288 batter (his '09 BA thus far) there is an 11.7% chance.

Assuming he is a .257 batter (his first half BA) there is a 4.1% chance.

They way I calculated this was based on his pre-game, 8/08/09 BA, versus various other past performances. I used BA because that is binomial (hit or out) and thus much easier to calculate. Luckily, Rajai's batting average has increased by nearly  the same degree as his OPS (1.37 vs 1.36) so this crude formula should do the trick. As for the math, I am using the binomcdf formula on TI calculators, subtracted from 1.

Things to keep in mind:

This does not factor in his increased SLG which has increased nearly 50%.

Nor does it account for his improved number of walks, which I considered counting as hits, but decided not to.

The percentages above represent his probability of having a .351 or greater BA and thus is greater than his probability of having exactly a .351 BA.

In general, if something occurs at a rate less than 5% it is considered unlikely.

In general, 50 independant events is sufficient to draw conclusions from, we are working with 57 AB's, and it is debatably if these are truly independant events or if streakyness is a factor, due to increased confidence, for example.

His July and August BA is better than his 2nd half BA and includes more AB's, so it may be more useful, although I thought that there might be something more significant about doing it this way because of the break.

This is post is not meant to discount Rajai's 2nd half achievements in anyway, I was just curious, and thought others might be too.