Expected Number of Bad Beats?

[slohar]

Let me start by saying that this is not a bad beat story. I suffered what seemed like a large number of bad beats this evening and it got me wondering what is to be expected.

I played 870 hands this evening (4 tabling) and suffered 13 bad beats. I define a bad beat as being clearly ahead on the flop and losing to someone with an inferior hand that beats me on the turn or river. I do not include being beat by people with flush draws, open ended straight draws or even 2 over cards. Here is where/how I lost:

Turn - 5 times
River - 4 times
Gut shot straight on turn/riv (not included in above) - 3 times
Runner Runner Flush (not included in above)- 1 time

You may be thinking that suffering a bad beat on 1.5% (13/870)of the hands played does not sound like much. Now to put it in a little more context, here are some more stats:

I saw flop 30.8% of the time or 267 times (this includes some short handed play)

I folded on the flop 10.6% of the time or 92 times. This leaves me with 175 hands.

I bet or raised 29.8% of the time on the flop or 52 times. 52 times i led out because i thought I was ahead (or semi-bluffed or led out with unimproved preflop raising hand) and i suffered 13 bad beats. That is is 25% of the time!

So I ask: what is a normal amount of bad beats that one can expect to experience over time?

Im case you are wondering, I lost 57.5 BB on these bad beats and 134.5 BB in total pots on these hands. I feel fortunate to have won a total of 34.5 BB in this session.