**WARNING** The illustration shown below contains analysis that is not strictly correct according to probability and statistics theory and would make any mathematician very upset... But it's probably close enough to illustrate the point***

Mike's stock answer for this type of scenario is that every event in the sim is independent hence these things can happen. (i.e. instead of hitting a batter once today and then once next month maybe a pitcher will hit two today and then not again for a while .... or maybe if the random number generator pulls up the hit batter number then he'll hit another one). Just for fun I thought it would be interesting to play with numbers on this.

I looked up El Duque's HBP stats for 1999. 8 hit batters out of 910 batters faced. In reality this gives a probability of about 0.009xx that any batter stepping to the plate will get hit. But to make the math simpler lets round it off to 0.01 (1 out of 100). This means that the probability of any single batter getting hit is 1 in 100. If he faces 30 batters a game then the probability of EXACTLY one of the 30 being hit is 30*.01=0.300

The probability of TWO CONSECUTIVE HBP would be (.01)*(.01) = .0001 (1 in 10,000) and the probability of 3 in a row is 1 in a million.

Now if you assume that every pitcher in the game hits 1 out of every 100 batters (which is obviously not true but I want a simple model) and that an average team in an average game sends 36 men to the plate then lets see what happens--

Probability of one batter on home team being hit = 36*.01 = 0.36
Probability of one batter on away team being hit = 36*.01 = 0.36
Probability of one batter on either team being hit = 72*.01 = 0.72

Probability of two consecutive batters being hit = 72*.01*.01 = 0.0072 (1 in 139)
Probability of three consecutive batters being hit = 72*.01*.01*.01 = 0.000072 (1 in 13,900)

I'm not sure how many games it takes to create a LARGE ENOUGH SAMPLE but I suppose that if you played 55,000 games you might expect to see the back-back hit batters about 400 times and the back-back-back 4 times.

Not including the playoffs each 20 team perpetual league plays 1600 games per year and each 24 team league plays 1920 games per year. With 16 20-team perpetual leagues and 17 24-team perpetual leagues in existance that adds up to 58,240 regular season games per year. Hence I suspect that back-back-back hit batters should happen in the regular season of perpetual leagues approximately 4 times per year.