What are the odds of seeing at least one grand slam for any MLB baseball game? That is if I go to a baseball game what is the percentage chance (expected value) I'll witness a grand slam?
Offensive statistics rise and fall over time. So to make things easier, I'm just going to look at figures since 2001. (2000 seems to be a bit of an outlier)
Baseball Almanac has grand slam totals for MLB by league over the years, but only through 2013. I didn't find a free reference for the stats after that time. Unfortunately the figures dip a bit in the 2011-2013 range, which may be part of a trend that is partially hidden by not having more recent data.
In the 2001 - 2013 seasons, there were a total of 1596 grand slams.
From Baseball Reference, we can see that each individual team plays about 4860 games each year, or about 63180 games in total. But there are two teams competing at each game, so just under 31600 competitions in that time. (Bryan Turriff pointed out that I had forgotten that you're watching two teams at a time).
This gives a 5.0% chance of seeing a grand slam in any random MLB game with similar offensive output.
As Philip Kendall noted, this gives us the expectation of grand slams per game. But it is too high if you are simply interested in the chance of seeing a game with at least one slam (since some games may have multiple slams). Fortunately the first reference (Baseball Almanac) lists all games with multiple grand slams, so this can be checked. For the 13 years in question, there were only 15 slams hit in a game that already had one. Removing those 15 slams changes the figure only in hundredths of a percent, so 5.0% is still a reasonable rate.