Home Run Streaks

Last night, the Jays hit a home run in their 16th consecutive game, which seems to be a fairly impressive streak. I wanted to find out if in fact it was impressive, and just how difficult is it to do?

First of all, this streak is now the second longest HR streak by the Jays in club history. It is also the second longest HR streak in the MLB so far this year. The 16 games in a row is only surpassed by the 23 games in a row in 2000. So while this isn't exactly uncharted territory, they do have a good streak going. What makes this streak really interesting is that, out of all HR streaks of at least 13 games, it is the only streak where they have a losing record (they are currently 5-11 in the streak, the next worst streak is when they went 7-7 in 14 games in 1996). Also interesting is that they have only scored 73 runs in the 16 games, which gives them a runs scored/game of 4.56, which is also the lowest of the ten times they have hit home runs in at least 13 games straight.

Another interesting fact is that while they have hit 31 home runs in the 16 games (1.94/game, as opposed to 1.51 HR/game the rest of the season), they are scoring fewer runs per game than for the entire season (they were averaging 4.65 runs/game in their first 129 games, they are averaging 4.56 runs/game in the last 16). So while they are hitting more home runs, those runs produced from the home runs seem to be just about the only runs they are scoring.

The last thing I wanted to do was figure out how difficult it is to hit home runs in 16 straight games. The Jays have hit 226 home runs so far this year, and have hit home runs in 107 of the 145 games they have played (here is a summary of every home run they have hit so far if you are so interested). So the probability of them hitting a home run in any given game is 0.738, or 73.8%. That means that the probability of them hitting a home run in n different games is simply 0.738ⁿ, as the probability of them hitting a home run in two games is 0.738*0.738, in three games 0.738*0.738*0.738, and so on up to n. So the probability of them hitting a home run in 16 straight games is 0.738¹⁶, which is equal to 0.774%. What this means is that out of 1000 "sets" of 16 games, the Blue Jays would hit a home run in each game 7.74 times, or one out of every 129.2 sets. Considering that there are 147 sets of 16 games in each season (games 1-16, 2-17, 3-18, ..., 146-161, 147-162), we can see that this should happen about 1.138 times this season.

So what we can see by looking at the math is that although this streak of home runs is impressive, it is certainly not out of the ordinary and mathematically probably should have happened at least once this season. Now, keep in mind that the Blue Jays are hitting home runs at a mindblowing pace this year (on pace for 252.5), in fact very close to the record for most home runs by a team in a single season (the 1997 Seattle Mariners hold the record with 264 HRs). So the chances of the 2010 Blue Jays to hit home runs in 16 straight games is a lot higher than the chance of any other Blue Jays team to hit home runs in 16 straight games. That is why this is the second longest streak in club history. It remains to be seen how long they can continue the streak, but don't be surprised if it ends tonight or during the weekend series with the Red Sox.