Fact of the Week VI: Home Runs Streaks (Part II)

This fact of the week is a follow-up to my post on Wednesday detailing the Blue Jays' current home run streak. Jose Bautista hit a home run in the 6th inning of tonight's win over the Red Sox, which is significant in two ways: it is his 48th of the season, which is a new Blue Jays single season record, passing George Bell's 47 in 1987. Secondly, it keeps the Blue Jays home run streak alive, now at 18. It is still short of the 23 they posted in 2000, but it is slowly creeping closer.

I just wanted to do some quick calculations on how likely the Jays streak is now that it is at 18 games and counting. They have now hit 228 home runs in 147 games, hitting at least one in 109 games for a probability of 0.7415. For 18 games, their probability is 0.7415¹⁸, which equals 0.459%. This means that they would hit home runs in 18 consecutive games once every 217.8 "sets" of 18 games, with a total of 145 sets of 18 games per season. So given their home run productivity this year, they were predicted to hit home runs in 18 straight games 0.6659 times. This is interesting, considering their prediction for 16 straight games was 1.138, which shows just how hard it is to continue streaks like these for longer and longer periods of time.

Now I wanted to do a calculation based on the longest home run streak by a team ever. This details the longest home run streaks by any team since 1920 (there would be no long streaks before then with the dead ball era anyway). The record is held by the 2002 Texas Rangers, who hit home runs in 27 consecutive games. I wanted to quickly calculate the odds of that team accomplishing such a feat, as I feel they will be quite low. The 2002 Rangers were nothing out of the ordinary, finishing 72-90, dead last in the AL West, except for one thing: they could mash home runs (their top two HR hitters were A-Rod with 57 and Rafael Palmeiro with 43....hmm). They hit 230 home runs, hitting at least one in 122 out of 162 games. So the probability of them hitting a home run in any given game was 0.753, and the probability of them hitting a home run in 27 straight games was 0.753²⁷, which is equal to 0.000473, or 0.0473%. This means that, on average, they would hit home runs in 27 games straight once out of every 2,114.4 sets of 27 games. Given that there are 136 "sets" of 27 games, they would be able to accomplish this feat an average of 0.0643 times that season. What this means is that with their home run production (which is one of the top home run totals ever), the probability of them hitting home runs in 27 straight games is only about 17%.

So we will see how long the Jays can continue their current streak. I predicted on Wednesday that the streak would end sometime this weekend, and I still believe that will probably be the case. It was a great night for the Jays, with the win over Boston, the continuation of the streak, and Bautista breaking the single season Jays record for home runs.