Cycles (June 27, 2003)
Mike's Baseball Rants looks at the odds of Cycles.
--posted by TangoTiger at 10:19 AM EDT
Posted 12:06 p.m.,
June 27, 2003
(#1) -
PhillyBooster
"Single: 17.10% Double: 3.83% Triple: 0.88% Home Run: 1.60%
Today doubles and home runs are more plentiful and singles and triples are rarer than the historical average (Actually a league has not recorded a single or triple percentage as high as the average since the mid-Forties)."
This makes a huge difference, though. Assume that the chances of A happening are 0.5 and the chances of B happening are 0.5. The chances of A and then B happening in sequential at bats is 0.25.
But what if the 0.5 is just an average? To simplify, what if at any given moment, the chance of A is either 0.8 or 0.2, and the chance of B is 0.2 (when A is 0.8) of 0.8 (when A is 0.2). Over the decades, the chance of A and B are both 0.5, but that is just an average.
Now, the chances of A and then B in sequential at bats in not 0.25. At any given time, the chance will be 0.8*0.2 (or 0.2*0.8), which is 0.16.
In an era with a very low triples rate, using the higher 0.88 number should increase your chances considerably. Also, for most of the time that the triples rate was high, the homer rate was much lower than the multi-year average, so the chances were probably overstated for the dead-ball era as well.
Posted 12:38 p.m.,
June 27, 2003
(#2) -
Andrew Edwards
Another explanation for why the actual rate of cycles exceeds the expected rate is that players might start performing to the cycle.
That is, if you're just missing a double, maybe you try to stretch that single. If you're just missing a home run, maybe you swing a little more for the fences. If you're just missing a single (and we've all seen this), maybe you pull up a bit on a borderline double.
If I was better at manipulating play-by-play data, I think I could check this. I should learn ASS sometime.
Overall, I'd say this is probably just part of why they beat expectations. I think 'bad pitchers' are the best explanation. I'm more likely to double off a guy who's already allowed me a single, triple, and homer than I am off a guy who I haven't hit all day.
Posted 1:00 p.m.,
June 27, 2003
(#3) -
Mike(e-mail)
(homepage)
True. Actually the all-time averages were just used in calculating the 4-AB, sequential cycles to illustrate the rarity. The historical expectation of 2.97 is actually around 2.49 adding up the expected values for each year. Of course, that's based on fractions of expected sequential cycles per year, so they are both basically based on funny money. The point is that a sequential, 4-AB cycle is extremely rare
The yearly expectations were all based on each league's odds for that year.
Thanks,
Mike
Posted 5:26 p.m.,
June 27, 2003
(#4) -
FJM
PhillyBooster makes a very good point about the danger of compounding averages. It's even more critical than that. Since the vast majority of potential cycles fail for lack of either a triple or a homerun, let's confine ourselves to those two stats. Last year there were a total of 921 triples and 5,059 HR's hit. Of the 5,059 homers, 1,189 (23.5%) were hit by players who didn't have a triple all season! So nearly one quarter of all HR's could not possibly have contributed to a cycle. Another 1,103 HR's (21.8%) were hit by players who had only one triple all season. While we can't rule out the possibility that these contributed to a cycle, the odds are overwhelmingly against it. So nearly half last year's HR's were essentially "wasted" on players who had little or no hope of hitting for the cycle.
Posted 9:01 p.m.,
June 27, 2003
(#5) -
dsm
I might add that most (non-neutral) ballparks favor either HRs or other extra-base hits. Few favor both (I could be wrong, but does anyone know if there is a park which increases HRs AND 3Bs?). This would tend to drag down cycles as well. Well, I guess in this era any pro-triple ballpark will increase the odds of a cycle, but you get the point.
Posted 2:02 a.m.,
June 29, 2003
(#6) -
Kostya Medvedovsky
", but does anyone know if there is a park which increases HRs AND 3Bs?). "
Actually, this appears to be more common than one would expect.
Arizona has a 3B factor of 1.57 and a HR factor of 1.01
Colorado has a 3B factor of 1.61 and a HR factor of 1.70
Houston has a 3B factor of 1.70 and a HR factor of 1.19
Kansas City has a 3B factor of 1.38, and a HR factor of 1.02
and
Texas has a 3B factor of 1.30 and a HR factor of 1.08
Now I don't suppose if anyone knows if a surprisingly large number of a cycles have occured in these stadiums?
Unfortunately, they are all relatively new stadiums, so the odds of a good sample size are minimal.
Posted 3:03 a.m.,
July 5, 2003
(#7) -
Bangkok9
A sequential cycle might be a little easier than it looks, particularly the 4 AB variety. If the cycler plays a full game he'll generally get his third AB (triple) against a tiring starter or a middling middle reliever (higher BAAs) and his fourth (HR) against a closer or relief ace who generally throw harder than middle relievers.
Posted 5:59 p.m.,
February 5, 2004
(#8) -
Matthew E
Another explanation for why the actual rate of cycles exceeds the expected rate is that players might start performing to the cycle.
That is, if you're just missing a double, maybe you try to stretch that single. If you're just missing a home run, maybe you swing a little more for the fences. If you're just missing a single (and we've all seen this), maybe you pull up a bit on a borderline double.
I can provide anecdotal support for this idea. Both Toronto cycles (Gruber and Frye) were completed when the player concerned 'stretched' a double into a single. The Gruber 'single' was borderline; it was (as I recall) a bloop to right center. He probably would have been safe at second but no guarantees. The Frye single was a double all the way, but the first base coach stopped him.