Chapter 3

page 39: The picture is of Greg Luzinski, when “The Bull" was with the White Sox, in Fenway Park. I was hoping to capture a Bull-ish , but the swing-and-a-miss was perfect for this chapter introduction. Does this mean I can go back and deduct the cost of Fenway tickets?

page 40 - This is one of the few examples of a calculus problem type called related rates that is worthwhile. The problem is inspired by Watts and Bahill’s Keep Your Eye on the Ball and appears in the Smith and Minton Calculus books.

page 41 - teams increasingly use virtual reality training techniques to help batters recognize types of pitches and predict the eventual locations of the pitches.

The softball pitcher is Kelly Higbie of Roanoke College. In 2012, Higbie pitched Roanoke to ODAC and regional championships and into a third place …nish at the College with a roster of 10 able-bodied women.

I have never found any video of Jennie Finch’s pitching against major lea- guers. There is a video of ‡ailing and failing against Michele Smith at https://www.youtube.com/watch?v=RT9ntDaFu1M (accessed 5/7/2016).

page 42 - Sport Science segments on softball pitching are at https://www.youtube.com/watch?v=QEtG5KvuWs4 and https://www.youtube.com/watch?v=JG8NOR6Lg2c (accessed 5/25/2016), the latter featuring Jennie Finch.

I am not an expert in neuroscience, but as of 5/25/2016 a Google search for sports occlusion experiments brought up several interesting papers. One, involving tennis players predicting serves, is speci…cally designed to try to tease out whether video occlusion experiments allow subjects to use clues that are not present in real life.

A YouTube of the Epstein-Gladwell discussion “10,000 Hours vs The Sports Gene" is at https://www.youtube.com/watch?v=iXBhINPoKEk (accessed 5/25/2016). I attended this live. Going in, I was worried that Gladwell and what I thought would be a warm-and-fuzzy support of the 10,000-hour rule would be destroyed in an uncomfortable manner by Epstein’sresearch-backed genetic evidence. In- stead, I found an enjoyable conversation between two intelligent reporters who have a thoughtful and nuanced view of the nature/nurture issue. Gladwell seems taken about by the public’s identi…cation of him with the 10,000-hour rule, which is at best a guideline best applied to intellectual pursuits.

page 43 - The …eld goal angle question is one of those situations where we need to overcome inertia and simply ask whether it is true that moving back

1 improves the angle. It seemed plausible to me for years that this is true.

page 44 - A good study would be to compute percentages of …eld goals made from di¤erent positions on the …eld. To my knowledge, this has not been done. Drew Pasteur and his student Kyle Cunningham-Roads and others have done studies on NFL kicking, but the hash marks in the NFL line up with the (narrow) goal posts, so angles do not change much. Nevertheless, the movement of the NFL extra point back gives us some data on where kickers like to have the ball placed.

page 45 - The picture is of Lanny Wadkins, who had one of the quickest backswings in golf.

page 46 - You can see an amazingly large forward bending of the club in several pictures of Long Drive contestants. A nice discussion of how cam- eras can distort the truth, along with a couple of nice pictures, can be found at http://www.tutelman.com/golf/measure/focalPlaneDistortion.php (accessed 5/25/2016).

I don’tactually know much about valgus torque, but I have been to a good academic talk about how the pitcher’selbow bends unnaturally.

page 47 - Roanoke College had the pleasure of hosting Bill Franz, the father of one of our favorite mathematics majors Lizzie Franz, for an excellent talk on several hard o¢ ciating calls including the o¤side call. Brain Games is an excellent series of shows on the National Geographic channel.

page 48 - The picture is from a Salem Red Sox game. The lesson I learned from attending multiple games with camera is that there are surprisingly few close plays at …rst. The only really good close play at …rst that I witnessed produced a picture of a blurred and very large fan walking in front of me at the wrong time.

page 49 - Galarraga and Joyce wrote the book Nobody’sPerfect: Two Men, One Call, and a Game for Baseball History. I have not read it, but I hope it has sold well because the two men deserve a nice reward for their sportsmanship.

The straddle or barrel-roll technique for high jumping is demonstrated at https://www.youtube.com/watch?v=RxsI0LRH5u0 and a survey of other tech- niques can be found at https://www.youtube.com/watch?v=-OtkrNq1fZg (ac- cessed 5/25/2016).

page 50 - The jumper in the picture is of Johnna Dominick. Thanks to Dave Knachel for his help. Photo credit to Virginia Tech Athletics.

2 page 51 - Exercise 3.5 - The calculations here ignore air drag. Do you think the relative reaction times would change much if air drag was accounted for?

Exercise 3.6 - There are a number of articles about the e¤ect of birth date in sports. Imagine a sport in which the “8-year-old" league consists of kids born any time in the calendar year 8 years ago. Someone with a January 1 birthday will a year older than someone with a December 31 birthday, but they will be in the same age group. The January 1 child is likely to be larger and more mature physically, and therefore better. Being better, the January 1 child gets more playing and opportunities for all-star leagues with better coaching, and the gap between the two players is likely to grow.

Exercise 3.9 - This is a nice way to get a bound on the limits of human performance. No matter how good the equipment is, energy cannot be increased. (Having typed this, I now wonder about motors inside the pole.)

Exercise 3.13 - The idea here is that the o¤side call is literally an impossible call.

Exercise 3.14 - The fact that everybody now uses the Fosbury Flop technique is strong evidence that it was revolutionary. It is interesting to try to …nd direct evidence of this in the data. You can imagine that a similar situation holds for steroid usage.

page 52 - Exercise 3.15 - If you are a baseball fan, does it look like a fastball drops a couple of feet on the way to home plate? Batters visually rede…ne the standard shape to be “level" and conclude that a ball that does not drop as much as usual actually rises.

Exercise 3.17 - Chad Bradford was featured in Moneyball as a pitcher with low velocity but an e¤ective delivery - in other words, an e¤ective player with a ‡aw (slow fastball) that would allow Oakland to sign him for little money.

Exercise 3.18 - See the ESPN documentary Jordan Rides the Bus (in which it is argued that Jordan was, in fact, a pretty good hitter by the end of his career) and Harold Klawans’book Why Michael Couldn’t Hit.

Exercise 3.19 - The times can be distorted if the subject anticipates when you are going to drop the ruler.

Exercise 3.22 - The information on long-distance runners and sprinters in The Sports Gene is enlightening.

Exercise 3.23 - Basketball announcers often talk about players who are really “long" due to a large wingspan-to-height ratio.

3 page 53 - Exercise 3.28 - Whether the tendency is contrary or not depends on whether the umpire is primarily watching the ball or the runner. Presumably it would be easier to watch the ball.

Exercise 3.32 - Mathematica code will be posted on the website.

Exercise 3.36 - Whether or not this calculation is of practical interest depends on where a goalie and defensemen would be positioned and whether the goalie’s reaction time is a¤ected by angle.

Exercise 3.39 - Lefthanded baseball players dying younger is a great example of a statistical “fact" that can create many di¤erent explanations of cause, but that ought to create proper caution when dealing with statistical results.

4