Monthly Archives: February 2014

Directional Statistics

At Booz Allen in 2012, I needed to find the average time of day that something happened as part of my code. Taking the normal (linear) average of times of day doesn’t work because there is always a discontinuity somewhere, usually midnight. Since times of day are periodic, 11:59 pm and 1:01 am should average to midnight, not noon. But they’ll average to noon (1200) if you average something like 2359 (military time) and 0001.

I thought we had stumbled on to an area of mathematics that needed further study: finding the average and variance of periodic variables. Because all of my internet searches were things like “how to average periodic variables” and “average time of day” and the like, I could not find anything on the internet about how to solve this problem. So I started to derive an answer and ended up with something very similar to what I now learn is called Directional Statistics. Wiki article on directional statistics. I never thought to search for anything like “Directional Statistics” or “Circular Statistics” or anything similar, so I didn’t find Directional Statistics until Dave Anderson showed them to me this week.

The basic idea (that AJ Mobley, Dave, and I derived at Booz Allen) is that you treat times of day as points on the unit circle, and then average the points in two-dimensions. Invert the “average point” to get the average time of day. Additionally, the farther the point is from the origin, the lower the variance of the points.

Other Roads Not Taken

Interesting post on Grantland about how Alex Rodriguez’s career could be remembered so differently if certain small things had turned out differently. He was a rookie during the ’94 strike season, and that year ended up counting toward his major league experience, so he hit the free agency market a year early. Later with the Rangers, he was almost traded to the Red Sox for Manny Ramirez and Jon Lester, but MLBPA nixed the deal because Rodriguez was taking a pay cut on his historically high contract with the Yankees. Just imagine how differently Rodriguez would be perceived if he had been a Red Sock the last ten years (2+ championships) instead of a Yankee (1 championship and tons of controversy).

5 Other “what-ifs” that I thought of in sports:
1. What if grass had grown in Houston’s spiffy new Astro Dome in 1965? Would so many teams have suffered the realities of Astroturf and other artificial turfs?
2. What if Kentucky had better shut down Dwayne Wade in the 2003 Elite Eight? Wade’s triple-double and the publicity it brought him propelled him to enter the draft after his junior year and he was taken 5th overall by the Heat. If Wade goes 15/5/5 instead of 29/11/11 and UK wins, does Wade enter the draft? Does The Decision happen in 2010 so Lebron and Wade can be buddy-buddy?
3. What if Hayward’s shot goes in? Does Butler get to a 2nd straight final the next year? Does Brad Stevens leave for Boston?
4. What if Bob Knight doesn’t choke Neil Reed in practice? Does he do something else stupid that gets him fired? Is he still coaching IU today (he’s 73)? Would we be spared the misery of listening him try to announce games?
5. What if the Colts and Rams’ owners never swapped teams? Do the Colts end up moving to Indy? If they never leave Baltimore, what does Art Modell do to the Browns? The Rams were in Los Angeles at the time of the swap; does Los Angeles have a football team today?

My definition of “Sports”

The Olympics kicked off yesterday. Whoever approves competitions for inclusion in the Olympics does not share my view of what constitutes a sport. Here is their list of Olympic Sports.

In my opinion, sports are athletic events that have an offense and a defense.

My definition limits “sports” to athletic events where you “score” a point/goal/run/etc on your opponent and the winner of the contest is defined in some way by who scores the most. Additionally, there must be some aspect of defense whereby each team is trying to keep the other team from scoring.

Let’s examine some of the events on the Olympic list to see if they are really sports.
Archery/Shooting/Bobsled/Skating/Skiing/Diving/Weightlifting: Not sports. You don’t even compete at the same time as your opponents, so there’s no defense.
Trampoline: Please. Kid’s backyard event. Not a sport.
Tennis/Badminton: Sports. You’re constantly trying to score points while keeping your opponent from scoring.
Table Tennis: The way they play, I guess these are athletic events. Maybe. Sport.
Swimming/Rowing: You compete at the same time as your opponents, but you have to stay in your lane and cannot affect their performance. Not sports. This goes for any “stay in your lane” track and field events too.
Boxing/Judo/Taekwondo: Offense-Hit opponent. Defense-Avoid opponent’s attack. Sports.
Volleyball/Soccer/Basketball/Hockey: Classic team sports.
Winter biathlon: Ski. Shoot. Ski. Shoot. Unless you can shoot your opponent to slow them down, not a sport.
Golf: There is some strategy involved in how you play which depends on how well your opponent(s) are doing, but you cannot really stop your opponent from doing well in any way. Not a sport.

Tougher calls:
Racing events (cycling/sailing/long-distance running/skating/skiing) where you don’t have to stay in your lane: You can sometimes interact with your opponent by blocking their path. But that’s not really the point of the event. The point is to get the finish line the fastest. Maybe some strategy involved in the pace that you set, but no real offense or defense. Not sports.
Curling: There is definitely “scoring” based on where the stones end up. And you can prevent the opponent from scoring by knocking out their stones. And it’s fairly athletic, so I’m going to say it’s a sport.

By my count, the only two real sports in the Winter Olympics are hockey and curling. The rest can be “athletic events”, but they’re not sports.

Additionally, watching athletic events with cryptic subjective scoring is annoying. Figure skating, “style” skiing events, gymnastics, and diving, I’m looking at you. Figure out a real way to decide the winner.

It’s a travesty that baseball/softball are not in the Olympics when trampoline is. The ancient Greeks would be ashamed.

Curling is pretty awesome.

My Super Bowl Prop Bets

I took some time yesterday morning to scour the internet for prop bets related to the Super Bowl. Here are the bets I designed and the payouts I set:

Super Bowl Prop Bets

If you watched the Super Bowl, you know that it was one of the worst games ever. The Broncos did everything they could to lose and the Seahawks were fairly flawless. If you didn’t watch the Super Bowl, what’s wrong with you?

We had a Super Bowl party at our condo, and charged $2 to enter our betting game. I was obviously not expecting the outcome of the game that happened, because I set “Seahawks win by 29.5 or more” as 100-1 odds. That came true and made calculating the winner pretty easy. Ryan and Nicole Van Klompenburg take home the winnings with their long-shot bet.