Waist-to-Height Ratio [EBP 4]

This was really the best picture I could find that wasn't a slim-waisted model with a casually draped measuring tape. Source.

So,

I'm sure I don't have to tell you that obesity has become problematic in North America.  In Canada, it could prove to be an especially difficult problem due to the health consequences associated with obesity coupled with the publicly-funded nature of our health care system.  Another problem is that defining or measuring "obesity" is particularly difficult.  The Body Mass Index (BMI) has been widely used since the 1970s, and it is proportional to a persons weight divided by the square of their height.  This has worked fairly well over large populations, particularly for identifying where mortality risks increase, though it has the obvious weakness of not taking muscular or skeletal structure into account.  So, is there a better way?

Really and truly, the thing with which we should concern ourselves is body fat percentage.  This would automatically take into account muscular and skeletal structure and give an accurate picture.  This is also difficult or expensive to measure.  One way is to use calipers to take a flap of skin and measure the fat tissue underneath, but to get an accurate picture one needs to a) own a set of Vernier calipers and b) have the proper training to convert this measurement.  Another way is to pass a small electrical current through the body (usually through the feet) to measure the resistance.  Muscular tissue will have a lower resistance than adipose tissue (or perhaps vice versa), and the net resistance can be converted to body fat percentage.  The problem with this method that it varies not only by gender but also by race, and the test is only calibrated well to white males.  The final common way to measure a persons body fat percentage is to suspend them in a sling/chair sort of apparatus attached to a scale, not unlike the tray you can find in a grocery store to weigh your fruits and vegetables.  The person sitting in the sling is then submerged in a pool and the change in weight due to buoyancy force is recorded.  Since adipose or "fatty" tissue occupies more volume with less mass, it will contribute to the water exerting a greater buoyancy force on the body.  So the greater the change in weight from dry to submerged, the greater the body fat percentage.

It's tricky to describe in words.  Source.

Unfortunately, all methods of measuring body fat percentage involve specialised training, specialised equipment, or both.  And even then, there is speculation that the distribution of fat on the body also appears to play a role in mortality risk.  While I couldn't [easily] find scholarly articles to support the assertion, the hypothesis is that fat in and around the "greater omentum" (i.e. "beer gut"), encases the internal organs and can lead to health complications.  As an interesting side note to this, apparently it also makes surgery very difficult.  But, as always, I digress.

So as it stands, what we should concern ourselves with is body fat percentage, and the most widely-used metric, BMI, doesn't really attempt to approximate this.  At this point, I'm tempted to hypothetically ask if there would be a better way, but my distinguished and top-hatted readers have no doubt already read the title of this post, and know darn well that's where I'm going.  "I bet it's the waist-to-height ratio!" you're probably yelling at the screen, excitedly and inadvertently popping out your monocle.

Excellent guess, it is.  The waist to height ratio (WHtR, and I have no idea why that's the abbreviation) doesn't concern itself with the weight of the subject at all.  The lean waist doesn't tend to fluctuate much with muscular or skeletal structure, so with the exception of very narrow-waisted females, it's a pretty good analog to body fat percentage.  That's all there is to the waist to height ratio, by the way.  You divide the circumference of your waist by your height (using the same units for both measurements).  It's unitless, so you can use centimetres, inches, furlongs, leagues, whatever your heart desires.  Just make sure to use the same units.  The only point of note is to measure your waist as the figures do in the top of this post.  Fashion would define your "waist" as being below the anatomical waist.  The anatomical waist is either the narrowest part of your torso, or about an inch above your navel.

Waist-to-height ratio is also well supported in the literature as a metric of mortality risk, by the way.  An excellent review appears in Nutrition Research Reviews (2010), 23, 247–269.  The data suggest that, though the WHtR has a couple fringe weaknesses like an inability to predict diabetes mellitus in Taiwanese males, it is overall a much better indicator than BMI.  Further, a lot of references pop up with WHtR being a superior metric to BMI when monitoring children's health.  Something to think about.

Finally, it's probably worth discussing what ranges WHtR usually fall in to.  The best summary chart I have found is on the relevant Wikipedia page:

I'll also mention that an excellent discussion with pointers to great references can be found here.  So really, the healthy and normal WHtR for people usually falls between 0.42 and 0.50.  If you're above that, you may be healthy, but WHtR would suggest that you are at an increased risk of health complications, and you may want to consider action.  Similarly, it cautions that should your WHtR fall below 0.42, you are at an increased risk of [albeit different] complications, and you may want to consider action.  It is interesting to note that the body requires a certain baseline body fat percentage in order to function properly.  If you're curious about the complications of low body fat percentage, read up on body building side effects, it's a little disturbing.

So there you have it.  The evidence would suggest that WHtR is a superior metric to BMI for measuring the health of individuals, and should probably see more use as a result.  This is particularly true if you have broad shoulders, a barrel chest, or even wide hips, because your BMI will likely be skewed.  Plus, a cloth measuring tape costs a lot less than a bathroom scale, and never needs to be adjusted.

NM

Update (2015-03-16): I want to include the latest table on the aforementioned relevant Wikipedia page, because it now contains some new, entertaining entries at the low end.

Universal Public Transit [MUt2]

OC Transpo's St. Laurent Station.

So,

In my last post I discussed the merits of enjoying alcoholic beverages for their deliciousness rather than their psychoactivity.  Now, this indeed raises the issue of drinking and driving, which is a legitimate concern.  After just one standard alcoholic beverage, your reaction times are significantly diminished.  So what do you do?  Designated drivers are one solution, but it's rare that people want to be the designated driver.  As a brief aside, Schlag has been known to provide free soft drinks to the designate, because they are a class act and thoroughly wonderful.  Cabs are expensive, and public transit can at times be sporadic and unreliable.  But what if something were to be done about that?

The benefits of public transit include cleaner air, decreased fossil fuel consumption per rider, decreased traffic congestion, lower road maintenance costs per rider, et cetera.  As such, it's surprising that cities don't seem to be trying harder to encourage public transit and alternative modes of transportation.  Cycling is fantastic when you consider that it offers all of the above benefits as well as being almost a non-factor in road wear since it scales to the fourth power of weight.  Since the weight of a bicycle is an order of magnitude less than that of a car, we're talking on the order of ~10,000 times less road wear.  In fact, each bicycle trip saves the taxpayer a dollar or so because of this effect, but I digress.

In short, it is in the best interest of cities to promote methods of transportation other than single-occupant driving where possible.  Now, couple this with the idea of economies of scale.  When the University of Ottawa negotiated the universal bus pass with OC Transpo, the figure they ended on was roughly $350 for the normal eight month school year.  This was a deep discount over the already discounted student bus pass rate of $90/month simply because of the scale involved.  However, consider that the University comprises roughly 45,000 students in a city of almost one million.  When roughly five percent of the population collectively negotiated, the price of the service was less than halved.

Now, what if the whole city did it?

I am not an economist, and this is potentially a flight of fancy on my part, but what if instead of charging for transit based on single users, what if the entire city was involved and the price of the pass was built into property taxes?  I realise that there will be diminishing returns on the discount for increased pool sizes, but if 5% of the population can negotiate to less than half the original price, I feel one could reasonably assume the cost would come to at least about a quarter of what it is now.  Further, I cannot believe that an annual sum of $250 or less would be the deciding factor in whether or not someone could afford to live in a home.

With a system such as this in place, I would hypothesize (or perhaps "guess" would be a more appropriate term) that annual funding would be more stable than it is now, and planning would be easier because the distribution of potential usership [ideally] becomes that of a population density map.  I would also assume that usage frequency would dramatically increase because the cost of the trip is effectively "free," since one needn't go searching for bus tickets or spare change.  Also, it allows lower income individuals to travel to and from work without the financial burden of a more expensive bus pass, making it easier to get and keep a job.  I can tell you from experience that bus fares aren't financially negligible when you don't have a stable source of income.

I would also imagine that this would have spinoffs on tourism and other economic activity as well.  Not only can one easily/cheaply travel to and from work, but one could just as easily travel to that shop that's a few stops down the road, or a tourist could hop on a bus to go, well, anywhere really.  To be clear, I assume that this system would mean you could freely hop on a bus, meaning tourists would be free to do so as well.  Though I also assume allowing tourists to freely travel on the transit system would generate enough income that it would make the expense well worth it.  Further, would a tourist be more likely to travel to a city where they wouldn't have to rent a car and pay for parking?  I think it might be a consideration.

Other fringe benefits?  In a population that is generally regarded as overweight, it gets people involved in semi-active transport rather than driving, which is more or less completely sedentary.  I would imagine service improvements resulting from stable and increased funding would make the trips more pleasant and effective.  Another consideration is the cost of parking lots.  They're surprisingly expensive, a parking space costs hundreds to maintain if it's ground-based, and can get into the tens of thousands to maintain in a parking structure.  That's a cost that can be diminished with such a transit scheme.  And maybe, just maybe, after responsibly enjoying an alcoholic beverage or two, you and your family could simply hop on a bus/subway/LRT to get home rather than having to worry about the hassle of driving.

NM

My Utopia [MUt1]

Sir Thomas More, who apparently coined the term "Utopia," and apparent "Mr. McGrumpypants."

So,

I've found myself talking a lot about ideas lately, which is often a sign that I need to blog about something, because for some reason I feel better once it's been hammered out and available to the general public.  It's not logical, but it's a reproducible phenomenon so I'll go with it.

I'm sure we've all had ideas we think would change the world, our country or even our city or neighbourhood for the better.  I, too, have these and shall jot down a couple.  I've gone ahead and tagged the title as [MUt1] so that there will be a handy label available should I decide to write down  more ideas for improving things.

The Public House:

I'm certain that many of you have attended a so-called public house, potentially without knowing what it actually is.  This is where the "pub" gets its name.  A public house, as opposed to a private house, is a place in which friends and/or neighbours can come in, eat, drink and generally be merry.  In fact, it can (and in Britain and Ireland has been known to), function as a makeshift community centre where the locals or regulars may gather, celebrate, discuss, or even mourn together as a group.  This could, if executed properly, fix a problem I see with North American society.

The drinking of alcoholic beverages is an ancient tradition, and I'm not being hyperbolic.  It has been widely hypothesized that beer was instrumental in the building of Western society.  In an era where microbial life was ill-understood and water-borne illness was likely rampant, beer offered a safe drinking water source due to the boiling of the brew prior to fermentation.  The irony here is that the microbial life form yeast was used to out-compete and combat other hazardous microorganisms without a solid understanding of either, but I digress.

The practice appears to date back almost 11,000 years, near the beginning of agriculture and civilisation as we know it.  In fact, beer was so ingrained in our society, we depended upon it so heavily that individuals of Western descent have increased alcohol dehydrogenase concentrations in their gut (I'll clarify that this is the more colloquial use of the word "gut" because I don't actually know where it is).  Alcohol dehydrogenase is a catalyst (or "enzyme" because the catalyst is a protein and we CLEARLY need to memorize more science-y words to maintain exclusivity), which breaks down potentially-toxic ethanol into more biologically compatible or innocuous chemical species.  Let me reiterate that a little more simply, over the course of about 11ka, the blink of an eye from an evolutionary standpoint, our bodies changed to handle alcohol (in the West anyway, in the East the boiled beverage of choice was/is tea).  Either that, or those of us with better physiological tolerances were more likely to thrive and reproduce, as per the genetic algorithm that is life.  Either way, beer is so important to us as a species that it changed us at the same time it helped shape our societies.  It's still helping, by the way.  Beer represents 1% of Canada's GDP, and every dollar spent on beer becomes roughly $1.12 for municipal, provincial and federal governments. For a full hour of fascinating, beer-related discussion, this podcast is highly recommended.

My cousin and I once participated together in this millennia-old tradition.  It was delicious.

Now to the problem which I believe the public house could solve.  See that beer pictured above?  It was delicious, it was shared among friends, and it was thoroughly enjoyed.  It wasn't used solely as a means of getting drunk.  It sure could have been, and it would have been cheap, too.  You can brew about three standard drinks for the price of purchasing one at the Beer Store.  In North America, it seems that we view beer this way, however.  I remember seeing a lot of commercials that would have me believe that beer is only brought out at parties, or when large numbers of friends have congregated.  Never is it advertised as an alternative to carbonated soft drinks, despite the fact that it is much healthier.  Molson-Coors won't tell you that a nice, hoppy IPA is a perfect pairing with a strong-flavoured hamburger.  No, beer is marketed as a party beverage.

What is the consequence of this?  Well, oddly, in a university town where one would assume parties are far more pervasive, you will find more people that appreciate beer as an interesting beverage and not as a means of intoxication.  Places like my hometown in the middle of rural Ontario haven't quite figured this out, and their knowledge is based more on marketing.  This is why I will get strange looks if I order a beer to accompany my lunch, or I can expect a strange look from boomers if I sit down to enjoy a beer in the afternoon whereas they wouldn't bat an eye if I had coffee.

This is a problem.

This is a problem because we, generally as a society, approach beer as nothing more than an intoxicant.  Prohibition is the norm when discussing minors.  Taxation is high to discourage drinking as a behaviour (did you know that those who consume a drink or three a day see a variety of health benefits?).  Regulation is heavy.  And all this when moderate consumption (and the key is moderation, binge drinking is defined as the consumption of four or more standard drinks), is a perfectly healthy behaviour.  Now, guess what happens when we approach beer as an intoxicant and nothing more?  Go watch a frosh week and you'll figure it out pretty quickly.  People leave the relatively supervised environment that is home, and they go overboard.  Not only do they go overboard, but they will associate this going overboard with fun and good times and will learn it as a behaviour.  This behaviour will likely last into adulthood, and beer will remain a beverage of intoxication.

Now, what if we had a place to introduce our children to responsible drinking?  I would say that it could happen in the home, but North American society doesn't seem to be working with that approach.  Perhaps we could introduce a venue in which children could witness responsible drinking.  Having a beer or a glass of wine with a meal, and leaving it at that.  Or perhaps having a conversation over a hard beverage rather than a soft, or caffeinated one.  I'll tell you that soft drinks are very sugary, and can ruin your sense of taste between bites of a meal.  A hoppy IPA will hit you with a quick punch of flavour, and then leave your palate cleansed for the next bite of your burger.  An amber ale often has a gentle hop to it, and a mild sweetness that goes extraordinarily well with a plate of fish and chips.  Granted, a nice sweet soft drink will go very well with a heavily salted pizza, but this is a use of extremes to negate one another.  But I digress, a place in which children could see drinking not as a means to excuse oneself from buying crack, but as a compliment to a meal or a delicious beverage on its own, I believe, would produce a tremendous social benefit.

And here, I will compliment a couple true public houses.  During the day, I wouldn't hesitate taking a child or family member to the Beaufort Pub in Belleville.  The décor is cozy and it is quiet and conducive to conversation.  The food is good and there is a nice selection of beers to accompany a tasty meal.  In fact, when I head down to the Beaufort, I have run into friends, family members, or even people I know through Church and haven't seen in ages.  It's an excellent spot to hang out, and I am genuinely happy to do so.

Then, there is my favourite pub of all, the Sandy Hill Lounge and Grill.  SHLG, or Schlag as I call it (a misspelling originally, but later rationalized and defended), is the finest example of a pub I have come found.  On a Sunday afternoon it is not unusual to see a retired married couple enjoying a meal next to a family and across from some University of Ottawa students and alumni.  All are welcome and it's not weird.  Were I to see a child in a bar (a place that goes to lengths such as increasing music volume to the point where conversation is impossible, causing the patrons to drink more), I might be concerned, but not at Schlag.  The walls are plastered with historical images of Ottawa and the Sandy Hill neighbourhood, the home of University of Ottawa, many embassies, and the historic Laurier House.  They have a wonderful beer selection, and a dedication to pub-style food that is inspiring.  There are the normal daily specials, as well as weekly specials which the chef has concocted.  They go to the point where they offer home-made ketchup to serve alongside the usual Heinz, just in case you prefer one or the other.  It is also the establishment that introduced me to sriracha, and thus I will be eternally grateful to them.  The German expression "mit schlag" means "with whipped cream."  The Sandy Hill Lounge and Grill is the "schlag" of life, it takes whatever it comes with, and makes it just a little bit better.  That is why, after originally misspelling, I will continue to refer to it as Schlag, and wish them many decades of prosperity.

So that was a lot of digression, so I'll briefly outline my point.  We treat beer and wine as a means of intoxication, and it shows in our behaviour.  Alcoholic beverages can play a normal and healthy part in our lives, and it should be treated as such.  I feel the best first step is to lead by example and drink responsibly together, as a community, in front of our children.  I'm sure that many a Maude Flanders is currently shouting in dismay, but to lead by example, one must involve children.  A public house is a perfect venue for this, and I would love to see a better pub culture in Canada.

NM

P.S.  Naturally, drinking and driving is a hazard of increased societal alcohol consumption, but that will actually tie into my next Utopian topic.  At over a thousand words, I'll cut this off here.  And not proofread because, as is apparently the norm, I'm now tired and want to go to bed.

A Brief Foray Into Fancy Stats

What happens when I should be working on other things.

So,

I must be back in school, because once again I find myself unable to sleep because I'm busy thinking about something.  Regular readers will recall that this was the reason I started the blog in the first place.  So now, at 01:23, let's go into why I can't sleep.  Fair warning: if you don't necessarily like or care about hockey, go ahead and skip this one.

I was partly inspired by this post by Cam Charron (all my figures are from stats.hockeyanalysis.com as well), and recent events.  Tyler Bozak is injured and Nazem Kadri has taken his place as the Toronto Maple Leafs' first line centreman.  In his article, Cam states that the common assertion that Bozak and all-star winger Phil "The Thrill" Kessel is simply not true.  He goes on to point out that the numbers would indicate that Grabovski actually has better chemistry with Kessel.  That, combined with the current fantastic output of Kadri, Kessel and James van Riemsdyk (JvR), led me to question whether or not there would be a way to easily quantify how much better players are depending on their centreman.  That led to the scribbles you see above, which are more neatly recorded below:

While many of my readers will have no problem reading that, and will doubtless find mistakes I made, I'll break that top line down a little bit.  Stated simply, I assume that over the course of a season, a player's total output (goals, assists, points, what have you), could be represented as the sum of his performances with various centremen.  More complexly stated, a player's performance is the linear combination of his performances with different centremen.  The second line says more or less the same thing, but is specific to the points scored, and time with centreman i.  The logical leaps start here.  I say that the total metric achieved with that player would equal the product of the time spent with that centre, T, the [hypothetical] basal scoring rate, B, and the coefficient C.  That means that, I assume, there is some rate at which the player in question would normally generate some metric, this will be multiplied by some coefficient depending on who the centre is and will also be time-weighted.  Now, in a perfect world I would have a giant dataset and would simply plug the above equation into gnuplot and use its fit function to generate all relevant B and C values.  Unfortunately, I don't have access to a large data set, and don't really have the programming ability to mine stats from the NHL.  So I assume that B is equal to the basal, or average scoring rate of a given player (their total metric divided by their total time-on-ice (TOI)).  I don't know whether or not a hypothetical B would differ from an average scoring rate, but the more I think about it, the more I think it would be the same.

In any case, we can see how to easily isolate a Centreman Coefficient from the data.  This data, for the record, is from the Leafs' 2012-2013 season, which is old and only represents a half-season, but is still young enough to be relevant to today's roster.  Let's take a look.

Table 1: Effect of Centres (left) on Wingers’ point production expressed as coefficient.
Player	Kessel	Lupul	JvR	King MacArthur
Bozak	0.9747	1.8027	0.8990	0.8613
Grabovski	1.2205	0.0000	1.6356	0.5637
Kadri	1.4784	0.9312	0.8918	1.3539

Table 2: Effect of Centres (left) on Wingers’ Corsi expressed as coefficient.
Player	Kessel	Lupul	JvR	King MacArthur
Bozak	1.0509	1.2619	0.9971	1.2195
Grabovski	0.8225	1.8974	0.8681	0.9794
Kadri	0.8967	0.8800	1.0587	1.0456

I'll briefly point out to those of you not familiar with #fancystats that Corsi is simply the difference between shots for and shots against a player's team while he is on the ice.  It also correlates very well with puck possession times.  That's why it's used, because the NHL doesn't track offensive zone time, but shots are readily recorded.  Go figure.  I'll also note that I have apparently suffered amnesia about the whole of the Leafs' last season, because I don't remember who anyone played with, so I went with four wingers and three centres.  Also, if you're not familiar with coefficients, look at it this way: in the case of Lupul, he was scoring at roughly double his normal rate when centred by Bozak, and 0 times his normal rate when centred by Grabovski.  You could also call it a multiplier.  So when centred by Bozak, Lupul is like Twopuls, and like no Lupuls when centred by Grabovski (by the by, I'm very tired...).

Conclusions?  Well, barring the fact that I shouldn't have included Lupul's data because he wasn't around very much last season, we can see a couple things.  One, and for reasons I can't really understand, it seems like Corsi and point production are inversely related in some cases.  The only explanation I can offer is that your Corsi might suffer if you rush out and score, and are pulled off the ice, but other than that, I've got nothing.  But then, the Leafs are especially challenging that way.  One surprising thing is that, which point production appears to be supressed by Bozak, he improves the Corsi of his team mates when he is on the ice.  Or rather, his wingers put up better-than-normal Corsi ratings when he is on the ice.  This isn't to be expected, because Bozak is routinely ripped on for his Corsi.  Kessel and JvR really liked playing with Grabovski, though their Corsi figures were suppressed at the same time.  As for Kadri as a centre last year, I'm as confused as you are.  I just... yeah.

Some other notes of interest involve disregarding the whole linear combination thing and just looking at how players perform with others.  The data led to some hilarious conclusions like how different goalies correlated with different metric production.  For the five minutes JvR played with Steckel, his point, goal and Corsi coefficients were 5.7, 11, and 2.4 respectively.  Kessel did very well when Fraser was on the ice, his point and Corsi coefficients were 2.2 and 2.7.  Also, Grabovski and Naz actually played together for 9 minutes, Grabovski scored twice and Naz recorded two assists in that time, and it led to similar hilariously large numbers.

I'll also say that while I can't find the piece of paper where I stashed the information I recorded while dickering with this idea, it appears that Bozak's point coefficient for Kessel was about 1.4 in the 9-10 season and has steadily decreased as the years go by.  I'd be curious to see what happened with the Corsi coefficient over the same period, but I'm tired and I'm not going to do it right now.  Also, considering Kessel for this year thus far, Bozak's point and Corsi coefficients 0.97 and 1.01 while Naz's are 2.01 and 0.76.  Again, why is point production so high when Corsi is so low?

So what to make of all of this?  Sure beats me, I don't even think the results are statistically significant.  I think these coefficients are a nice and simple number to compare how wingers perform with a given centre.  Or even another winger, or goalie, or whatever you feel like calculating.  If anyone is interested, I can always forward the .xlsx I have, though you also have the equations above, which is really all you need.  I'd say I hope you all find this terribly interesting, but frankly I'm happy to have gotten this down in a semi-organized fashion, and can hopefully go to sleep now.

NM

P.S.  Is that the first equation on Vodka and Equations?
P.P.S. All data was for 5 on 5 situations.