The Trouble With Stats (or the people who pretend to use them)

My father also used to enjoy telling me "figures don't lie, but liars figure." He was essentially trying to explain why people often don't trust those who use numbers to explain things that don't naturally appeal to our (highly flawed) instincts. There is a Simpsons quote along similar lines, but for those of you who are fans, you already know it, and for anyone else, it would be a waste of time.

There is another, larger problem, however, that also damages the reputation of statistical analysis and the things it can tell us about our world. It's when people know/do just enough to be dangerous, and without basic rigour produce findings that are unsupportable. When they spread those findings, people who don't have a strong understanding of the analytical process tend to take them at face value, and then end up being let down later. Rather than blaming the particular culprit who practiced the bad stats, they just blame stats in general. These bad actors aren't always guilty of malice, but it doesn't absolve them of crimes against science, and there is a perfect example on ESPN.com today.

Obligatory picture of Nomar, 'cause baseball!

Check out the article here (it's an Insider article, so if you aren't already behind the pay wall, you won't be able to read it). To summarize, Mr. Keating is trumpeting the value of a simple composite stat, runs per hit (R/H from now on), as some sort of gem in terms offensive value, in both real and fantasy terms. He begins, ironically enough, by pointing out that "many sabermetricians [statisticians who study baseball] barely glance at stats like runs and RBIs, which depend heavily on a player's offensive context" (which is true), and then immediately goes on to make a vague declaration about other skills he must have (not true).

Keating proceeds to provide a handful of historical examples of other players with a high R/H, in fun anecdotal fashion. Fully three of the seven paragraphs in the article don't talk about the particular player that it focuses on, Brian Dozier of the Twins, and even the ones that mention him hardly focus on him. The examples provided vary widely across run environments, from the height of the power-infused steroid era, to pre-WWII baseball, with no accounting for what the differences in offensive numbers looked like at those times.

Finally he cherry-picks a few contemporary data points that support his assertion, none of which are particularly relevant to the point that he is making (and in some cases, contradictory).

At no point does he cover anything like the methodology he used to arrive at his conclusions, or even imply that there was any methodology, which might be more disturbing. Here is one thing I know about people who appropriately use statistics: they love to share the gory details.

Now, I will admit, I had a little prior experience with this particular stat, because I had looked into it a few years ago, and ultimately rejected it as useful. However, context always matters, so it was worth another look. One of the first things that Keating does in the article is subtly undermine sabermatricians and complex statistics, which is curious for a guy who's bio at the bottom of the page says that he covers statistical subjects as a senior reporter. Basically, what he says is that R/H is a stat "...that is so simple you can calculate it in your head and it'll tip you off to hidden fantasy values" (I challenge both parts of that statement).

He mentions BABIP later on without any explanation, so he is assuming a certain amount of sophistication on the part of his readers, which is understandable since most fantasy enthusiasts have more exposure to statistical analysis than an average baseball fan. Certainly, anyone interested in "new" composite stats would also be familiar with OPS, and quite possibly wOBA and wRC as well, so the assumption has to be that R/H offers something that these other stats don't.

This is where the whole thing falls apart under scrutiny. Keating says that R/H is a good proxy for identifying other skills like speed, walk rate, and power, but all of those other stats I just mentioned do the same thing, but the difference is, they actually work. Depending on your analytical preference (or which site you get your baseball fix from), you might choose to believe in OPS, wOBA, or wRC (or base runs, etc.), but the reality is, they are all pretty good, and so they correlate very highly to one another (r values of above .95 between all of them). R/H, on the other hand, correlates with none of them, not even close.

Of course, those are all stats meant to capture real-world offensive value in a context neutral way, and maybe R/H only works for fantasy value. So the obvious thing to do would be look at R/H against ESPN fantasy player values. Unfortunately, once again, R/H has almost no correlation to the player rater values (whereas the fantasy rater correlates really well with those other stats).

"Wait," you might (and should) say, "the fantasy player rater is going to be heavily weighted towards counting stats, and thus might not be appropriate when comparing against a weight stat like R/H." Sadly, you, like Mr. Keating, would be wrong again, as Dozier was 7th in the majors in plate appearances (PA) among qualified batters, so he actually has an unfair advantage in this case.

The truth is, of players who had enough plate appearances to qualify for the batting title last year, 4 out of the top 5 by R/H were not in the top 30 fantasy players, and only 4 of the top 15 made the cut. Most of whom were not even guys with an balanced speed/power/discipline profile, like Dozier (which Keating says the stat should identify), but power hitters like Donaldson, Rizzo, and Bautista. If you look at wRC+, every single one of the top-15 players was in the top 40 by fantasy value, and has an r value twice as high as R/H (.71 vs .31).

A common way to look at how much noise might be in a particular stat is to look at year-over-year correlation, and I will say that for players with at least 350 PA in both 2013 and 2014 there was a slight correlation. At just below an r value of .5, however, it wasn't particularly strong, highlighting just how much luck goes into this formula by including runs, and frankly, this number would probably change by looking at more years (I admit to not going deeper here, but I will point out the failing if someone wants to look into it).

Bottom line: runs per hit is not a great stat over all, and it is not a great stat in the context of fantasy baseball value. I won't venture to say that Keating did this analysis and decided to hide the results from his readers, nor will I say that he was too lazy to do any analysis, but I do know that it took me all of thirty seconds to start finding problems with the assertion. As someone who plays fantasy baseball, I have no interest in giving my competition an advantage, but I also can't figure out how this kind of misleading "analysis" does any good for the field.

The issue isn't just that the number doesn't say what Keating claims it does, because it will, by the nature of its component parts and some of the reasons he gives, have some relationship with the skills he is trying to identify. The issues are that it does so very inefficiently due to flaws in the components used, that we already have much better stats for highlighting the same information. The last, biggest issue is that despite being at least somewhat aware of these flaws, Keating is touting this approach nonetheless, under the guise of statistical analysis, without providing any evidence in support.

Dozier is a good player, and has fantasy value, but anyone using R/H to evaluate players is going to be disappointed in their fantasy season. It is neither predictive nor descriptive of a player's skill, and shouldn't be used that way. The problem is that by placing this article behind the pay wall of an authority like ESPN, the false premise is given a credence that it doesn't warrant, and undermines statistical analysis as a whole.

Have Some Respect for Your Founding Fathers

One thing that really irks me in the debates that fill the public discourse, is the way that people say, "Obviously our founding fathers couldn't have foreseen [insert some eventuality], when framing the Constitution." [Note: I'm also going to include the Bill of Rights in this umbrella term from now on] This is followed by that person using it to justify his or her position in the debate. Now, the first thing that I should say is that I also hate when people use this rhetorical/logical device in support of positions that I myself back.

Allow me to make an example. "The founding fathers can't possibly have foreseen the kind of weapons that we have in society today, so the second amendment can't be taken as a literal statement, applicable in our time."

Now, without going into details that are off-topic, I generally agree that some additional gun control would be good for America, but I have also been a hunter and shooter for most of my life. Despite that, I can't support any attempts to dismiss, off-hand, the decisions made during the formative years of this country based on the clairvoyance of our predecessors.

For one thing, making that argument is somewhat self-defeating. If you are saying that people can't possibly imagine the legislative needs of a future version of their own society, then why are you supporting a particular approach? Doesn't that mean that your efforts are doomed to let down your great-great grandchildren, constraining them to a set of options ill-suited to the problems they face?

Now, that response is as spurious as the argument it refutes. I didn't spend much time on that back-and-forth, because it doesn't seem to bear much effort in my mind, due to the mechanical inconsistency involved (if you disagree, please comment, I would be very happy to see another point of view). As such, I'm going to get to what I think is the central issue, which has more to do with a basic misconception.

I think that what bothers me most is what could be considered an amalgam of two common cognitive biases; recency and confirmation. We want to believe that we are the smartest, most well-informed people ever, and so we gravitate towards evidence that supports that notion. We are also most familiar with our contemporary situation, which puts evidence in support of our modern sensibilities at our finger tips at all times.

...And that's fine. It isn't new; our grandparents suffered from those biases, and so did the framers of the Constitution. You know what else we have in common with them? The ability to consider a large data set, identify patterns, and extrapolate possible futures. We don't have a monopoly on that kind of thinking. We didn't invent it, we inherited it.

By the time the Constitution was being written, humans had investigated cause and effect pretty thoroughly, and utilized geometry and calculus (which they had already invented) to describe and predict the movement of heavenly bodies with a high degree of precision. The ability of humans to evaluate a situation taking into account nuance and subtlety was well established long before the United States came into being (a process which also took place over about hundreds of years, not in a moment).

It's not even a very complicated thought process, and there is extensive documentation proving that people of that era (and every one before it) were aware of the evolution of western armaments, along with many other things. Does anyone really think that members of the colonial aristocracy didn't understand the significance of the difference between the weapons possessed by the Native Americans and European settlers? Are people so arrogant as to believe that the founding fathers didn't have a sense of history very nearly as advanced as our own? Do people think that imagination is a recent evolutionary development?

There is no chance that Thomas Jefferson wasn't consciously aware of at least the following progression:

Humans throw rocks at one another
Invent slings to better throw rocks
Invent bows and arrows, replace rocks as missiles
Invent crossbows, replace bows as delivery mechanisms
Invent primitive firearms, replace both the launcher and ammo
Invent muskets, replace delivery mechanism

With plenty of iterations in between these leaps (one of the big advances in crossbow technology was the windlass, which required less strength to more quickly cock the weapon). When we represent things like photon torpedoes, light sabers, and ice-nine, we are taking our current understanding of technology, and applying our imagination to a projection of observed trends to create that image. It's a brilliance that, as far as we know, is unique to humans, but isn't unique to humans in the past 30 years.

Temporally, our distance from those colonists is only about 200 years, even if the technological gap has accelerated lately. That is about the same distance as they were from the 16th century, a time that saw Copernicus and Tycho Brahe challenge the widespread assumptions about the heavens and propose a heliocentric rather than geocentric system. The founders were building a new democratic society on a continent that had hardly existed on maps 200 years earlier. They were the inheritors of a network of settlements created by Protestants as a result of Martin Luther and the Reformation, you guessed it, about 200 years earlier. These were massive scientific and philosophical advancements that had radically changed Western civilization, and to suggest that the founders would not have been self-aware enough to recognize social evolution is either silly or arrogant.

Are we writing laws to control the proliferation of civilian models of future-government space lasers? Of course not. We are dealing with our current problems, not trying to legislate the solution of tomorrow's problems.

[Understand that this isn't a gun control argument, that's just an example of one way that the false dichotomy that I am illustrating is manifest] 

Quite frankly, any discussion of the framers' intentions is pointless because we either have their own words expressing their thoughts, or we are guessing. If it doesn't inform our attempts to solve our current problems, it's no more than an interesting academic exercise in the context of the current debates (I say this as someone with a history degree). The Constitution is an important document, but it isn't the Ten Commandments, carved in stone. If we want to sanctify it, then it should be lovingly retired and removed from issues of public governance, because at that point it is no more than an idol for dogmatic worship. If it is sacrosanct and immutable, then it is a religious document and has no place in politics. If we treat it as a vital, living part of our republic, however, then we should be able to shape it and change it to suit our needs the same way that we would a bill that funded local road improvements.

If the founding fathers didn't create rules for us today, it's because they trusted that we would be able to handle that ourselves. We shouldn't belittle their contributions to the growth of this nation in order to justify our own. The United States, as a nation, continues to evolve, as does the body of documentation that defines it. We should feel free to change the Constitution because it is our responsibility to safeguard the well-being of this country today, not because we need to correct the ignorance of yesterday.

Attention Spans are Not Getting Shorter

A great deal has been made in recent years about how the attention span of the average American has been dropping precipitously. This complaint is most often leveled by people who are also most likely to wax nostalgic about how much better things used to be, have a deep-seated mistrust of social media, and are on the long side of 30. That hasn't stopped the narrative from spreading, however, and it has been picked up and repeated in some form across the social spectrum, even by those members of the younger generations who are believed to suffer most notably from this malady.

While the cause of such a disease has yet to be formally identified by the medical community, a list of usual suspects is generally paraded about by the media for public condemnation. In the 80s & 90s it was that kids watched too much television and played video games that rotted their brains. The 2000s saw the internet stretch its tentacles into practically every household occupied by people under 60, with damnable effects like email, instant messaging, and YouTube videos. Then we saw the blame shifting to blogs, Twitter, and Facebook, as mediums that encouraged communication in an ever shrinking range of word and character counts. Now, with the popularity of emoji, Instagram and Snapchat, people don't even have to write anything to get a point across!

Kids today, amirite?

This has been coming up a lot at my work, both in terms directing creation of the content that we sell (should we be making shorter videos to accommodate these shrinking attention spans?), as well as the way that we communicate with our users (are our emails too long? are we making enough image-only content?). Someone recently sent me an email about a report showing that Instagram users had overtaken Twitter users:

"Instagram (300 Mln) overtakes Twitter (284 Mln) in 2014, suggesting a trend towards an even shorter audience attention span - from 140 characters to a single picture!"

...to which I jokingly replied:

"Early human communication was visual, moving from literal pictographs (cave paintings) to metaphorical ones (hieroglyphics), then to cuneiform and eventually written words.  We are now moving back in the other direction to more visual forms of getting our messages across."

I didn't even think about it again, or realize that my joke might be taken seriously without a sarcastic tone of voice, until my response was referenced seriously weeks later. I didn't mean what I had said at all, and I am actually dismissive of the notion, but we have come to a point where a suggestion that human communication is regressing to a preliterate state can be taken at face value, and given the direction of public discourse on the matter, I couldn't blame the recipients of my flip remark.

Let's first get one thing straight: in a literal sense, there is no way that our "attention span" (whatever that is) could possibly have changed genetically in the space of a generation or two, as a result of the technology that we are exposed to. Evolution is simply not a process that happens that quickly. Children born today will have the same natural attention span as their great grandparents, no matter how many tweets their 30-something parents have sent. So, any change in the actual communication preferences of people today is habitual, not hereditary. Now, this is not to say that there can't be any kind of biological change over the course of a person's life, brain chemistry is mysterious beyond my personal kenning, but I will leave that argument to scientists, rather than media theorists.

Perhaps the constant electrical stimulation of certain nerve clusters has indeed rendered us a bunch of easily distracted simpletons, but I submit that the growth of short-form mediums is in no way evidence of any such change. This is yet another example of a classic post hoc fallacy, an attempt to craft a narrative to explain an observed phenomenon. There are, however, alternative explanations that don't rely on faulty casual conclusions.

The simplest explanation for the proliferation of micro-communication has to do with resources, both technological and chronological. Essentially, pieces of media have gotten shorter because it is easier and cheaper to create and disseminate content.

Understand that the situation we are observing is nothing new, but the continuation of process that has existed since the birth of human society. When writing required materials that were difficult to produce, very few things were written down, because the cost was prohibitive. Even with the invention of the printing press, mass production was difficult and expensive, so books were rare. As the technology for making paper and printing became better and cheaper, we saw broadsheets and newspapers come into being, and film and television likewise made it possible to create content that reached a wider audience, but there were still physical limitations to deal with.

Think about it this way: 30 years ago, if you wanted to make a movie and show it to millions of people, you needed not only the time and resources to produce the original content, but then you had to spend huge amounts of time and money to get it broadcast over the airwaves, or distributed in theater chains across the country. It literally cost millions of dollars and thousands of hours, with a substantial risk that you would not return even a fraction of those investments. 99.999% of people simply couldn't afford to take part in such an economy of scale, and for those who could, it wasn't efficient to create anything that short.

Now? Anyone can make a 30-second video with their phone and upload it to YouTube. The investment requirements in time and money are minimal, meaning there is no risk, so there is no downside to creating something that no one actually cares about.

In the past, if I wanted to share a picture of my awesome dinner with the world, it would require taking out a magazine ad (which of course no one ever did). Now I can just post it to Instagram effortlessly. Because the barrier to entry in content publication is all but non-existent, there is essentially no threshold for evaluating the "worth" of any communication that can exist digitally.

eBooks are cheaper, so the same revenue means more authors

Obviously, these are all issues of creation and distribution, and can easily explain why there would be such a growth in micro-content, without making any assumptions about attention spans. It doesn't explain consumption, however. A tree falling in the forest and all of that, a million cat videos (and counting) in the world wouldn't lead to the current conversation if no one were watching them.

I would suggest that attention spans have not declined, simply that people devote about as much attention to any particular piece of media as it warrants. There is a great deal of content that takes only seconds to consume, and those fit easily into the spaces that exist in a modern schedule while being conveniently formatted for the smart phones that are never far from our hands.

I think that an additional point that needs to be made (and shoe-horned into this post) is that too much of the conversation around new media and attention spans implies that length or medium is somehow equivalent to value. If an Instagram post is considered less valuable because it is visual rather than text-based, what of a classic painting? Does the time that something takes to consume related to the time that it takes to produce? That picture of of a fancy dinner may only take a second to compose, but some chef could have spent a great deal of time on the dish.

What of a haiku, or a sonnet? From Seamus Heaney to Shakespeare, plenty of great poets created works ranging from a few lines to thousands. Some of the greatest prose writers in history utilized a variety of forms, from novels to novellas to short stories, adapting the medium to the muse, but no one questions their artistic merit.

For all of that, the same people who read thousands of texts and tweets, and scan the Reddit headlines without reading the linked articles (myself included), still somehow manage to marshal their mental faculties long enough to watch feature films and even remain gainfully employed. I have it on good authority that people even still read actual books, printed on paper.

It's perhaps a less compelling narrative, but the truth is that the medium simply fits the message, so as mediums are created that are more convenient for delivering short-form messages, it is only natural that more such messages will be crafted. A story that is worth telling, or is worth hearing, will receive the attention it deserves.

As a man in my thirties, I have grown up with all of the offending technologies that should have stunted my ability to focus, from the Nintendo I got as a child to the Twitter account with which I shared this post. On any given day I will check my email, Instagram, Twitter, and several forums, and watch a YouTube video or two. At the same time, I am ten weeks into an online statistics course, 500 pages into Anna Karenina, and recently watched a two and half hour movie. I will spend hours cooking a meal, or a whole day exploring a short stretch of river out of cell range. I am not alone in this, because movies, books, and Rolling Stone still have audiences.

So I suppose that my point is, far too many words later, that our attention spans are fine, just so long as we turn them towards objects that are deserving.

[Of course, the fact that probably only one person in a hundred made it this far into the post doesn't say anything good about the value of this blog. If you are reading this, congratulations on your attention span!]

Putting the 'Fun' in 'Logistic FUNctions!'

So, this weekend I was playing around with R to graph some data sets and get the variables that go into the formula for doing logistic modeling.  While trying to figure out some f(t) or t-values given the inputs, I was annoyed at calculating the results by hand, even if I was able to get the variables from R.  It's pretty normal math for this kind of work, and it's good to know how to do it manually step-by-step, but eventually the fun wore off, and I just wanted to get it done.

Anyhow, I built a "Logistic Function Solver" aka calculator in Excel, and figured I would share it on the off-chance anyone else needs such a thing and doesn't feel like taking the time to build one.  It's already been useful at work.

Here it is

Anyhow, you should be able to access the file on Google Drive with that link, and then make a copy for yourself.  Let me know in the comments if this doesn't work for you.

Basically, cells with the light yellow background and green text are ones in which you should enter your values, and then your desired output will be in the green background with red text.  (Leave the other cells alone, they have formulas)

Enjoy!

Marketing & Data for New Businesses, Pt. 2: SEO

I'm going to start with the rub.

As I have mentioned before, the death of traditional search has been widely heralded, and patently disproved. It is a trendy thing to write about, but has little place in today's business world, because it's a prediction that has created many fools. If you were a weather forecaster, and just showed up each day and said "It's going to rain today," you would eventually be correct, but couldn't brag too much if those showers followed three weeks of sunshine. One day, traditional search will indeed see a serious decline in relevance, but that day is not yet come.

As such, small/new businesses have to continue to care about search, and SEO in particular. Why in particular? Primarily because it is "free," but also because it can scale better than any other channel, as organic search almost automatically encompasses your entire target audience.

A search for "Elizabeth Warren" probably wanted a result about this one

So where's the rub? SEO, boon and lifeblood that it is, can be extremely difficult for new companies. In large part, this is because the number one concern of the search engines* (here I will cease deliberately referring to them collectively, and start just using "Google" or "the engines" interchangeably, because, let's face it, Google still calls all of the shots in most countries) is authority. Authority is a somewhat (deliberately) vague term that describes the likelihood that a particular result is the most common intended target of a query.

Example: If someone searches for "Elizabeth Warren," Google is going to assume that they are looking for the official website of the politician (or recent news results, or her Wikipedia page), and not a PDF of the marriage announcement of a woman with the same name from a 1978 edition of the Albuquerque Journal.

Ultimately, authority (and SEO) is about probability. The more specific the query, the easier it is for the search engine, but most users start with something fairly broad, hoping that the engine will guess their intent, and show them a set of results that contains the desired website. The problem is that for a new business, unless you are filling a niche that no one else has ever tried to fill, it's very unlikely that you will have a great deal of authority for any search other than your brand name.

It takes time to build authority, which looks at historical data, including the clicks of users following a particular query (which is one of the few times that a confirmation bias is actually an appropriate thing). However, this isn't to say that a new business should not care about SEO, just that it is a more difficult path early on.

So what can you do?  Here are a few recommendations:

• Authority is based on a lot of legacy clout. Macy's has been Macy's forever. So try to compete most strenuously in areas that are newer, for example:
• social signals are only gaining relevance in SEO, so make sure that your brand is extremely active on all of the social platforms, especially Google+
• also, make sure that for each platform, you create the right type of account, that best represents your business
• secure your site - Google has recently said that they will give slight preference to sites that are operating on HTTPS instead of HTTP; this is a pain to overhaul for sprawling legacy sites, but should be easy if you are new 

• Get it right from the start. Many companies have websites for years before they start worrying about SEO. Don't wait until you are big enough to pay a consultant to follow best practices:
• audit your pages up front - proper metadata and linking from day one
• make sure that you have enough content (500-1000+ words) on your important pages, even if some text is hidden to the viewer (but not to crawlers)
• authorize yourself as the owner of your site on Google and Bing webmaster tools, because they will be the respective canaries in your coal mine

• Publish or perish
•  Content and SEO will only be more inextricably linked, so get writing! Provide value and you will get traffic, which will in turn get you authority
• if you are going to blog or produce other types of content, keep it on your primary domain; Wordpress may be easier, but you are just dividing your 'authority points'
• if your content/blog does live offsite, make sure to cross-link it to the most relevant page on your main site, with appropriate anchor text

• Measure what you can
• On a basic level, use Analytics (or whatever you have) to keep an eye on the number of visits, and new visits (to separate people who just don't use bookmarks or type in the nav bar), from organic search
• the move to a 'not provided' world from a keyword standpoint in Google Analytics hurt, but you can see what searched terms brought organic traffic to your site in webmaster tools, so identify those queries that should be central to your business and pull that data monthly to identify trends
• Webmaster tools will also provide you with information about your rankings for various keywords, which is important in tandem with your volume of traffic from each term; use a combination to identify shifts in search behavior and effectiveness of on-page SEO

That should be enough to keep any new SEO busy for a while! It looks daunting, but the key is to just try and do the right things, generally. The engines ultimately want what is best for the consumer, and will reward sites that provide real value in an authentic manner. Keep SEO in mind with everything that you do, even if it is never the top priority, and you won't have to go back and clean it all up after the fact.

For more tips for small/new businesses, check out part one of the series.  Feel free to post questions in the comments.