Fun with Statistics (or why I don't bet the NFL...anymore)

Without data, all you are is just another person with an opinion.
--Unknown

Tim Wilson and I were debating (some would say hijacking) in Rafael's thread 7.8 Reasons why Felix should start about the value of statistics.  I thought I'd explain my position here so as not to waste everyone's time, but maybe also to inform.

What I'm NOT trying to say is that statistics are useless.  Fantasy Football lives and dies by individual and team statistics.  However, as I try to explain below, it is very important to understand what statistics can and cannot prove.  

The holy grail for the multi-Billion Dollar industry that is NFL betting is to find a predictive statistic on who will win a game, Division, Conference Championship, and of course the Mt. Olympus of sports betting, the Super Bowl.  Think about that!  A sum that exceeds the GNP of most countries, wagered annually.  And millions of people have been searching for this holy grail, exceeding The Crusades in scope and resources.

Add to that, the fanatical following of us lunatics trying to justify our opinions in blogs, barroom debates, and the Theatre of the Absurd that is Fantasy Football...and you have yourself a ripe environment for the (mis)use of statistics.

If there was any predictive statistic or set of stats that could accurately predict what will occur in any given game, there would be no shortage of "experts" that would be paid Millions (Billions?) for the information and fantasy football dynasties would be common place to those with the information.

Data vs. Statistics

Facts are stubborn things, but statistics are more pliable.  ~Author Unknown

These are completely different things that are often used interchangeably.  Simply, Data is the "What"; Statistics are the "Why".  For example, most of the "statistics" kept by the NFL and available on most NFL web sites are really just data points.  Yards, YPC, YPA, Receptions, and even QB ratings are simply data measurements of what occurred during a game.  They don't explain the whole story of why a team won or lost a game.

How many times has our Cowboys dominated a game "statistically", yet came up short?  How many Super Bowl Champions have middling statistics?  How many "truths" are continually disproved or are written off as statistical anomalies?  (BTW, this could be argued to be an argumentative fallacy)

Statistics, on the other hand, is often used to tell us "why" something happened.  This is the area where Benjamin Disraili's quote  "Lies, Damn Lies, and Statistics" becomes so prevalent.  All of us can watch the same game and come to different conclusions as to why something occurred.  Too often, we spout statistics that back our argument, while ignoring or dismissing others that do not agree with our opinion, often "twisting" the debate, a condition known as Ignoratio elenchi (aka, Red Herring).

Predictive Statistics

Statistics can be made to prove anything - even the truth.  ~Author Unknown

The most common fallacy that I see when statistics are used in discussions of the NFL is that one or more are predictive in nature (see Holy Grail above).  However another common use that drives me to drink is the whole idea that player, unit, or team statistic means a team is better.

Football, unlike many sports, does not lend itself to predictive statistics...thus the truism "On any given Sunday".  The parity that was designed into the whole process, from talent acquisition to scheduling, and the non-statistical causes of the outcome (injuries, homefield, and the nature of sport itself) often invalidate a causal relationship (Correlation does not imply causation (cum hoc ergo propter hoc))

The fact that some statistics correlate what happened does not mean they are causal, nor predictive.  As you can see below, the data is highly correlated, but hardly causal.  Logic tells us that you must have a necessary and sufficient condition which I've yet to see.

 via en.wikipedia.org

Some of the more colorful fallacies that commonly arise in NFL debates include (edited from Wikipedia) both formal (logical) and informal (argumentative):

Formal

• Ad hominem: an argument that attacks the person who holds a view or advances an argument, rather than commenting on the view or responding to the argument.
• Appeal to probability: assumes that because something could happen, it is inevitable that it will happen. This is the premise on which Murphy's Law is based.
• Conjunction fallacy: assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them. (My base premise...btw)
• False dilemma (false dichotomy): where two alternative statements are held to be the only possible options, when in reality there are more.
• Red Herring: also called a "fallacy of relevance." This occurs when the speaker is trying to distract the audience by arguing some new topic, or just generally going off topic with an argument.

Informal

• Argument from repetition (argumentum ad nauseam): signifies that it has been discussed extensively (possibly by different people) until nobody cares to discuss it anymore
• Appeal to ridicule: a specific type of appeal to emotion where an argument is made by presenting the opponent's argument in a way that makes it appear ridiculous
• Argument from ignorance("appeal to ignorance"): The fallacy of assuming that something is true/false because it has not been proven false/true. For example: "The student has failed to prove that he didn't cheat on the test, therefore he must have cheated on the test."
• Correlation does not imply causation (cum hoc ergo propter hoc): a phrase used in the sciences and the statistics to emphasize that correlation between two variables does not imply that one causes the other
• Fallacy of the single cause ("joint effect", or "causal oversimplification"): occurs when it is assumed that there is one, simple cause of an outcome when in reality it may have been caused by a number of only jointly sufficient causes.
• Gambler's fallacy: the incorrect belief that the likelihood of a random event can be affected by or predicted from other, independent events
• Inconsistent comparison: where different methods of comparison are used, leaving one with a false impression of the whole comparison
• Moving the goalpost (raising the bar): argument in which evidence presented in response to a specific claim is dismissed and some other (often greater) evidence is demanded
• Perfect solution fallacy: where an argument assumes that a perfect solution exists and/or that a solution should be rejected because some part of the problem would still exist after it was implemented
• Retrospective determinism(it happened so it was bound to...a large assumption in DVOA v6.0)

 Conclusion

Again, I am not saying that all NFL statistics are useless.  They often provide great weight to an opinion to explain why something occurred.  But the nature of the NFL prevents a Causal relationship, especially when trying to predict what will happen.  I've yet to see a stat or series of data that would meet the Pareto principle (80/20 rule)...my personal Mendoza line for meaningful predictions.  (BTW, Vegas success is often weighted to the "house" so that non-causal statistics that don't reach >70% are irrelevant to the bet)

Further, while statistics can help "rank" individuals and units, and justify team rankings, they make inane arguments of "who is better?".  Just remember, my dad can beat up your dad.

I'm not trying to create a Loki's Wager: the unreasonable insistence that a concept cannot be defined, and therefore cannot be discussed.  I'm just saying that I've yet to see a predictive stat that I couldn't find fallacious with one exception...that the team that scores more points than its opponent will win.

With all that b.s., I can statistically say that the Cowboys are the best team in the NFL.  Want proof?