Super Subs and Selective Cutoff Points.

Not content with calling itself home to one super sub, Manchester inducted a second on Saturday night, when Javier Hernandez, also known as Chicharito accounted for two and a half of the goals that saw off Aston Villa in a night of blood letting for footballing cliches.

First to go, depending upon you view point was the invincibility or vulnerability of the two goal lead. That was quickly followed by the ability (or not) of the best to come up with needed late goals at will and in doing so Chicharito's 87th minute winner also cemented his lot as another super sub. An early rebuttal of the 90's claim that "you'll win nothing with kids" was hastily shelved following Villa's tame second half demise.

Chicharito was inevitably hailed as a super sub throughout the press. The Daily Mail, The Express, The Independent each dedicated articles to his super sub status and The BleacherReport had to fall back on "uncategorizable" as the defining quality of such a player.

Chicharito. A Talented Striker.

I argued here that super subs arise through a combination of recency bias, small sample size and a failure to account for the richer overall goalscoring environment in which substitutes inevitably play. But there is another selection bias that is present in the statistics that accompany these articles that almost guarantee that such a player's record as a substitute will appear to be much better than his record as a starter.

Gambling touts make extensive use of the technique of using selective cutoff points when describing their profit (or loss) record, invariably starting and/or ending their "fully verified" record with a string of winners. And model builders can also unwittingly fall foul through insufficient out of sample testing of their new toy, leading to a randomly discovered favourable cutoff point in the original sample becoming the precursor to imminent, real time failure.

In sport, the selective cutoff point is a "tool" often used to support a preconceived notion about the relative merits of two players. At it's basest you select a period of time during which Player A excelled at the metric of your choice and Player B didn't and then use this biased comparison to demonstrate that A is the superior athlete.

In this post I showed how selectively restricting the the goal scoring record of Park Ji-Sung to shots from certain distances artificially inflated the apparent difference in his shot conversion across two different seasons. Selectively setting his scoring record to include only goals scored from within 15 yards of the target included all of his goals in his "up" season, but just some of his strikes in his "down" year.

A similar thing is happening when players are being designated as super subs, although the process is almost certainly being unconsciously applied. Very few expensively bought attacking members of a top EPL team's 25 man squad wake up on a Monday morning to find they have become super subs after a barren weekend from the bench. If they've bagged two out of his teams three goals, as Chicharito did as a starter for United against Braga as recently as last month, he's even less likely to be dubbed as the new David Fairclough.

But score two out of three goals from the bench, as Chicharito did on Saturday evening or two out of two as Dzeko did against WBA at the Hawthorns and the narrative is already written....and just as importantly a biased cutoff point has been set that will guarantee an inflated strike rate from the bench to back up the story.

Understandably and apparently diligently, the super sub's club career statistics are then used. However, in combination with all the other flaws, a biased cutoff point, immediately following a game where the player has performed an outstanding and atypical example of the identifying trait, has been applied to seal the "proof".

The drip, drip of unreliable numbers gradually cements the myth.