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Thursday, April 09, 2009

Median yards per attempt?

Average yards per attempt is the most important stat for measuring efficiency. But what about median numbers?

Pro-Football Reference Blog:

You’ve probably never thought about this before, but how many yards do you think the average QB gets on his median pass attempt? The answer is zero, and for most of NFL history, it was less than that. 2008 was the greatest passing season of all time (by adjusted net yards per attempt), but even this past season, the median pass attempt probably went for only one or two yards.

The average completion percentage was 61% while the sack rate was 5.9%; this means that on every 1,000 dropbacks, 59 times the QB was sacked. On the remaining pass plays, 574 times (61% of 941) of the time the QB completed a pass. So only 57.4% of all pass plays were completed, and surely a bunch of those completions went for negative yards or no gain.

In 1998, the completion percentage was 56.6% and the sack rate was 7.2%; this means only 4.8% of all completions would need to go for no gain (or worse) to make the median pass attempt be zero (or negative). In ‘88, the numbers were 54.3% and 6.8%; only 1.2% of completions would need to go for no gain (or worse) to make the median pass attempt be zero (or negative). In ‘78? A leaguewide completion percentage of 53.1% coupled with a sack rate of 7.9% meant that 51% of all pass plays did not gain yardage even ignoring all completed passes for negative or zero yards.

Passing is high risk, high reward. The large gains offset the risk, which is why teams average more yards per pass than yards per rush. For the passers, frequency of success isn’t nearly as important as quality of the success.

What about rushing? Just the opposite. In modern times, most RBs have a median carry length of three yards. I suspect that’s been the case for the majority of RBs for a long time. LenDale White and his 3.9 YPC last season? Median rush of 3 yards. Adrian Peterson and his 4.8 YPC? Median rush of 3 yards.


Grotus' Acorn said...

Hey Chris,

I'm a little skeptical of median statistics being applied to football. Median (as opposed to mean) tends to cancel out the effects of skew in a distribution. Essentially, this makes the analysis less sensitive. If QB A's yards-per-attempt distribution is skewed negatively and QB B's yards-per-attempt distribution is skewed positively, QB A is the better QB. Median statistics would make them look the same.

We should not be analyzing football non-parametrically because negative skew is good.

I ran into a similar problem when calculating Sharpe ratios. Your example (initially) was two QB's who throw for 10/10/10/10 yards or 0/0/0/40 yards. Certainly we prefer the first QB. But say we have two QB's who throw for 9/10/10/10 yards and 9/10/10/20 yards (changed the numbers so I can calculate an STDEV.) Clearly, we prefer the second QB. But the Sharpe ratio is misleading: SR for the first QB is 19.5, and for the second QB is 2.36. What would seem to be a clear statistical decision is actually very misleading.

I was poking around and found something called a bias ratio. I don't have too much familiarity with that statistic, but it would seem to be capable of rewarding negative skew. What do you think?

Thanks for the excellent, excellent blog. I can't tell you how much it's improved my understanding of football and my Madden playbook.

Chris said...


Good points -- I will have to respond more in depth later. (The Sharpe stuff was written like four years ago so it's definitely not sufficient, but still has some useful ideas for trying to identify consistency in certain plays.)

But I agree that offensive production distributions are wildly skewed. The fact that almost all runningbacks have around 3 yards median carry is fascinating: it says to me that maybe the sine qua non of good runners is big play capability. Then again we can maybe break down further some power back types who get the right amount routinely; not quite sure yet. I just threw this up as food for thought.

Unknown said...

To be clear, I don't think median statistics are relevant to QBs. My point was that QBs should be judged by adjusted net average yards per attempt because skewness matters with QBs. (FWIW, QBs don't all have the same median yards per attempt.) With running backs, it's less relevant. Obviously I'm not saying we should judge RBs by median yards per rush since that would be no help at all. Rather, my point is that judging RBs is difficult and I'm not sure they should be judged by yards per carry. Because it's hard to judge RBs, carries should enter the analysis -- they're an indicator of talent and ability, if not necessarily production.

Chris said...

Chase, I wasn't trying to be misleading; I just found the arts rather interesting. I mean it conports with what I thought, though for runners I think it has interesting implications. I know you're trying to rank RBs; I'm thinking more in terms of team stats and overall offensive productivity. And on that score I still think yards per rush attempt is important, especially for equilibrium/passing premium purposes. And if median winds up being the same for most carries, and I'm -- at least on first down -- trying to max out my per attempt amounts, then I want high variance runners, ie guys who can rip off explosive plays (not necessarily the same thing as "to the house" types but possibly similar.

Brian Manning said...

Using both statistics is very useful. Median is often ignored, but if you compare a player's median yards per attempt (or yards per carry) versus the average, I think that you get a great indicator of consistency.

Like what you said in your comment, it will give you an indication of a player's variance and you can use each in different and appropriate situations.