Avoiding The Sticks
While doing research for our upcoming book, I started to look into solving a problem that's been on my mind ever since my first article for Football Outsiders, the "Four Downs" in which I first started analyzing Chris Chambers and his low catch rate; namely, adjusting a player's catch rate for the distance and location of the throw, as well as the situation the throw came in.
The idea, of course, is to create a purer "Hands" metric that measures a player's ability to catch the ball versus something approaching a league-average receiver.
The bad news is that the research didn't pan out; after adjusting for various situations and running a simple regression, the best hands in the league belong to ... Ike Hilliard. That's too close to my "Horizontal Yards" parody for comfort, so I'm going to shelve the system for now. (The worst hands on a per-play basis, by the way, were Ashley Lelie's.)
As part of doing the research, though, I came across an interesting side note that I thought was worth bringing up as an XP. One of the variables I was accounting for in my analysis was the number of yards between the location where the pass was caught (or ruled to be incomplete) and the first down marker; it was an attempt to adjust for players getting easy catches eight or nine yards down the field on third-and-12 or second-and-20. (Keep in mind that this analysis strictly considers the yardage in the air of passes, not any yards after catch.)
In looking at completion percentage by yardage totals relative to the first down marker, I found a very interesting trend. Take a look at the 2008 completion percentage of passes thrown to within two yards of the marker on third downs:
|Down||v. ToGo||Cmp %|
That's right -- it's about 20 percent harder to complete passes at the marker than it is to complete them within two yards on either side of the marker.
Now, this would seem to make sense -- defenses know that the offense is looking for the sticks on third down, so they're comfortable dropping their linebackers or even their corners right at the first down marker. What if we look at first or second down?
|Down||v. ToGo||Cmp %|
Although the effect isn't as pronounced, it's still there; it appears that teams simply are better off going past the yellow line if they want to move it.
I say "appears" because the possibility exists, naturally, that this could be a mathematical fluke, a small sample, or a reporting issue (maybe official scorers and/or our charters are inherently more likely to report a pass going just beyond or before the sticks for some reason). We're looking at samples of several hundred passes for each "yard" being measured, though, so there appears to be a legitimate effect in play.
Are teams accounting for this in their offense? Hard to say. In 2008, the offense that threw the highest percentage of its passes to the sticks was Kansas City, at 9.6 percent; other offenses above eight percent included the Giants (8.7 percent), Indianapolis (8.4 percent), San Francisco (8.6 percent), and Jacksonville (8.1 percent). If we look strictly at third down, Houston threw 15 percent of its passes right at the yellow line, followed by Kansas City (14.9 percent) and both Indianapolis and New England (14.0 percent).
On the flip side, Tennessee stayed away from the zero-yard line; only 4.3 percent of its third down passes and 4.7 percent of its total were at the sticks, both league-lows. Dallas (4.6 percent) and Baltimore (4.8 percent) were the only other teams below five percent on third down, while those teams, Minnesota, Cincinnati, St. Louis, and Pittsburgh were all below six percent overall.
I'm interested in hearing your thoughts on why this effect might exist in the comments.
54 comments, Last at 02 Jul 2009, 7:50pm
#1 by Kibbles // Jun 30, 2009 - 2:50am
>That's right -- it's about 20 percent harder to complete passes at the marker than it is to complete them within two yards on either side of the marker.
Eh, 11%, 20%, same difference.
#2 by Phill (not verified) // Jun 30, 2009 - 3:28am
I thought the same thing... but then, I wondered if he was using '20% harder' in the same kind of way as 'twice as hard'; i.e. there is a factor of 1.2 in the relative difficulty. It's not an intuitive way of expressing it (to me), but might be what he meant.
Anyhew, it would be very interesting to find out if it is a real effect or (as suggested) an artefact of how scorers decide how many yards a play went for (or how the referees spot the ball, even). But I suppose that would be very hard to answer without looking at tape of a lot of plays and either assigning a more reliable measure of yards, or looking at whether defenders really are camping the 1st down marker in a way that would make a difference.
#3 by Thomas_beardown // Jun 30, 2009 - 4:42am
I think one thing could be receivers making a catch right at the sticks, and stretching for the first, getting that extra yard past. I could see scorers marking this as a catch and tackle 1 yard past the first down line. If the receiver drops it or the pass is defensed the scorers mark an incomplete at right at the first down markers.
#9 by bengt (not verified) // Jun 30, 2009 - 7:21am
IMHO it should read '11 percentage points' or 'roughly 40%' harder, but I'm not a native speaker.
#10 by Anonymous2 (not verified) // Jun 30, 2009 - 8:23am
It's 11 percentage points, but 20%. If the completion rate is 49% right at the line and it's 60% a couple yards off the line, that means it's 1/5 harder to complete at the line.
#15 by Bowl Game Anomaly // Jun 30, 2009 - 11:04am
Correct. "Percent harder" essentially means that completing a pass at the marker is only successful at X% of the success rate before or beyond the marker. "Of" means multiply. Hence, 49=60*X. X=about 80%, thus 20% harder than completing away from the marker.
#4 by Greg Trippiedi (not verified) // Jun 30, 2009 - 4:46am
It's stressed to receivers from their high school days that routes should be run PAST the first down marker, for you don't want to risk coming up short of the first if you cut it just a half yard short. Expounding on this, I would suggest that a pass thrown right at the marker represents, in many cases, a situation where the defense has already won the early part of the play: either they got pressure on the QB quickly, or they jammed the receiver and altered his route. Obviously, both of these results would affect completion percentage negatively.
As for why the passes thrown short of the sticks are completed more often...well, that's obvious, isn't it?
#8 by Pouringlizards (not verified) // Jun 30, 2009 - 7:01am
We have a winner.
Add to that, the fact that someone catching the ball at the first down marker is A) likely to be thinking about the hit coming and how to squirt for those extra yards, and B) actually about to be hit, that's a good recipe for increased drops.
#5 by sswoods (not verified) // Jun 30, 2009 - 5:16am
Here's my theory.
Every defensive player and coach in football knows that the key to stopping an opponent's possession is to not allow first downs. Defenses are built to prevent the first down, and everything from scheme to philosophy will have a focus on where the marker is -- and the more the defense pays attention to something, the more likely it will be effective at it.
Or something like that.
#6 by Bright Blue Shorts // Jun 30, 2009 - 5:36am
Wow ... now you're talking rocket science ... no more theory please ...
#7 by Raiderjoe // Jun 30, 2009 - 6:49am
This is good comment. You right every team knows it has to stop first dowms fom happening, touchdowns too. Touchdowns of fourse more imptant than first downs but if defense can stop first dowms from happpening more likely that other team has to punt which is not a good wqay to score. Lets see as example if Rams have 3rd and 6 and other team is Falcons, all falcons have to do is set up defense in way that Rams have trouble getting 6 yards oir more yards. Can maybe use 5th dback if Falcons use 3 Wrs and make them play man covegrage. So loook at down and duistance and you have answer to problem.
#21 by Briguy // Jun 30, 2009 - 12:06pm
if defense can stop first dowms from happpening more likely that other team has to punt which is not a good wqay to score.
I figured it out! Raiderjoe is John Madden!
#22 by J.D. (not verified) // Jun 30, 2009 - 12:11pm
MOAR POINTS = WIN
#54 by BroncosGuy (not verified) // Jul 02, 2009 - 7:50pm
Bill, don't you feel a little silly now? Had you simply asked Joe your question by email, you could have saved a lot of time.
#43 by Kibbles // Jul 01, 2009 - 2:13am
Of course, the glaring problem with that theory is that you could just as easily flip it around- every offensive player and coach in football knows that the key to continuing their possession is to continue getting first downs. Offenses are built to achieve first downs, and everything from scheme to philosophy will have a focus on where the marker is -- and the more the offense pays attention to something, the more likely it will be effective at it.
Now we need a compelling reason why the defensive focus would somehow outweigh the offensive focus.
#44 by DrewTS (not verified) // Jul 01, 2009 - 11:38am
The defensive guys want it more. They also have more swagger and toughness.
#45 by Mr Shush // Jul 01, 2009 - 1:09pm
Because if a defensive player and an offensive player are both where the ball is supposed to go, the defender usually wins. Offenses succeed primarily by throwing the ball to where defenders aren't, not by winning battles where they are. So if a defense decides to sell out in defending a particular piece of territory, it will usually succeed - though that success may come at the price of a significantly reduced ability to defend everywhere else. It's for pretty much the same reason that yards are harder to come by in the red zone.
#11 by qed // Jun 30, 2009 - 8:41am
Could we have a psychological bias on the part of the scorers to place incomplete passes that are NEAR the first-down line exactly ON the first down line? I know when I'm charting games that "distance traveled in the air" is a very subjective call for an incomplete pass but is much easier to determine when the ball is caught. If I see a quarterback overthrow a short route or underthrow a long route right near the first-down marker I think I would tend to just say the pass was "intended" right at the sticks. If the complete passes are scored without bias, but the incomplete passes are biased toward "0", that would explain the difference in completion percentage.
Which begs another question, especially for the game charters: how do you determine PYds on incomplete passes, especially those where the receiver doesn't touch the ball? Do you base it on where the receiver was? Where the ball actually hits the turf? The yard line the ball was passing over when it was about 5 feet above the turf? I think we've agreed its a subjective call. And it's not one we have to make often, since in most cases we just use the official scorers numbers. But it might be interesting to try to define the "right" answer.
#13 by Sergio // Jun 30, 2009 - 10:03am
As you mention, we no longer chart the PYD/YAC numbers (they come pre-filled by the official scorers in the NFL), but when we used to, I usually based myself on where the receiver was, unless it was an obviously wrong route (in which case, it was an estimate based on where the ball was going).
-- Go Phins!
#27 by nate_richards // Jun 30, 2009 - 12:53pm
I always base it off where the receiver is, because if it was caught that's where the PYD would be. This is only a problem on the few occasions where the receiver fell or ran into someone and is nowhere near close to where the ball was thrown.
#12 by DrewTS (not verified) // Jun 30, 2009 - 8:42am
I have never followed a team that employed Ike Hilliard, so I'll ask a possibly dumb question. Why is the idea that he has the best hands in the league so ridiculous? Best hands doesn't mean best player, or even that he's worth a damn when it comes to getting open. It just means he's more likely to catch the ball when it comes to him. Is he notorious for stone hands or something?
#17 by Bowl Game Anomaly // Jun 30, 2009 - 11:11am
It's not ridiculous, but it does imply that "best hands" isn't a terribly useful measure if an utterly mediocre WR known for running exclusively short routes ranks #1. I think Barnwell was hoping that it would promote receivers who run longer routes, not shorter routes. We already know that guys who run shorter routes catch a higher % of passes, so this measure failed to come up with anything new.
That's my guess, anyway.
#33 by DrewTS (not verified) // Jun 30, 2009 - 3:58pm
But I guess that was kind of my point -- just because he's mediocre doesn't mean he doesn't have good hands. He might be mediocre because he's a step slow, or runs bad routes, or forgets the play regularly. Those factors all function independently of each other, and say nothing about his ability to catch a ball that comes near him.
To me, having a player you wouldn't expect rate highly doesn't necessarily mean that a metric is bad. It certainly could mean that, but it could also mean that you're actually digging into something. If the metric just spit out a list of all the guys you already knew were good, THAT would not be a useful measure in my opinion.
#19 by E // Jun 30, 2009 - 11:53am
I was thinking the same thing as DrewTS and can add that, as a Giants fan, I remember the days of Ike Hilliard playing inside of Amani Toomer - I always thought he had great hands. (People forget that Toomer was not a possession receiver early in his caeer, he was the outside guy.) In fact, as Steve Smith (NYG version) has emerged as a possession-based 3rd down receiver, my dad and I specifically discussed how he reminded us of Ike Hilliard's days as a Giant. I believe that if not for early career injuries, Hilliard might have become a very good NFL WR, along the lines of a Bobby Engram or Wes Welker.
That's a long way of saying that I wish Bill would have continued with his research as it may be truer than he was willing to believe
#25 by Bowl Game Anomaly // Jun 30, 2009 - 12:40pm
As I said above, the issue is not whether it is true, but whether it is useful.
#46 by Mr Shush // Jul 01, 2009 - 1:17pm
Useful for what? Fantasy projections? Probably not. Defensive game-planning? Quite possibly. Interesting what I suspect to be 100% of the Houston Texans fans in South Oxfordshire? Definitely.
#49 by Bowl Game Anomaly // Jul 01, 2009 - 4:07pm
1. Useful for giving us new information that we didn't already know. Hilliard has great hands? OK, that's nice, but it's not earth-shattering.
2. It's also not useful for identifying talented players- if Hilliard is #1, then it's not measuring global WR skill, it's measuring one small aspect of receiving. Again, nice to know but without much larger significance.
#51 by Kibbles // Jul 01, 2009 - 7:58pm
Taken on its own it might not have much larger significance, but what if every single WR skill could be parsed out and studied individually? What if you could tell exactly how good a WR's hands were, how good his straight-line speed was, how good his ability to sell moves to defenders was, how crisp his route-running skills were, how good his burst was, how good his concentration was, how good his improvisational skills were, etc? That would, to put it mildly, have "much larger significance", making the "hands" research a key component in research that potentially could have much larger significance.
Also, I completely disagree with saying that this doesn't have much larger significance in the first place just because Hilliard is #1. So what? Unless the list is 1 name long, there's much more to it than just Ike Hilliard. Where does Terrell Owens rank and what does that say about the popular opinion that his hands were so terrible? Where do Chris Chambers' Miami years rank and what does that say about the hypothesis that his catch% was so much worse than Welker's almost directly as a result of the comparative length of the routes each was running? There are a lot of theories and arguments and hypotheses floating out there that these numbers can go a long way towards settling.
Basically, if you look at this is a ranking of the best WRs, then it's useless... but then again, looking at a list of WRs ranked by straight-line speed tells us nothing about which WRs are the best, but it still gives us plenty of useful information in terms of evaluation of WRs.
#52 by Bowl Game Anomaly // Jul 01, 2009 - 11:22pm
OK, that's a pretty good point. I admit, I also wanted to see the whole list. It sounds like Barnwell is still playing with it, so maybe we will see it eventually.
#38 by shake n bake // Jun 30, 2009 - 5:17pm
I was actually doing the same kind of thing as Bill (with much less data) just the other day.
For WRs with 50+ targets over the last 8 seasons (n=664) there's a weak correlation (r^2=.13) between catch% and AirYards per reception.
The formula for expected catch% I got does love it some Ike Hilliard. Also Dennis Northcutt's 2002 season (which DVOA is ga-ga over too).
Also turned it into a counting stat (catch% over expected times targets=receptions over average), which loved Marvin Harrison's record breaking 143 reception season (205 targets, catch% of 70, only slightly below average AirYards per reception).
Here's the top and bottom 20 seasons lists.
#14 by Spike (not verified) // Jun 30, 2009 - 10:52am
Have to agree with the defensive bias around the sticks. Seems like you'd get a lot of LBs and DBs milling around that line, looking to stop anything short of it or knock passes down that go overhead.
Do you have the number to expand this to + and - 5 yards from the marker?
#16 by qed // Jun 30, 2009 - 11:11am
I think that would explain why the short passes have a higher cpt %. I don't think it explains why passes that travel a yard or two beyond the marker have a higher cpt% than ones thrown right at the marker. It seems like the all the traffic right around the line would stop those passes just as effectively, if not more so, than passes thrown right at the marker.
#50 by Mr Shush // Jul 01, 2009 - 7:33pm
One possible mechanic which could explain this if it is a real phenomenon and not just scorer bias: it's possible that different types of route tend to be run to the line and a yard or two past it. Perhaps hook and curl type routes tend to be run to the marker, but crosses and outs tend to be run two yards past. And perhaps crosses and outs are more successful, in this context, than hooks and curls. I'm not saying I think this is the case, but some mechanism along these lines could be in operation, and could explain the findings.
Also, I suspect any hands metric that adjusts only for catch location (or anything similar) will fail to overcome the Simpson's paradox issues that plague all WR rate statistics, including (especially?) DVOA. To take the extreme case, no quarterback is going to chuck a hopeful jump ball at double-covered Ike Hilliard. If Larry Fitzgerald or Randy Moss or Andre Johnson catches such passes 50% of the time when the catch location is 8 yards down the field, that says something very positive about their ability to bring the ball in, but any statistical approach along those lines will see it as a negative.
#18 by Temo // Jun 30, 2009 - 11:52am
There was a study related to this over at AdvancedNFLStats.com. I'll try to find it.
The most popular theory about it thus far is that official scorers are less likely to list a successful play as being right at the yard marker needed.
IE: A team is at it's own 30 yard line needs 3 yards for the first down. The running back plunges ahead for 3.2 yards, earning the first down and the ball is placed at the 33.2 spot. Now the scorer can either mark the run as being 3 yards, or 4 yards. He cannot say the RB ran for 3.2 yards.
Scorers are biased towards marking it as 4 yards rather than 3. The same could apply to passes. If it's a 10.2 yard pass is incomplete , the scorer will just mark the closest yard line (ie, a 10 yard incomplete pass). If it's complete, he'll add a yard to the fractional yard gained (ie 10.2 yards becomes 11 yards and a first down).
The study there was very complete and convincing, though I'm having trouble finding it again.
#20 by Temo // Jun 30, 2009 - 12:01pm
Ok, so I guess I read it months ago and it wasn't exactly what I remembered, but it does point out the issue of official scorer bias:
#23 by qed // Jun 30, 2009 - 12:21pm
Very interesting article, thanks for the link. It seems to suggest that the scorer's markings may be biased toward putting COMPLETED passes exactly at the marker instead of one yard off, since that would (partly) explain the 5/10 yard correlations in that data. If anything, that should make the "0" completion percentage HIGHER than the +/- 1 yard completion percentage.
I suspect the 5-yard spikes in the field position distribution may simply be explained by the "starting on the 20" rule and the fact that penalties come in 5 yard increments. Not sure how to test the statistics on that one other than through simulation.
#24 by Costa // Jun 30, 2009 - 12:22pm
Very interesting! The only thing I worry about is a selection bias on incomplete passes... I have a feeling the tendency for a charter on an incomplete pass anywhere close to the sticks would be to just report it as the exact number of yards for the first down, since that would logically seem like what the offense was trying to do in such an inexact measurement.
If the catch is made, it becomes easier to discern where exactly the receiver caught it because there's a clear point when the catch is made, so an attentive charter can see that the pass traveled for 8 yards and be confident to mark it as such even though it was 3rd and 7.
If it was batted away from a defender, thrown over the receiver's head while he's on the run, thrown behind him as he's doing a diagonal cross or slanting, it becomes less clear what distance should be listed as it's not as evident when the pass goes from intended to incomplete as it is from intended to complete. Under situations like that, it would seem logical for the charter to assume the play was aiming for the sticks if it was nearby and thus mark it as such, whereas had the catch been made, the charter could better see that it actually traveled 8 yards rather then the 7 needed for the 1st down.
Note: I've never charted a game, so I can't say firsthand whether this type of situation arises often enough to truly poison the data. Someone with experience will have to chime in on that.
#31 by Jeff M. (not verified) // Jun 30, 2009 - 2:55pm
I think the comments so far have come up with a few theories about biased recording that together explain the phenomenon pretty well.
First, let me posit a scenario for what actually happens: if difficulty of completion increases with distance (that is, these results are due solely to biased reporting), the optimal attempt distance should be at the sticks (maybe a quarter- to half-yard beyond if there's some error term in where receivers run routes), so attempts should cluster right around there.
Now, a charter/official scorer sees one of three things on a pass right at/near the sticks: 1. incompletion, 2. completion for first down, 3. completion that fails to achieve first down (ignore INTs, etc.). I would imagine that (as others have collectively surmised) the tendency is to report (1) as at the sticks, (2) as +1 yard (since we know the receiver was *past* the sticks), (3) as -1 yard (since we know the receiver was *short* of the sticks). Of course, some charters may chart anything with a measurement as at the sticks, but if enough process the way I describe above, completion percentage is biased significantly upward for +1 and -1 and downward for at the sticks.
#26 by Jef (not verified) // Jun 30, 2009 - 12:43pm
Your "hands" analysis sounds like the firefighter discrimination suit. They came up with a test but, just because they didnt like the results, ie Hilliard having the best hands, they threw the whole thing out.
#28 by Temo // Jun 30, 2009 - 1:40pm
If you came up with a statistical system and in the end it told you that Joey Harrington was the most efficient QB of the past 5 years, would you not throw out the test?
Not quite as extreme an example, but it's the same idea.
#29 by the silent speaker (not verified) // Jun 30, 2009 - 2:30pm
Is not the point of this very website that they did essentially just that? Not with Joey harrington, obviously, but they creted a tatistical system that produced results contrary to conventional wisdom and in some cases downright counterintuitive, and hae been sticking to their guns and insisting that it is the conventional wisdom that is wrong.
It might cause you to reevaluate how important "hands" are, taken alone, but no skill set when taken alone makes an NFL receiver anyway.
#34 by Bad Doctor // Jun 30, 2009 - 4:18pm
I don't think that's a good analogy. The proper analogy would be if your statistical system was just trying to measure one small part of successful quarterbacking, such as avoiding sacks or not throwing balls where a defender has a chance for an interception. If Joey Harrington came out as most successful, it would be interesting in measuring that skill, but it would not necessarily be an indication of his superiority as a quarterback overall.
For a baseball analogue ... if a statistical study showed that Jeff Francoeur had the best outfield throwing arm in baseball, nobody would consider it out of hand. We'd just say it doesn't ultimately matter because he's so terrible at everything else that even his great arm can't make him a decent major leaguer.
#35 by Bowl Game Anomaly // Jun 30, 2009 - 4:45pm
Exactly- Ike Hilliard may have the best hands, but that doesn't mean he isn't still Ike Hilliard. If "best hands" is just a proxy for length of routes, it doesn't contribute anything new, especially because the whole point was to control for length of routes.
#37 by Temo // Jun 30, 2009 - 4:54pm
Yea, that's a better analogy. Doubly so because I'm a braves fan. :(
#30 by Bill Barnwell // Jun 30, 2009 - 2:48pm
Geez, everyone. I never said I was throwing the research out. I said I was shelving it for now. There is definitely a difference.
#32 by Joseph // Jun 30, 2009 - 3:52pm
Bill, maybe you should have said something like, "I am not sure I have the variables right, and will have to research this further." Before reading your comment, I sure got the impression of "Bill thinks the results are bogus, and therefore thinks his study is worthless." Which according to your comment here, is NOT AT ALL what you meant.
Even though I dislike NE, where did Welker come in?
#36 by Temo // Jun 30, 2009 - 4:53pm
Should teach you to share incomplete work. Now everyone's gonna wanna to see the whole list.
You big stat tease you.
#40 by Theo // Jun 30, 2009 - 5:44pm
So you MIGHT come back with a 'hands' research, where Ike Hilliard comes out as the best.
ps. Is it a 'who's the best receiver' stat, or a 'first down machine' stat?
He does have the highest catch rate, 81%, and a low yards/catch and is not the starting receiver for his club. So it's not that stupid that Ike comes up as a player who "catches it at the sticks".
#39 by Marver // Jun 30, 2009 - 5:28pm
In response to official scorer bias: why don't you -- Bill, or some other FO reporter -- just compare statistics from a few games that had several measurements at/around the sticks and see if they're properly recorded. I realize that finding one or two improperly recorded events isn't significant, but it would certainly help motivate your findings if you can show that, over several games, measurements were consistently accurate.
#41 by qed // Jun 30, 2009 - 6:09pm
I think that project would require two things: review of the official rules for PYds, and access to game footage from this past season. My NFL Game Rewind subscription is apparently done, and I don't think I'm motivated enough to pay $20 and spend a couple days doing the analysis. Assuming the hypothesis is correct (PYds for incomplete passes near the chains are biased toward being exactly at the first-down marker) does anyone think this is actually a significant and useful thing to prove?
#42 by tonic889 (not verified) // Jun 30, 2009 - 11:23pm
I don't know why it does or doesn't work, but I can tell you as a Ravens fan, a difference does exist. Brian Billick was the king of throwing to the sticks and coming up a yard short.
#47 by Kevin from Philly // Jul 01, 2009 - 2:48pm
I'd be willing to bet that the Eagles have the most 3rd down passes thrown 2 yards short of the marker. I'll never figure out why they do that with receivers that can't get yards after the catch (Westbrook excepted).
#48 by Bowl Game Anomaly // Jul 01, 2009 - 4:02pm
Redskins are frequently guilty also.
#53 by J.L. White (not verified) // Jul 02, 2009 - 2:36pm
This is a very complicated issue, and there may never be a true "Answer" for it. The most common response so far has been that the defense knows, for a lack of a better word, where the first down marker is, and is determined to stop their opponents. That makes a lot of sense to me, and although it doesn't appear to me, watching the games, that defenders act different near the hashmarks and coaches position defenders to guard that area, they very well could and I just never noticed. At the same time, it seems that the offense wants to advance the ball as far down the field as possible, while the defense wants to limit the offense gain as much as possible, if not even push them back. Unless an offense is going for it on 4th down, I'm not sure the hashmarks are the primary focus of either side.
So lets look at this at another angle, just for kicks. First of all, lets eliminate all forms of offensive and defensive technique; no running backs or tight ends catching the ball, no complex running routes by the receivers, no play-action, no blitzing or zone defense, no double-teaming potential receivers, no stunts or defensive lineman going into pass coverage, or anything else. Every formation is completely basic, and every players is completely average in every way; no faces, no numbers, no good or bad tacklers, no good or bad hands, nothing.
The offense has a basic set: 5 offensive lineman, one tight end, two receivers, two running backs and a QB. For this purpose the running backs are of no consequence, and are nothing more than blockers. There are going to be three plays; one is a pass to a receivers 2 yards shy of a first down, the next is a pass 2 yards beyond the first down, and the last is a throw right to the marker. Only a receiver will catch the ball, and there is no importance to the throw going up the middle or towards the sidelines.
The defense is, actually, what we're going to focus on, and they are in a basic set as well: 4 lineman at the line of scrimmage, three linebackers behind them, then two safeties in the secondary. No, I haven't forgotten the cornerbacks; in fact, they are perhaps the most important players on that side of the ball (for these examples). Cornerbacks, essentially, line up in front of the receivers and follow them, so while they are considered a part of the secondary, their general location is wherever the receivers go. In these examples there is the defensive line, linebackers and safeties; 3 different groupings of players, each on their own "line" on the field. Each line encounters their opponents in their own zones; while lineman generally engage the offensive line to attack the quarterback and running backs, in this scenario they could also be expected to pursue a receiver that might be close by.
In essence, the lineman are at the line of scrimmage, the linebackers are at or near the hashmarks, and the safeties are some distance behind the 'backers (for this scenario they are an equal distance from the 'backers as the 'backers are from the line, even if that is rarely true).
Example #1: The QB throws a pass to the receiver 2 yards shy of the 1st down. Obviously it's easier to throw a pass accurately 2, 4 or 8 yards than it is beyond 10 yards, which is a factor. The receiver will catch the ball with 4 linemen behind him, 3 linebackers ahead of him, and one corner nearby (for all these examples the other corner will be following the other receiver, and too far away to impact the play). As you no doubt concluded, this example has the most defenders near the receiver; 8, if you don't assume some of the linemen and 'backers are too far away. So it looks bad, with the highest possible amount of opposition, except there is also a high concentration of offensive support; blockers. While a pass 2 yards from scrimmage and 8 yards from scrimma 2 yards shy of the 1st down may be up to 8 yards away from the line of scrimmage, which changes a lot of things.
Example #2: The QB throws a pass 2 yards beyond the 1st down marker. This pass is thrown 4 yards farther than in example #1, so for all three examples this pass has to be considered the least accurate. It also looks bad since there is just one receiver against not just one corner, but also (potentially) 3 linebackers and two safeties. Odds due look pretty bad, but look at it this way: when throwing 2 yards shy of the 1st down, there are 3 linebackers in front of you, and 4 linemen behind you. In this case, the pass is behind 3 linebackers and in front of just 2 safeties (who, in the real world, predominantly play farther away from the 'backers than the 'backers play to the linemen). You could say that the cushion that is created by the extra field space makes up for a lack of blockers.
Example #3: The QB throws the pass to the receiver right at the 1st down marker. In this case you've got one corner already covering the receiver, plus three linebackers already at that point. In this scenario the 'backers are neither rushing up the field or falling back, and let's just say that here all three 'backers have an equal shot at engaging the receiver, even if in a live situation that wouldn't be possible. So not only could there be up to four defenders already at that line, but (again, in this scenario), both the 4 defensive linemen and the two safeties have an equal chance to backpedal/move up to engage the receiver, too.
Do these 3 examples prove that catches to the 1st down marker are inherently more difficult? I don't know; you could just as easily say that each example has its own challenges, and they should all equal the same, or that the further the ball is thrown the harder it is to catch it. In my own defense I do know that the linebackers don't always line up on the hashmarks, but in general you could say they line up closer to the line on short-yard situations, and farther back when the 1st down if farther away.
I just think that if you look at enough plays, all the tricks and advantages and disadvantages and everything else that has helped evolve football strategy on both sides of the ball cancel each other out, and this is what you're left with. Just wanted to throw that out there.