Obstuctions in the Scope are Larger than They Appear

If you have spent a significant amount of time hunting, you have missed your fare share of shots.  This November, on opening weekend of rifle season, I suffered through a clean miss at 30 yards.  I got down from my stand and looked for any signs of blood.  After searching long enough to be certain that it was in fact a miss, I turned my attention to why.  My mind started running through the typical list of possible reasons... 

Was my rifle sighted properly? Yes, I shot it when I arrived at deer camp the afternoon before.

Did I flinch? Not likely.  I had a steady rest and I had calmed my breathing before pulling the trigger.

I couldn't figure it out.  I  climbed back in my stand and had a look around.  That's when I spotted it.  In my shooting lane about 15 feet from me was a single 1/2 inch diameter twig that was freshly broken and splintered.   The shooting lane was clear with the exception of this single small twig.  I thought that the odds of hitting that twig must be astronomical.  I certainly didn't even consider the possibility that I would hit it when I was aiming at the deer.  I don't even remember seeing it as I focused my eyes down range.  But the evidence showed that I had hit that measly twig and it sent my .30/06 bullet wayward. 

It wasn't the first time I had missed and it probably won't be my last but it sure would be nice to understand how it happened so I can minimize the chances of it happening again.  I'm a math teacher, so I sat down to analyze the miss from a mathematical perspective.  Here is what I came up with...

Our mind sees and opening for a shot but a projectile (bullet or arrow) needs a certain amount of clearance around any obstruction.  We don't see the clearance needed.

We see this.

But what we need to think, is this.

Conceptually that is what is going on.   I went ahead and analyzed it further.  I wanted to answer the question, "By neglecting to consider the buffer, to what degree are we lying to ourselves?"   Consider this simple example of a one inch wide twig, passing through a three foot square shooting lane.



1" branch with no buffer

1" branch with .30" buffer in red

This branch takes up just shy of 5% of the window for the shot, setting our expectation for success at 95%.  But what about the clearance for a .30 caliber bullet?  If we add that buffer in and count it as area that the bullet must avoid, our expectation for success drops below 92%.  Sure, that doesn't sound too bad but consider this. 

The branch excludes 60% more space than your brain told you initially.   



1" branch with 1.5" inch buffer in red



Bullets are small.  What about arrows?  I conservatively estimated that an arrow flight would need 1.5 inches of clearance for broad heads, fletching and wobble.   That changes the game significantly. 1.5 inches around the same twig blocks over 20% of the lane.  Going from 5% obstructed (what you see) to 20% obstructed (what you need to account for) is a 300% increase. 

The Takeaway

Anytime you intend to thread the needle from the deer stand you need to adjust your thinking about how  narrow an opening  you have.  It doesn't take much to deflect a bullet or arrow.  A branch or twig that you thought was inconsequential could sent your shot off target causing a miss, a wounded animal or a carom to who knows where.   And it is more likely to happen than what your brain normally tells you.

What can we do about it?

As hunters, we want to be as concealed as possible with cover between us and our quarry to shield our movements.  One key part of the solution is back cover.  Cover behind you serves to breakup your outline and can be very effective concealment.  Another key is well cleared shooting lanes.  When setting up your stand before the season, consider what your lanes will be like in throughout the fall.  During early archery season the leaves will still be on the trees but expect many of the leaves to be shed by the rut.  You can avoid obstructions altogether by setting your stand on a telephone pole. Or you can bury yourself in a briar patch too thick to draw a bow much less thread a shot through.  There is definitely a balance to be struck.  To help find that balance, try visualizing the buffer around the branches that might obstruct your shot.   After you give yourself that buffer and if you are uncomfortable with what you have, trim a little more. 

-KF

Archimedes and the Non-Typical Rack

Making the Case for a Volume Based Scoring System


A non-typical rack is by definition, unusually shaped. This makes them difficult to judge on the hoof and difficult to score with a tape measure. The ultimate question is, "How big is it?" So why do existing systems rely on linear measurements? Even a typical rack is measured awkwardly. Inside spread, outside spread, circumferences at the basses, circumferences in between the tines. It is all trying to get a general picture of how much space the rack takes up. Volume. But here is the problem, volumes of irregular shapes cannot be accurately measured by a series of surface dimensions. Water displacement
is the way to go. Even if we concede that typical racks will continue to be measured with the Boone & Crocket system, non-typical racks are perfect candidates for volume scoring by water displacement.

Until Janet Jackson's "wardrobe malfunction," one of the most famous instance of public nudity in history was when Archimedes climbed into his bathtub only to have the water he displaced spill over the sides. He had discovered a method by which he could measure volume or irregular shapes. At the moment of discovery, he ran out of his house and down the street in his birthday suit shouting, "Eureka! I've found it!"

Now is that "Eureka" moment for scoring non-typical racks. The Beatty Buck is a great example of a huge rack where a tape measure just doesn't do it justice. I don't want to know how many inches you can add up after putting a tape to it a couple of dozen times. I want to know how big it really is. How many pints? How many gallons? Would it make my bathtub overflow? Linear inches can't answer these questions.

If the hunting community adopts the Flatau & Archimedes system you might take your deer to the local bait shop to check in your buck. While you're there, you can dunk his headgear in the live-well and find out what he scores on the spot. You might give your hunting buddy a ribbing for the half-pint he shot last season or have the whole neighborhood come over to see the gallon deer hanging in your garage. Just be prepared for the day you arrive at that long anticipated Saskatchewan hunt. Your guide tells you about the 2.8 liter buck he has been seeing and you start scratching your head as you work out the conversion.
-KF

The Mathematics Behind the Best Deer of Your Life

"This is the biggest deer of my life."  How many time have you said those words?  If you are like most of us you've only made that statement two or three times.   The first buck a hunter harvests is automatically his first personal record (PR).  By using a little math we can divide  hunters into three categories.

The Math of Record Setting # Bucks Expected # of PR 1 1 2 1.5 4 2 10 3 31 4 80 5 227 6 616 7 1674 8 To calculate how many new records you can expect to set we can use the concept of expected value.   For a random sample, the probability of setting a record on your first buck is 1/1.  Because we have randomness the second buck has a 1/2 chance of being the biggest. The third has a 1/3 chance, 1/4 for the fourth and so on.  Say we assign a "payoff" of $1 for each personal record set.  If we do this we can calculate the expected value by summing the products of $1 payoffs and each of the respective probabilities.  It looks like this, where a is the number of bucks harvested.  We sum this series for the number of bucks we have harvested and we get a mathematical expectation of how many personal records we should expect to set.  Some notable calculations are shown.

Type-1

Consider yourself a type-1 hunter if you have set two or fewer personal records after ten bucks harvested.  Whereas mathematically, you would expect three PR's after that many events.  My brother-in-law fits this category. It is not because he is a bad hunter but because of his first buck.  His first buck was an Iowa freak of nature with headgear that looked like a swing set.   If you set the bar that high that early, it will take a long time before setting a new PR.  Imagine if Uasin Bolt ran the 100 meter dash in the ancient Olympics.  He would have set a standard so out of sync with his contemporaries that after a few hundred years, humanity would have long grown weary of a quest for a new world record.  The only hope is that runners would compete because they enjoy the personal challenge and the experience.  This is the situation of type-1 hunters.  I doubt Milo Hansen grabs his rifle each November expecting to shoot the next world record.  Type-1 hunters, enjoy your season but don't hold your breath for a new PR.

Type-2

A type-2 hunter has set a PR four or more times in their hunting career.  This can happen by sheer numbers.  The math indicates that it would take 31 randomly harvested bucks to expect four PR's. If you set four PR at a faster pace than that, it is probably because you are not randomly harvesting deer.  These type of hunters practice a managed hunting strategy that is focused on taking trophy deer.  To achieve a mathematical expectation of 5 PR it would require 83 bucks.  Not many of us reach those kind of numbers.  But there are hunters who set five PR's.  They likely set a standard for themselves that only allows them to take bucks near or above their current PR.  If they are doing this they certainly aren't harvesting 83 bucks in their hunting career because they are letting a lot of deer walk. 

Type-3

Then there is the rest of us.  We hunt for the experience, the camaraderie and the freezer.  Our experience closely fits the statistics.  After our first four or five bucks, we've set two PR's. By the tenth buck we set our 3rd PR.  It could be that in our beginning years hunting, we took a couple spikes.  My first buck with a bow was a fork horn six-pointer and it remains one of my proudest hunting moments.  As we get a few deer under our belt we can start to let the spikes walk.  But generally speaking, we shoot the first legal, delicious deer that presents an ethical shot.  This makes the deer we harvest effectively random.  And so our situation fits the mathematical expectation nicely.

So what does this mean for you as you head to the deer stand this fall?  First, identify which type of hunter you are.  If you are satisfied, go out and keep enjoying yourself.  If you are a type-3 hunter and want to make the transition to type-2, your hunting needs a paradigm shift.  Suggesting the wholesale slaughter of deer, so that you can slant the odds in your favor is ridiculous.  So, it really takes a concerted effort in habitat and herd management that may or may not be practical for your hunting situation.  If you are a type-1 hunter and you have already killed the biggest beast in the woods, you will have a hard time finding sympathy.  You can do all the habitat improvement and QDM you like and depending on how high the bar has already been set, you might get lucky.  Or you might not.  So your focus should be the experience (as it should be for all of us).   

In statistics it is important to consider the possibility of outliers so let's not leave them out here.   Maybe a member of a TV pro-staff gets sent to 10 states each year for ten trophy hunts.  The number of bucks they kill and the number of PR's that they have set, have no reason to match ours.  It doesn't take a statistician to tell you that something is different there, as we sit and watch them from the couch.
-KF