Monday, February 3, 2014

Arm Length: Pythagoras Was An O-Line Coach

This is probably going to seem incredibly obvious/pointless to most people, but I thought I would discuss the subject of arm length, as it relates to offensive tackles (though it applies to other positions too).  I suspect almost every aspect of this has been covered before, but I wanted to throw in some basic mathematics.  The idea of a player being able to reach farther than his opponent, and the advantages this might create in blocking them has been discussed many times.  If you have ever had an older sibling plant the palm of their hand into your forehead, just to watch you flail about, unable to reach them with your stubby toddler arms, you've already experienced the potentially humiliating impact of this subject.

Yes, that is a perfect, and emotionally painful, dramatic reenactment of my childhood.

Still, I rarely make any mention of this arm length issue, since I think there are a number of factors that make the utilization of this measurement a bit problematic.  First of all, I don't entirely trust the accuracy of the arm length measurements that are taken at the NFL Combine.  Secondly, though related to the first issue, I'm not certain that the method of measurement (arms extended out to the side) is really the ideal approach.  Finally, unless a player has an arm growing out of the top of their head, I would be more interested in knowing a player's height at their shoulder, which is a rather impossible number to come by.  This is where they are reaching out from, after all.  I'll get into this a bit more, as we go along.

Despite the natural assumption that taller players will have longer arms, this often isn't the case.  Most people weren't designed according to DaVinci's Vitruvian Man, and their proportions can be a bit surprising.  Consider Ron Jeremy, if you doubt me.  These irregularities in human proportions are what I really want to focus on here.  I'm going to have to make some fairly broad generalizations here, but stick with me for a second, and it will hopefully make sense when we are done.  First, let's look at a basic right triangle.

Fascinating, isn't it?

Now, just for the sake of keeping things somewhat simple, let's pretend an imaginary offensive tackle is facing an average sized opponent who is 6'3" tall.  I chose 6'3" since it is fairly close to the average height of an outside linebacker or defensive end, but really we could have chosen any height that was less than the average height of an offensive tackle.  Since most offensive tackles are taller than 6'3" (generally they are about 6'5" or taller), they will have to reach out at a somewhat downward angle to block this shorter opponent.  The degree to which a tackle has to reach downward is obviously going to decrease the effective length of his arms.  Yes, a tackle could also crouch, to play at the same level as his opponent, and maintain a possible advantage in arm length, but for now we are just going to pretend that all tackles have an equal ability to crouch (they don't), and ignore that aspect of the argument.

Now, normally, the average length of an offensive tackle's arms is just a smidge over 34 inches.  When a tackle's arm length drops to 33 inches it becomes a bit of a concern, while a reach of 35 inches is a very exciting result.  This is just a difference +/- 1" we are talking about here (relative to the average), between the worrisome and the potentially exceptional.  So, we're already well into the realm of obsessive compulsive geekery, if we are fretting over 1 measly inch.

So, we'll say that side A of the triangle represents the difference in height between our imaginary tackle and his 6'3" opponent.  Side H, the hypotenuse of the triangle, will be our imaginary tackle's actual arm length, aimed downward towards his opponent.  Side B, will tell us what our tackle's effective arm length is (B =.the square root of H² minus A²).   Yes, I know this is all very basic and stupid.

Imaginary Tackle #1- 6'8" tall, with a 34" arm length
Side A= 5" (height difference compared to opponent)
Side H= 34" (arm length)
Side B= 33.63" (effective arm length vs. a 6'3" opponent)

Imaginary Tackle #2- 6'5" tall, with a 34" arm length
Side A= 2" (height difference compared to opponent)
Side H= 34" (arm length)
Side B= 33.94" (effective arm length vs. a 6'3" opponent)

With all other things being equal, except for imaginary tackle #2 being 3" shorter, there is a 0.31" difference in how far they will be able to reach in order to plant their hand in their 6'3" opponent's head (or, wherever), with the shorter tackle having the advantage.  This may not seem like a big difference, but these little things can potentially add up.  Considering the rather small difference between an above average or a below average arm length (again +/- 1 inch), a 0.31 bonus could have a potential impact.  Suddenly, our imaginary 6'8" offensive tackle is looking a bit below average.  The extent to which superior arm length matters is debatable, but not judging these things in relationship to a player's height seems a bit odd to me.  If nothing else, it demonstrates how simply being taller, without a proportional increase in arm length, is probably of questionable value.  Being taller may even be a handicap.

Let's now look at a more extreme example, this time using actual NFL tackles matched up against our imaginary 6'3" opponent.

The Unfortunately Not Imaginary Tackle, Adam Terry - 6'8" tall, with a 32" arm length
Side A= 5" (height difference compared to opponent)
Side H= 32' (arm length)
Side B= 31.607"

The Ridiculously Proportioned Tyron Smith - 6'5" tall, with a 36.375" arm length
Side A= 2" (height difference compared to opponent)
Side H= 36.375" (arm length)
Side B= 36.32" (effective arm length vs. a 6'3" opponent)

For some bizarre reason, once described Adam Terry as having "the hand usage and long arms to lock on and steer", when they discussed this 2005 second round draft pick.  This little bit of scouting is probably best forgotten, or treated as comedy.  Against our imaginary 6'3" opponent, he ends up losing 0.393" of effective arm length, due to his height.  This penalty is particularly painful, since his arms were already significantly below average, at 32" in length.  Either way, while Tyron Smith already had a 4.375" reach advantage over Terry, when we factor in Smith's shorter height this increases to a 4.713" reach advantage, which is just ridiculous.  It should also be noted that Tyron is only losing 0.055" of effective arm length in this situation.  I'm really only throwing this comparison in here to show how wildly physical proportions can vary.

At some point, I figure somebody is going to argue that our imaginary 6'3" opponent's head should line up quite nicely with a taller offensive tackle's shoulders, so why would there need to be a downward angle to his outstretched arms?  Well, first of all, thanks for ruining my excellent Spaceballs sourced visual demonstration.  Secondly, if an offensive tackle really targeted his opponent's head, there would be a reasonable chance of a penalty flag being thrown (not that people don't get away with this), which is why....Thirdly, linemen actually go for the shoulder pads or chest of their opponent, which means that against a shorter opponent, guess what?  Yup, once again their arms will still probably have to be aimed downward just like we would expect.  This relationship between two opposing player's shoulder levels, is one of the reasons why I would be curious to know a player's height at their shoulders (or, if we treat them like horses, their withers), rather than just at the top of their head. 

In the end, I think people can sometimes make too big of a deal about arm length.  While Adam Terry failed, he had numerous other issues beyond Tyrannosaurus Rex arms.  I prefer to consider other athletic traits first, and then look at arm length as just the icing on the cake.  Superior arm length probably won't make a bad athlete great, but it could make a good athlete even more effective.  Arm length probably does play some role in a player's success, and as long as it is discussed in its proper context, is somewhat interesting to consider.  However you choose to look at it, I think we can all agree that what we really want to find is another HervĂ© Villechaize, but with 36" long arms.  It could be difficult.

Yes, I clearly have too much time on my hands.


  1. Very interesting stuff! Obviously you show arm length by itself is overrated. As you said the taller they are the more they have to reach down yet this doesn't account for knee bend. There is really much more to arm length then just the pure number of inches. This is a great first step to looking at it from different angles. Love your stuff, I wish you could post more!

    1. Yeah, this was just something goofy I had been thinking about, so I figured I would post it up. Accounting for knee bend is tricky, but I've been thinking about seeing if we can approximate it by looking at a player's short shuttle and 3-cone times, then connecting that to arm length. It might be difficult to prove though. Either way, I'm glad you enjoyed the post.

    2. Thanks for the reply. I feel this may be an issue that needs more than numbers. With true arm length in conjunction with technique being important.

    3. I'm always happy to reply to the captain of the U.S.S. Enterprise.

      As far as technique is concerned, I'm not really qualified to say much on that subject. Considering the low success rate that teams have with drafting players, I tend to suspect their expertise in this area is a bit debatable too. If they can't evaluate good technique correctly, then I probably can't either.

      On the other hand, the rate at which remarkable physically superior players end up succeeding, is rather noteworthy. That is an area that I feel pretty comfortable analyzing. Of course, a lot of bad assessments of supposed physical superiority are made based on overly simplistic factors like a player's 40 time or their bench press, which gives this sort of analysis a bad name.

      I'm just hoping to figure out which factors may matter, and determine whether teams could make better picks based on data that is less subjective. This doesn't mean that I completely discount the importance of more subjective things like technique, but I can't contribute much in that area. Calling the analysis of a player's technique "subjective", may seem insulting, but that isn't my intention. It's just that different scouts appear to have different opinions about a given player's technique, which means such analysis is just an opinion, which obviously can't be relied upon as an objective fact.

      Still, it is something interesting to discuss. Hope to hear more from you in the future.

  2. In all honesty, I was named after him. Those trekkie parents of mine.

    In regards to football, I completely agree with your opinion. Scouting is subjective, that's what makes some scouts way better than others. I think what you are doing could be helpful to any team as part of the whole picture. I think looking at the advanced numbers you find before scouting gives you an idea of what to look for when scouting. Find the best athletes and then see if they are football players.

    I love what you are doing and have been slowly trying to do the same thing myself but data accumulation is the hardest part for me right now.

    Thanks for all the hard work, I now know the type of effort involved in getting to where you are at.