Last week, when Jared Goff's hands measured in at a Burger King-esque nine inches, the online scouting community erupted. For the uninitiated, there is a sort of truism within scouting circles that a quarterback must have hands that measure over a certain threshold, or they are doomed to failure. Some people take this threshold value more seriously than others, using it as an absolute minimum and crossing anyone who doesn't meet it off their board entirely. Others view it more as a red flag than a hard line in the sand, but pretty much everyone will tell you it matters.

I think those people are crazy. I think they are trying to apply concepts they don't understand to a problem they don't fit. I'm going to explain why I think all this talk about hand size is nonsense, and hopefully by the end you'll agree with me. Fair warning, there are going to be lots of plots, and a tiny amount of statistical theory. I promise you can handle it.

First let's examine the claim being made. It goes something like this:

Quarterbacks who have hands smaller than 9.125 inches have historically not panned out in the NFL

First of all, I want to point out that there seems to be some disagreement on the actual threshold, with some people bumping it up to 9.25 inches. I went with what I perceived to be the more common number. Now, let's break down what is being said here. There are two basic ideas being proposed: (1) small-handed quarterbacks have been less successful, and (2) this relationship is not random, but causal. I frankly don't believe either of those things are true. Let's start with the first part.

People have linked hand size to a few different aspects of performance. The one that has become a hot-button issue with Jared Goff specifically is ball security, but experts have also pointed to accuracy and arm strength as other traits that could be influenced by hand size. I will address each of these, along with overall performance.

To examine these correlations we need a data set. Using Pro Football Reference, I compiled a list of every quarterback drafted or signed as a UDFA since 2008, the year hand size became an official combine measurement. Then, to ensure my rate stats were at least somewhat meaningful, I selected only those quarterbacks who had been sacked 50 times. This left me with a sample of just 26 quarterbacks. Of those 26, only two fell under our hand size threshold. Right away alarm bells should be going off. The fact is that very few quarterbacks with small hands have ever even been given a chance to play poorly, so any conclusions we draw from their play are suspect at best. Now, it is possible that this lack of opportunity is itself a result of a lack of ability, but I don't believe that to be the case, for reasons we'll come back to later. For now, let's just pretend everything with our sample is good, and jump right into overall performance, as measured by PFR's Approximate Value. In order to account for the fact that most of these QBs are still playing, I express AV as a rate stat per start. [UPDATE: R values for the following plots are shown at the end of the article]

Does that look like a correlated data set to you? The two players with small hands (Ryan Tannehill and Chad Henne, by the way) fall within basically the same range as everyone else. So ok, there's no correlation between overall play and hand size, but that's going to be true for pretty much any single attribute. Let's instead look at the more specific areas a small-handed quarterback might struggle: arm strength, accuracy, and ball security.

#### Arm Strength

Throw power and arm strength are hard to measure in any empirical way. Here, I've used each player's measured combine throw velocity and yards per attempt as proxies for arm strength. I wrote last year about how I don't really trust combine velocity at all, but it's probably the best we can do for a measure of arm strength. So let's see what our correlation looks like.

Again, no discernible correlation. The sample is also even smaller on this one, because not everybody throws at the combine. If someone really wanted to, they could extrapolate the single data point below 9.125 inches into a trend, but that would be, to put it kindly, ill-advised. The other number I used to determine arm strength is yards per attempt, under the extremely naive assumption that quarterbacks with stronger arms would have an easier time completing longer passes. This is probably not smart for a number of reasons, but it's kind of all we've got.

In what is itself a trend at this point, we see no trend in the data, and the two quarterbacks with small hands are right in line with everyone else. I made a big deal about the unreliability of these last two datasets, so I want to take this chance to make an important point. We don't usually need to know a player's hand size to form an opinion on the traits that hand size is generally linked to. We don't need to know Jared Goff or Carson Wentz's hand size to know how hard they throw a football, because we can watch them throw a football. If a quarterback can make NFL throws, he isn't going to lose that ability because someone held a ruler next to his hand. In that sense, hand size is more or less a pointless redundancy, even if you believe it has a major impact on quarterback traits.

#### Accuracy

The second place many people believe small hand size might hinder a QB is their ability to accurately deliver the football. This is a little easier to measure than throw power. The main number I looked at was career completion percentage:

No correlation. Yawn. Completion percentage isn't just a measure of accuracy though, things like scheme and receiver skill are wrapped up in there too. So in addition to completion percentage, I looked at interception rate. The idea behind that being that windows are small in the NFL, so if a player is routinely missing windows, they will throw more interceptions. That's not perfect either, because many interceptions are a result of bad decisions rather than bad throws, but hey, it's one more thing to consider.

Alright, we're really on a roll here. So far hand size doesn't seem to be a controlling factor in anything. But we really haven't gotten to the main issue that came up this offseason.

#### Ball Security

What has my life come to that I know how many times Jared Goff fumbled the ball off the top of my head? The answer is 23. As soon as Goff's hand came in at a measly nine inches there were a lot of people quick to point out that Goff had 23 fumbles, and gosh, 23 sounds like a lot. Well, it is kind of a lot. But it's also devoid of any important context, mainly, how many opportunities to fumble did Goff have? The answer is a lot. He fumbled a lot because he had a lot of chances to fumble. That's actually a good thing, it means he started a lot of games and scored a lot of points. If you want to see what Goff and Wentz's ball security looks like relative to the NFL, here's a handy plot of pass attempts/fumble vs. hand size:

So blah blah no correlation blah, but you'll also see that Goff and Wentz fumbled at nearly identical rates, and both were middle of the road relative to NFL quarterbacks. I used all pass attempts as a way to account for fumbles that were not the result of getting hit, but why don't we narrow that down just to really drive the point home. Here is a plot of sacks/fumble vs hand size:

It turns out neither Goff nor Wentz did a great job holding onto the ball when hit, but they were still nearly identical (Goff actually had a slight edge). Also, while this might just be statistical noise, Goff cut his rate in half during his last season, so there's some reason to believe he might have improved his ball security to be more in line with the NFL average. Maybe Wentz can do that too with some more experience under his belt. You might be inclined to think that some of Wentz's fumbles are a result of him running more often, but there really isn't a ton of separation between him and Goff in that regard: 216 carries to 170.

#### Why Sample Size Matters

Hopefully I've done a good job convincing you that there's no evidence of a correlation between hand size and NFL performance. "But," you might be thinking, "you haven't addressed the sample bias!" That's true. Based on everything I've shown so far, it would still be possible to argue that the reason so few quarterbacks with small hands get a chance in the NFL is that their hands are holding them back from even being good enough to step on the field. I've made arguments using similar logic before myself, for instance when it comes to the odds of a career backup turning into a long-term starter. But I don't think that's what's happening here, I think we're essentially looking at small sample size noise, and I think I can prove it. But first you'll have to stick out a very brief explanation of significance tests and frequentist statistics. It sounds more complicated than it is.

In statistics, there's this concept called the "null hypothesis." This is the baseline hypothesis you would go with lacking any other information. In the Frequentist school of statistics, it's common to set the null hypothesis to some variation of "this result is based on random chance," and then prove that your data doesn't fit this null hypothesis, and thus *isn't random.* If you can't do that, then there's a decent chance that your result really is nothing but random chance. So that's what I'm going to do here.

I'm going to do this by performing a significance test. This is where you calculate the probability of obtaining your result under the assumption that the null hypothesis is true. If you get a low probability, you can reject the null hypothesis. To do this, I need a new sample. For this procedure I used a list from Other League that includes everyone who got their hands measured up through 2013, all 104 quarterbacks from Cam Newton to Jerrod Johnson. Ideally I would include those from 2014 and 2015, but for what I need to do this should work.

Out of those 104 quarterbacks, 17 have hands smaller than 9.125 inches across. We want to know if there is any relationship between the amount of playing time given to these players and their hand size. Our null hypothesis is going to be that playing time is essentially random with respect to hand size. So now we're going to do two slightly different significance tests to see if we can rule that out.

First let's do something simple. Out of our 17 quarterback selection, only two managed to accrue a full season's worth of starts. Using MATLAB, I draw a random sample (without replacement, for those wondering) of 17 quarterbacks from our full list of 104 and count up how many were able to make 16 starts. I repeat this 100,000 times, keeping track of the resulting number each time. This allows me to build up an expected distribution of the number of quarterbacks who get 16 starts out of a 17 person sample. If it turns out that we usually get significantly more than two, we can conclude that our sample of small-handed quarterbacks is not random.

While two is a little on the low end, it's not exactly unexpected. In fact if you do the math, there's about a 22% chance that if you pull a random sample of quarterbacks from our list that only two or fewer will have made 16 starts. If that seems like a small chance to you and you're feeling tempted to say it means our sample isn't random, consider that in most sciences 5% is considered too big to confidently rule out the null hypothesis. Furthermore, if a guy like, say, Jared Goff was to bounce this number up to three, all of the sudden there would be a 45% chance of getting that value through nothing but random chance. I don't know about you, but I personally think it's pretty safe to assume that Goff will get 16 starts.

While that's all well and good, we can still do a little more. Our last example used a simple cutoff of 16 starts just to get an idea of whether or not someone warranted an extended look, but that puts guys like Geno Smith and Joe Flacco on the same level. This time, we're going to randomly select 17 players again, but this time we're going to total up all the starts made by all of those players. This should accurately capture the difference between consistent starters and early flame-outs. Collectively, our sample of small-handed quarterbacks made 101 starts.

According to our simulations, there's again about a 22% chance that our small-handed sample is totally and utterly random. And just like last time, if some small-handed player comes along and makes about 10-20 starts that number will skyrocket. So there's no real reason to believe that the lack of playing time given to small-handed QBs is anything but random.

#### Wrap Up

At the beginning of this piece this is how I laid out the claims under scrutiny: (1) small-handed quarterbacks have been less successful, and (2) this relationship is not random, but causal. I hope that I have shown you here that not only is there no performance-based evidence of such a link, but any playing time based link is likely random. The reason no QB with small hands has ever had sustained success is that both of those groups are incredibly small, so the likelihood of crossover is even smaller. You might as well point out that no three-armed professional accordion player has ever won the lottery in Ohio. It might be true, but it doesn't mean anything, and the sooner we can all stop pretending it does, the better.

**UPDATE: **By request, here are the R-values for each plot.

AV/S vs. hand size: 0.104

Velocity vs. hand size: 0.036

YPA vs. hand size: 0.088

Cmp% vs. hand size: -0.195

INT% vs. hand size: 0.123

Attemps/fumble vs. hand size: -0.271

Sacks/fumble vs. hand size: -0.429