Measurement Error: Exploring the Volatility of Pre-Draft Measurements

Note: After posting this I received an email from a trainer who offered up a very logical explanation for the standing reach volatility in particular. They noted that inconsistent application of the standing reach test means that players can effectively "tank" their standing reaches by slouching, extending their elbows slightly, etc., which lowers their standing reach. Why do that? Because vertical leaps are typically calculated based on the difference between max (jumping) reach and standing reach.

Thus, a player can to some extent manipulate their measurements--if they want a more impressive vertical then they can tank their standing reach, though obviously it's a tradeoff. Guards may find it particularly beneficial to inflate their verticals at the expense of standing reach, which is probably not scrutinized nearly as closely by teams. Similarly, players with reputations for being un-athletic could see value in inflating their verticals to combat those opinions--Kevin Love's 37" max vert looks rather fishy in that light.

DraftExpress' sortable historical measurements database is a fantastic resource for draft nuts and NBA fans alike, as their most recent update provides detailed data on vertical leap, agility drills and bench press in addition to official height (with and without shoes), weight, wingspan and standing reach data for most prospects drafted since 2000.

And while I obsess over this data as much as anyone, browsing for a few minutes reveals plenty of examples where the numbers don't seem to do a player justice. For instance, does anyone believe that Monta Ellis (31.5" vertical) and Andre Iguodala (34.5" vertical) are less explosive leapers than Coby Karl (35.5"), Jeff Green (38") and Chris Quinn (37")? And how much do you care that Chris Kaman's short arms (6' 11.75" wingspan) are dwarfed by those of Patrick O'Bryant (7' 5.75"), Darko Milicic (7' 5") and Eddy Curry (7' 6")?

But to me the most interesting players in the measurement database aren't the players who became all-stars or spectacular busts. Rather, the most insight into the data itself comes from the small subset of mostly pedestrian players who weren't good enough to stay in the draft the first time around--and as result attended the pre-draft camp twice.

Thanks to the NBA's rule allowing players who don't hire agents to withdraw from the draft and return to school after the pre-draft camp, 30 players have been poked, prodded and measured twice since 2001. And thanks to this quirk of the draft system, we can compare their year-to-year measurements for some insight into just how accurate these measurements are and how players change from one year to the next. Not all players had agility, strength, and vertical data for both years, so for now I focused on the four primary measurements: height without shoes, height with shoes, wingspan and standing reach. The results suggest a number of things:

• Players rarely had the same measurements twice in any category. This is likely the result of daily variation in height, actual growth between years, measurement error and wearing thicker- or thinner-soled shoes (which affects in-shoe height and standing reach).
  
• Standing reach data varied the most from year to year. Nearly half the players in the sample had standing reaches that differed by more than an inch from year to year, and a quarter varied by 2" or more.
  
• The variance in measurements for height, wingspan and standing reach were often fairly uncorrelated.
  

For each player I simply calculated the difference between year one and two in each of the four major categories, and then took both the simple average of the differentials (either positive or negative) as well as the average of the absolute value of the differentials (an error measurement of sorts). It's not an error measurement in the econometric sense of the word, but let's go with it for now.

The simple average (positive or negative) tells us if players were trending taller or shorter in their second camp, while the average error helps show how much overall variance there was. For a sample of some of the more interesting players, check out the table below and the general summaries that follow. First year measurement is listed first:

• Standing Reach. According to Chad Ford, standing reach has joined wingspan as the most important measurement to NBA personnel, but it was by far the most erratic of the four measurements considered in our sample. The simple average of differentials was only +0.07", suggesting that there was almost no bias one way or the other from year to year. Yet the average differential in absolute terms was a rather eye-opening 1.12", reflecting a rather significant degree of variance within the sample. In fact, eight of the 30 players had differentials that were +/- 2" or more (four taller, four shorter). Since we wouldn't expect players to shrink, it would seem rather obvious that standing reach measurements are surprisingly inexact.
  
  But perhaps the strangest part of the standing reach data is that for a number of players the changes from year to year are completely uncorrelated with the observed changes in height and wingspan--which obviously are the major components of standing reach. In 2004, Andre Emmett had the same height (6'4.5" in shoes) and wingspan (6'9") as in 2003, yet his standing reach was measured 2.5" shorter. In 2006, Torin Francis had the same height (6'10" in shoes) and wingspan (7'1") as in 2005, yet his standing reach was a whole 3" shorter. That same year, Steven Smith measured both a half inch taller and longer, yet his standing reach somehow was measured a full two inches shorter than in 2005. But perhaps the strangest case is that of Sonics' guard Damien Wilkins, who declared way back in 2001 before transferring from N.C. State to Georgia and playing two more collegiate seasons. When Wilkins was measured a second time in 2004, his height with (6'6") and without shoes (6'4.5") was the same and his wingspan fell by a quarter inch compared to his 2001 measurement (7'0.25"). Yet somehow his standing reach increased by four inches (8'6" to 8'10"). While a quarter inch here or there won't have much effect on a player's stock, adding or subtracting an inch or two (much less four) certainly will be noticed.
• Height. While height with shoes has become the standard way to measure NBA height, looking at natural height allows us some insight into whether the players grew from year to year--and whether it's accurately measured in the first place. For the 30 player sample, the simple average of the differentials was only +0.06", but the average error was 0.23", meaning that while most players didn't measure the same year-to-year, there wasn't a major bias towards measuring taller. So while it wouldn't seem uncommon for players to grow during their college-aged years (David Robinson going from 6'6" to 7'1" while at Navy being perhaps the most extreme example), that wasn't typical of the group in question. This could be in part because most of these players were in their junior years when they first came out, so they're less likely to grow than a freshman, for instance. Moreover, given that above-average height is usually a prerequisite for playing major college basketball, it stands to reason that the best players have already done most of their growing.
  
  Of the 20 players who had a different measurement from year to year, 13 were taller while 7 were shorter. Most players were only a quarter inch off, with the extremes being Joseph Jones (+0.75" in 2008) and Marcelus Kemp (-0.75" in 2008). So while it doesn't appear common for players to grow between camps, small measurement errors were common. Aside from human error, the differentials could also be attributed in part to the time of day when they were taken, as people tend to be slightly taller in the morning before their spine and joints have had a chance to compress.
  
• Height with shoes. It's perhaps not surprising that the players in our sample tended to wear slightly thicker soles the second time around, since wearing disco platforms to camp is the most obvious way to game the measurements. I would assume the NBA doesn't allow players to switch shoes between their measurements and the physical testing portions of the camp, but I've never heard any verification of that. Still, wearing thicker soles is especially understandable considering that players who attend multiple camps tend to be fringe prospects looking for any edge that they can get. The simple average differential was +0.18" with an average error of 0.33", as 16 of the 20 players who measured differently were taller the second time around. James Mays (1" shorter in 2008) and Mustafa Shakur (1.25" taller in 2007) were the major outliers.
• Wingspan. Though it shouldn't be possible to game wingspan measurements like height in shoes, wingspan was the category that had the clearest tendency towards increasing from the first year to the second. The pure average difference was +0.23" while the average error was 0.36", with 18 of the 23 players who measured differently getting longer in their second camp. Blake Schilb and Chris Massie (1" longer) were the biggest gainers, while Coby Karl (1" shorter in 2007) had the biggest dropoff.
  
  I'd speculate that wingspan is the most accurate of the measurements taken for a couple reasons. Practically-speaking, there's no reason to think that players are really any smaller the second time around, as the height and standing reach data might have you believe. And if you believe that, then the fact that only five players had shorter wingspans and four of them were only a quarter inch off seems to suggest that the wingspan numbers aren't as subject to the same inexplicable downward variance as the other numbers. This also makes sense given that the spinal compression which changes an individual's height over the course of the day doesn't change the length of one's arms.
  

So what does all this mean? Players are generally measured again during team workouts, so possible errors in the Orlando data should be caught before they harm a player's draft stock. Of course, that might not be the case for teams like the Bucks, who have struggled to schedule workouts for a number of prospects that they might draft on Thursday night. If our panel of data is any indication, the Bucks might want to think twice before relying too much on the Orlando data. Moreover, fans and media generally don't have access to individual team data, which can help further perpetuate the notion that a guy is an inch too short or athletically less-inclined when more qualitative evidence suggests otherwise.

At the very least, we should question whether measurements make sense in the big picture--either because a player "plays" bigger or smaller, or because the measurements themselves seem somewhat contradictory. For instance, this year Patrick Ewing Jr. measured 6'6" barefoot with a 7'0.25" wingspan (above average for his height), yet his standing reach is listed at a tiny 8'1.5", a full half-foot below average for his height. Unless Ewing's wingspan was all shoulders and no arms, he'd never post such a tiny standing reach, and indeed no player 6'2" or taller had a lower standing reach. Clearly the measurement was botched somewhere, whether by the people doing the measuring or when it was logged into the database.

Fortunately, pretty much everyone agrees that watching guys actually play and analyzing college stats are far more important bases for judging players than pre-draft measurements. And while the historical data on twice-measured campers suggests that the pre-draft data probably isn't as precise as it's usually assumed to be, it's hardly without value. The key is putting it in the context of a player's overall body of work. And if a player's physical dimensions are still cause for concern, just try measuring him again--preferably right after he wakes up.

Note: I'll try to post the excel file with the raw data when I get a chance. Unfortunately I discovered after I input the data that my version of Excel doesn't recognize heights (in feet and inches) for calculating purposes, so I ended up just manually inputting the differences rather than converting all the measurements into inches first. Let me know in the comments if you have alternate theories on any of this--I'm sure I've missed some.