I've been thinking a lot about draft age over the last few weeks. This year's freshman class has underwhelmed at the college level, giving the appearance of a weak draft class, as freshmen have been primary drivers of value since the dawning of the one-and-done age. Given the amount that the Sixers have invested into this particular draft class, with as many as four potential draft picks coming this year, seeing a devaluation due to a lack of high-ceiling young players would be a major disappointment for this stage of the Sixers' rebuild.

So I've looked for value elsewhere, attempting to talk myself into high-producing players who lack the physical tools usually seen as a prerequisite for the NBA. Recently, I've been reading some of Rubes' material over at Deep(ish) Thoughts, where he has advocated for a more open approach towards valuing older players. Detailing each draft year going back to 2003, he shows that the players who have reached the highest ceilings are varied, including both players as young as high school seniors and as old as college juniors and seniors, despite the public's presumption that the latter are lower-ceiling players.

This was a compelling argument to me, but is at odds not only with conventional wisdom, but also with a landmark baseball study from 2011 that I had recently come across. The study, written by ex-Grantlander Rany Jazayerli, showed not only that conventional wisdom is right, but that it's even more right than we tend to believe. That is, teams were accounting for age in their draft evaluations, but still drafting the youngest players far below their appropriate valuation had teams understood the extent of age's impact.

Jazayerli showed this aging curve, demonstrating the expected value of an average baseball player's career. He wrote of the curve:

The implication of the aging curve is that, the younger a player is, the more likely he is to improve over a short period of time. Take two players who are equally valuable today; if one of them is 25 and the other is 26, the difference between their long-term projections is minor. If one of them is 20 and one of them is 21, the differences can be massive, and much greater than you would intuitively expect. Nearly a quarter-century ago, Bill James addressed this very point in the 1987 edition of his Abstract: Suppose that you have a 20-year-old player and a 21-year-old player of the same ability as hitters; let’s say that each hits about .265 with ten home runs. How much difference is there in the expected career home run totals for the two players?" As best I can estimate, the 20-year-old player can be expected to hit about 61% more home runs in his career. That’s right—61%.

Jazayerli went on to conclude, "This is, all modesty aside, quite possibly the most impressive and significant finding of my career. When it comes to the drafting of high school hitters, even slight differences in age matter. At least when it comes to high school hitters, young draft picks are a MASSIVE market inefficiency."

Again, this seems intuitively right to me, and it follows that it should translate to basketball, too. After all, Father Time remains undefeated across all sports, not just baseball.

But if that is the case, then why are so many of the new stars in the NBA appearing after several years in college?Draymond Green, Steph Curry, Jimmy Butler, and Paul Millsap could all be considered Top 10 or Top 15 players in today's league. How can it be that 40% of the top players in the league were drafted as college juniors or seniors, but also that younger players have higher ceilings and more potential? I decided to do some digging.

Methodology

Basketball is a different sport than baseball, where games are impacted by isolated events, and each batter has limited opportunities affect a single game. In basketball, where each of the parts interact with each other throughout the game, superstars have an outsized effect. Thus, it is each player's peak efficiency that most determines his contributions towards a championship.

If Brandon Roy was a Top 10 player for 2 years but ineffective for the rest of his career due to his knee, having him for those 2 years brought his team closer to a championship than having Caron Butler, even though Butler provided more value over the course of his career than Roy did (50 win shares to 37). It's the peak that matters most.

So, I've ordered the players from each draft class according to their Peak BPM. I started in 2012 and went back to 2003, giving us 10 years of data and each class at least 4 years to demonstrate its value. Using information from basketball-reference, I then ordered the players from each class according to their Peak BPM and their age during their rookie year (which B-R defines as, "Age of Player at the start of February 1 of that season"). If a player did not immediately come to the NBA after being drafted, I adjusted their age as if they had, so that they were given credit for the evaluation they received among their draft peers.

To avoid fluky BPM totals in either direction, I ignored players who did not appear in approximately 80 games over at least 2 seasons of NBA play. As we'll discuss later, this affects some portion of the analysis, but I don't believe it alters the big picture.

As a secondary portion of the study, I looked at expected value from each of the draft classes. Looking at past years, I determined that a 3.0 BPM places players approximately 30th or above in the league in a given year, while 5.0 places players in or near the Top 10, and 7.0 or above places them in or near the Top 5. So I ordered players by the number of times they hit these benchmarks over their careers, with the added requirement that they must have played two seasons with a BPM at or above 3.0, in order to remove one season flukes (Hey, Cole Aldrich and Jared Dudley!).

I then determined the proportion of top players using their draft age.

I would add here that, while I am comfortable with data and enjoy statistics, I am by no means a statistician, nor am I terribly experienced with math. I was limited not only by ability, but also by time in this analysis, as I entered all of my information manually, and it took several days to accumulate it all. Given these two restrictions, it is entirely possible that there are mistakes, or that I've missed obvious opportunities for analysis. Please forgive any missteps you might notice, and by all means explain why I might have made each mistake.

Expected Value by Age

The initial finding from this exercise is remarkably dull: younger players tend to perform better than older ones. This proved more true as more data was introduced.

As you can see, the trendline is decidedly downwards as a player's age gets older, with about 1.5 more points per 100 possessions expected for 19 year olds than for 22 year olds. This would become even more pronounced if the myriad second rounders who were ineligible for my data threshold had played enough to merit inclusion. Large swaths of those players were aged 21-24, with almost none of them younger than that. As they were flushed out of the league relatively quickly, it is probable (although by no means assured) that they would have produced negative BPM peaks, adding to the strength of the negative trendline.

However, while there is a clear tendency towards younger players excelling more, the chart also shows many, many variations from the trend. In fact, the correlation coefficient for the data is only 0.24, indicating that there is a lot of inconsistency throughout this sample. (A coefficient of 1 indicates a perfect line, while a coefficient of 0 indicates perfect randomness).

Furthermore, the 1.5 points per 100 possessions gap is remarkable, but perhaps less noteworthy than a similar production gap in baseball would have been because of the more fluid nature of the game. In fact, even the highpoint of the trendline, just above 2 BPM would rank around 50th in a normal season. A team full of those players would struggle to compete against the top teams in the NBA (although it would perhaps look similar to this year's Celtics' team).

What the data suggests to me is that there may be something of a soft floor in the age of one-and-done college players. The season of college provides enough information to evaluators that, for the most part, massive misses such as Kwame Brown and Jonathan Bender are filtered out, while the players who achieved at a high enough level in college to still be drafted usually have enough skills to complement their physical tools, giving them a decently high floor compared to their older peers.

But this doesn't doesn't give us terribly much information about finding the stars. The poor correlation between the trendline and the data shows that there are plenty of older players who go on to become stars, even if the average outcome for 22- and 23-year-olds is closer to replacement level.

How To Define a Star

In an attempt to get a narrower slice of the data, I used a higher BPM threshold to compare different drafts. In looking back at past years, I noticed that a BPM around 3.0 usually delineated a Top 30 player in the NBA, someone who could be a second or third best player on a championship team, depending on who the best player was. Similarly, a BPM near 5.0 usually put a player in or near the Top 10, while a BPM near 7.0 indicated a Top 5 player or better. This varies from year to year, but it provides a basic template for determining who the best stars are-- namely, who hit these thresholds, and how consistently were they able to do so?

These thresholds turned into pretty good differentiators between players who were primary superstars, secondary stars, and "supporting stars", who did everything necessary to get a team to victory, but lacked primary creation ability.

For instance, LeBron James has had an incredible 12 seasons above the 7.0 BPM (insane, given that he has only played 13 seasons), which makes sense, since he's the most dominant player of his generation, and since he literally dragged a team featuring Zydrunas Ilgauskas and Donyell Marshall as its next best players to the NBA Finals. But it works beyond that, too. Chris Webber is an all-time great, but he needed a teammate similar to his own quality to be a championship contender. Fittingly, he has no seasons above 7.0 BPM, but is among the leaders of players who missed that level, achieving 5 seasons at or above 5.0 BPM, and 10 total above 3.0 BPM. Andre Iguodala, meanwhile, was always a second or third banana masquerading as a first option, and his BPM shows it-- he never reached the first two levels of stardom, but had 7 seasons at or above 3.0 BPM, among the most by players who never reached 5.0.

This exercise provided two interesting considerations:

1. How many players reach this star level in each draft?

2. How does a player's age impact whether he reaches this level or not?

How Many Stars Are In Each Draft?

The way that the draft is usually discussed, it seems like each year is teeming with stars, if only they could be groomed correctly. Here's how Chad Ford writes about Marquese Chriss, a power forward who can neither rebound nor defend, yet is projected as the 8th pick because of his high potential (emphasis mine):

He's a high-risk, high-reward player, but after Simmons and Ingram (and possibly Bender), I'm not sure there's a player in the draft with more long-term upside.

He has written similarly about Jaylen Brown, claiming that he has elite upside, and about many, many others over the years, many of whom failed to reach said "upside." Every year, players' upsides are described as if there are 15 All-Star candidates in a given draft. It has probably been one of the major driving forces behind the talk about this year's draft class as "weak": simply put, there are fewer high-achieving players with outstanding physical tools, and therefore there is less "upside" than most years.

But an actual look at past results reveals that very few years have more than a few prospects with true "star" potential. In fact, if we hold "All-Star" to mean, "about as valuable as a Top 30 player," we still see very few players in each draft that fulfill this requirement.

In 2012, there have only been three players so far: Anthony Davis has reached 7.0 BPM once, Draymond Green has reached 5.0 BPM twice, and Damian Lillard has reached 5.0 BPM once. Here are the equivalent tables for each of the three years preceding 2012:

As I sifted through more data, it became clear that these are not unusual numbers. In fact, they're almost exactly the norm. Through 20 years of drafts (1993 - 2012), there were 18 players who qualified for a "Top 5" season, 44 who qualified for a "Top 10" season, and 88 who qualified for at least two "Top 30" seasons. That means that on average, there are 0.9 MVP-quality stars per draft, 2.2 second-tier stars per draft, and 4.4 supporting stars per draft.

1999 and 2008 have been the two deepest drafts of the last 20 years, with 8 and 7 "supporting stars" in each draft, respectively. Still, the two were outliers. A far more common outcome is 3-4 stars per draft, an outcome which has occurred in 11 out of these 20 drafts.

When viewed through this lens, the 2016 draft actually looks about average. We can't be certain on this count, but both Ben Simmons and Brandon Ingram look likely to reach "supporting star" status at least, as both are outstanding prospects. Beyond them, only two other players would need to step up for this to be an average draft class. That seems eminently do-able between players like Denzel Valentine, Wade Baldwin, or Ivan Rabb. Surely someone will be put in a place that highlights his strengths more than his weaknesses, allowing him to perform at "supporting star" level for a few years.

How Does Age Impact Star-Status?

This is the question that has been driving us from the onset. How possible is it for older players to reach the highest echelons of NBA superstardom? If they are able to do so, why do we bother putting such a premium on age? After all, it's more important to identify the 22-year-old who will become a superstar than it is to grab the teenagers with high floors, right?

The quick answer is that if two players are equally skilled, the younger player almost certainly has an advantage at the next level. I needed to shrink my data field back to the original 10-year period for this portion (goodbye, Manu, you beautiful Argentine unicorn), but the results seem to be pretty clear.

2003-2012 18-19 years 20 years 21 years 22 years 23+ years Top 5 3 6 1 1 0 Top 10 2 1 1 6 1 Top 30 5 11 4 4 0

Over this time period, 46 players qualified for at least two years of "supporting star"-level play. Of those stars, only one, Marc Gasol, was in-line for a 23-year-old rookie season when he was drafted (Gasol's actually rookie season was not until 2008, despite having been drafted in 2007). In fact, of the players who reached star status, 61% were 20 years or younger in their rookie season. This trend becomes even more pronounced as you raise the bar-- a full 82% of players who put out seasons of 7.0 BPM or more were 20 years or younger as rookies.

In fact, in this ten year period, only two players older than 20 were able to reach this superstar threshold-- Dwyane Wade and Stephen Curry. In each case, there appears to be a mitigating circumstance that precluded them from proper evaluation. Wade had struggled with poor grades, missing his freshman season at Marquette after being under-recrutied from high school. He played as a 20-year-old freshman and 21-year-old sophomore before garnering enough attention to jump to the NBA. Curry, meanwhile, was also under-recruited and wound up playing at a mid-major, where he needed to light the world on fire for THREE years before the NBA realized he might actually be pretty good. Look how that turned out.

Another way of looking at this is the likelihood that players reach stardom given their age. One way to do that is to look at the number of players drafted in an age class, and compare it to the number of players who reached stardom from that age class. For instance, 3 rookies aged 18 or 19 went on to record years with a BPM of 7.0 or more. In these 10 drafts, there were 46 such players who were drafted.* 3 out of 46 is 6.5%, meaning that a generic teenager drafted into the NBA has a 7% chance at stardom.

*This is still only including players with at least 80 games played in at least 2 seasons in the NBA. I didn't think of calculating this statistic until after I had sunk hours into this project, and I couldn't stomach going through 600 players, one by one, just to record their ages when drafted. It probably affects the numbers slightly, but it you'll see that it doesn't affect the overarching point.

Here's how this looks for each of the different age groups:

2003-2012 18-19 years 20 years 21 years 22 years 23+ years %T5 v. Age Group 7% 8% 1% 1% 0% %T10 v. Age Group 11% 9% 2% 6% 1% %T30 v. Age Group 22% 23% 7% 10% 1%

Keep in mind that the number of players drafted in the 22- and 23-year-old age brackets is probably higher than the number I used to calculate these totals. So the percentage for each of those brackets is even lower than what is demonstrated here.

There are two important takeaways from this table. The first is the relative frequency with which players 20 years and younger become stars. Each of those age groups present better probability than 1-in-5 to find at least "supporting star" player, which is pretty outstanding.

On the opposite end of the spectrum is the other takeaway: it is nearly impossible for players 23 or older to develop into stars. Marc Gasol was the only instance of success out of 73 players that I had logged, and there are many players who failed to make the league that would drag that percentage further down had I included them.

The relative success of young players and complete lack of success of older players to develop into stars demonstrates that age is very important. However, there doesn't seem to much of a difference between 21-year-olds and 22-year-olds in likelihood of success, and there is a pretty steep drop to 23-year-olds. Therefore, allow me to suggest a few conclusions to be drawn from this dataset.

1. Young players have relatively high floors. As discussed earlier, it appears that players aged 20 and younger are less likely to bust out of the league completely. There are certainly examples of those types of players who failed miserably, (I'm looking at you, Marquis Teague), but for the most part, if a player demonstrates high skill-levels as a freshman in college, it is likely he will be somewhat useful in the NBA at the very least.

2. Players aged 23 and up have low ceilings. This is the only conclusion to be drawn from the paucity of players in this age group to excel in the NBA. If you're drafting a player who turns 23 early in his rookie year, chances are just very low that he'll be a key cog on a contender. Marc Gasol is an extreme outlier in this case.

3. Players aged 22 may have high ceilings, but are unlikely to become MVP-level stars except in outlier cases. There have been enough of these players who have developed into secondary stars, that asserting they uniformly have low ceilings seems fallacious to me. However, the only player within this age group to achieve top-level stardom since 2003 is Dwyane Wade, who both had mitigating circumstances preventing him from displaying his potential early and was drafted in the single year closest to the prep-to-pro's inception. The prep-to-pro generation shifted the cultural paradigm in a manner that necessitates a differentiation between those two periods in serious analysis. Because of those two dynamics, I think it is fair to extrapolate a sort of soft ceiling on 22-year-old prospects (7.0 BPM), except in the most extreme of outlier cases.

4. NBA teams are relatively successful at identifying Top 5 players. It's the secondary and tertiary stars where draft acumen truly separates itself. In the ten years included in this study, 11 players reached a BPM of 7.0 or greater; 9 of them were selected in the Top 7 of the draft. The other 2 were Kawhi Leonard and Kyle Lowry. Leonard's fall was a mild surprise at the time; DraftExpress had him rated as the 10th best prospect in the draft. Consensus may have been a little low on him, but it wasn't off by much.

Lowry's case may be one of the most unique out there. He only has one season qualifying for top-tier stardom, and it has been this year, at the age of 29. As of this posting, he sat at exactly 7.0 BPM, so he is more likely a late-blooming, second-tier star enjoying a career year.

Beyond Lowry and Leonard, NBA evaluators have gotten every superstar mostly right. It's the secondary stars where they have struggled: Draymond Green was selected 35th; Jimmy Butler was selected 30th; Danny Green was 46th, and George Hill was 26th. Paul Millsap, Gilbert Arenas, and Marc Gasol were all underdrafted vis-a-vis their eventual value. Giannis Antetokounmpo, Rudy Gobert, and Nikola Jokic will all likely join this group of undervalued steals within the next few years, too.

These are the types of stars on which hitting when everyone else was wrong can fundamentally alter the direction of your basketball team. These are the players for which talent evaluation can differentiate between the best management teams and the worst.

Overall, I think it's clear that the age of prospects certainly plays a role in their development in the NBA. The first portion of this analysis suggests that it matters, but not to the extent that we should write off all 3rd or 4th year college prospects who have demonstrated true skill. The second portion showed that, while players of all ages have reached star status, younger players are more likely to do so, and older players are unlikely to become game-altering, primary superstars.

But what, I think, is shown overall, is something that we already knew: Age matters, but it's only an element in the evaluation process. Skills matter first and foremost; if two players are equal in skill, the tie goes to the younger player.