Trade down or keep No. 1 pick: Which is more valuable?

— -- Saturday's news that the Boston Celtics and Philadelphia 76ers have agreed in principle to swap top picks should shake up the NBA draft.

We know the Celtics' No. 1 pick is more valuable than the Sixers' No. 3 pick, but how much more valuable? What else does Boston need to make the trade work? How much is too much for Philadelphia to trade? Let's take a look.

Rebuilding a trade value chart for draft picks

When NFL teams swap draft picks -- which happens much more frequently than in the NBA, with seven rounds of picks available to trade rather than two -- they can rely on a handful of charts showing their relative value.

Most famously, as head coach of the Dallas Cowboys during the 1990s, Jimmy Johnson used the history of pick-for-pick trades to put together? a value chart that teams used for years. More recently, Chase Stuart of Football Perspective has constructed his own chart based on how much value teams actually derive from each pick.

Some NFL teams, including the Seattle Seahawks, have also replaced Johnson's chart with one that reflects how the relative value of picks has changed with the advent of a new rookie scale.

Because there are fewer pick-for-pick trades in the NBA, determining the value that teams put on each pick isn't realistic for the league. After all, while the Cleveland Cavaliers traded Andrew Wiggins after taking him No. 1 in 2014, the top pick hasn't been dealt between the May lottery and the end of the June draft since 1993 -- when the Orlando Magic sent the No. 1 pick (Chris Webber) to the Golden State Warriors for the No. 3 pick (Penny Hardaway) and three future first-rounders.

Two years ago, I used the typical value that players picked at each spot provide over their rookie contracts to construct an NBA equivalent of Stuart's NFL value chart. At the time, however, I acknowledged I was probably undervaluing picks at the top of the draft because I wasn't considering the value top prospects provide beyond their rookie contract.

To try to account for that shortcoming, I took a look at how players drafted between 2003 and 2007 performed in their fifth through ninth seasons in the league -- the amount of time a maximum rookie extension would cover. For players who signed extensions or re-signed using Bird rights, I compared their on-court value each season (as measured by wins above replacement, or WARP, my value metric) with what they were paid. (Note that I excluded the 2008 draft class because the 2017 spike in the salary cap meant their second contracts were unusually favorable for teams -- something that's not likely to recur in the near future.)

Here are the best values over that period:

Amazingly, James provided the most surplus value despite playing just three years on his second contract with the Cleveland Cavaliers before opting out and signing with the Miami Heat. (It helps that James was the league MVP two of those three years.)

Here's what it looks like when we plot all these values by where players were drafted:

We can derive the expected value each pick will provide from his fifth through ninth season in the league from the logarithmic trend line on the chart, which shows the No. 1 pick providing an average of $8.8 million over that span (each WARP has a dollar value). That's a substantial addition to the $37.4 million surplus value I estimate a typical No. 1 pick would provide with this season's rookie scale.

By adding those figures, we can put together a new trade value chart:

As expected, factoring in post-rookie contracts shows the top picks are more valuable relative to later selections than the old trade value chart suggested. Here's how the values compare:

Relative value of No. 1 and No. 3 picks

With the new trade value chart in hand, let's consider a possible Celtics-Sixers swap. The top pick of the draft now appears substantially more valuable than the No. 3 pick -- the latter is worth almost exactly one-third less under the new chart as compared to about 27.8 percent less based on the old version.

Still, making up the gap between the two picks wouldn't require Boston to get another top-five pick. The chart shows the difference between No. 1 and No. 3 as 1,330 points, about equivalent to the No. 14 pick, the final pick of the lottery (1,320 points).

Since Philadelphia doesn't have any first-round picks besides No. 3 this year, the Celtics are reportedly also acquiring a future first-rounder from the robust collection amassed by former 76ers GM and president of basketball operations Sam Hinkie. In addition to their own picks, the Sixers have extra first-rounders coming from the Los Angeles Lakers next season and the Sacramento Kings in 2019, both of which are likely to be substantially better than Philadelphia's picks as the team moves into contention -- and the trade reportedly guarantees that Boston will get the rights to one of those picks.

Certainly, a pick now is worth more than one later in the same draft position, but since the Celtics' roster likely must already make room for 2016 first-rounders Guerschon Yabusele and Ante Zizic, Boston is well-positioned to wait a year or two for a more valuable, higher draft pick. Though the Lakers and Kings won't have any incentive to lose to improve their lottery odds, the most likely outcome for both of those picks is much better than the 14th pick, with a reasonable chance they'll end up in the lottery's top three.

If the pick that Philadelphia sends is the 2018 Lakers pick, it will be in the top five -- it conveys if it is anywhere from No. 2 to No. 5. It's not the Lakers pick, the Sixers will send along the Kings' 2019 pick (unprotected), likely a lottery pick. So on paper, the No. 3 pick and the Lakers' (or the Kings') pick would very likely exceed the No. 1 pick in value.?

While it's not the kind of haul the Magic got for moving down two spots back in 1993 -- the three first-round picks Orlando got eventually included Vince Carter and Mike Miller, though the Magic had long since dealt the pick used on Carter -- the Celtics would do well, in value terms, to add another likely lottery pick to their own cache.