Stat Nerd Post: The Adorably Curious Nature of Pick Swaps and a Case for "Vertical Stacking"

[scott]

I had a little bit of downtime, and as often happens when I have such downtime, I decided to use it on satisfying some statistical curiosities, specifically the value of multiple pick swaps in the same draft.

Right off the bat, some acknowledgements and a call for others to expand on this work.

• Shout out to Ariel, who does some fantastic statistics and quant work on this message board for nothing more than the gra ude of other Spurs fans. Often times, Ariel's high quality quant work makes me lazy, and just rely on them (sorry Ariel, I don't actually know whether you are a he or a her, or anything else) to actually calculate things. However, Ariel does inspire me to actually dig in from time to time and do my own work, which is a good thing. Thank you for being a great contributor to my free time when I'm thinking about the Spurs.
• Also a shout out to Seventyniner, who provided a fantastic link which validates one of the key assumptions behind this analysis, which I'll go into a little later.
• Lastly, thanks to a few of my favorite posters who contribute really high quality, quan ative based opinions that I really cherish. I wanted to specifically shout out SpursBills, Chinook and LeBowen. There are many more people who's opinions I really enjoy and value on this board, but they seem to put a lot of thought, logic and supporting data behind their takes which pushes me to not be so lazy with my own.

With that said, let's get into it.

The basic question presented here is, what is the value of adding multiple swaps in a given year? Swaps on their own, I really don't place a lot of equity in - they tend to be worth about as much as an early second round pick in terms of trade value (Credit, Zach Kram: https://www.theringer.com/nba/2022/1...Dround%20value!). However, where Swaps really add value, is when viewed holistically with your own pick (which is gets attached to) and the potential outcomes for that single pick, now enhanced with the potential results of a different team's season.

I wanted to take a look at the degree to which a team's pick is enhanced by adding multiple swaps in a given year, which I will refer to as "vertical swaps". With the Spurs having DAL and MIN swaps (ignoring the Top-1 protection for now), I was curious at just what that meant for the potential outcomes for that pick. So this led me to a more specific question: What are the odds that a pick will land in X range for an n number of swaps obtained.

To do this, there are some variables which are either very difficult to model or I just haven't wrapped my brain around how to do it yet. For example:

• Protections on swaps add some difficulty. I know this can be solved, but I just haven't taken the time to do the work in building out the algorithm for it, and frankly I doubt I will.
• The probability that a team will be good at any given point in the future, and the fact that some franchises are historically better than others. I deal with this another way, which I'll explain below.
• The draft lottery. This adds a wrinkle that I don't really want to deal with right now, so I'm just ignoring it completely and (admittedly incorrectly) assuming that swaps occur before the lottery. This is not correct, and this is acknowledged from the get go, but it saves me the trouble of laying on an extra set of probabilities that I haven't thought about how to work with yet. I'm hoping maybe someone else wants to pick up the torch on this front.

On order to deal with the second bullet point, I'm going to look at far-out swaps. I had an existing hypothesis that after 5 years, the outcomes in the NBA were all subject to natural variance, and that seems to be supported by an article that Seventyniner directed me to (here: https://www.theringer.com/nba/2019/6...- le-windows). Long story short, that 5 years into the future, only about a third of good teams are still good; a quarter of bad teams are still bad; and half of decent teams are still decent. To me, this is good enough to support the hypothesis that you can't really predict which teams will be good or bad in 5+ years.

So with that, I'm going to assume that at 5+ years out, all swaps have an equal probability of landing anywhere between pre-lottery seeding of 1 (worst team in the league) to 30 (NBA champs).

One last key note when thinking about swaps: whether or not the swap conveys, at some point becomes irrelevant. What matters is whether or not the ultimate outcome falls within a certain range, and that outcome may actually come from your own pick, not a swap. This is because I approach the valuation of draft picks from a trade value perspective, and how much more valuable do swaps make your pick. The acquiring team cares not whether or not the swap conveys, they merely care about the ultimate outcome (and so should you, if you don't trade the pick). So with that said, we are looking to see what the probability is that our pick falls within a certain range.

I used the concept of complementary probability. Instead of finding the probability that at least one of my picks end up in a range, I found the probability that none of my picks were in that range and then subtracted that from 1. The result is the following table:



The way to read this table is as follows: the vertical axis is the number of swaps you own plus 1 (your own pick), and the horizontal axis is the desired range you want your pick to land on. Let's start with some very basic examples to help understand what is happening here. If your final ranking is random (which we are assuming) and you only have your own pick with no swaps, then there is a 50% chance your pick will land in the top half (top 15). That is the upper left hand corner of the table. Should be simple. Alternatively, if you owned swaps with EVERY team in the league, you would have a 100% chance of landing the #1 spot, because there are literally no other potential outcomes.

What this table shows, however, is that you need not achieve true certainty to have virtual certainty. For example, if you're desired range is a lottery pick (Top-14 position), you only need to own 4 swaps to have a greater than 93% chance of getting a lottery pick. By the time you have 7 swaps, you have greater than a 99% chance. Where you see a 1.000 in the table that is NOT black, that is a greater than 99.9% chance (but not true 100%). Black cells mean a true 100% certainty.

As you can see, in 2030, when the Spurs have two swaps (ignoring the protections), they have a 86.2% chance of our pick ending up a lottery pick. That makes that pick extremely valuable, because otherwise a pick with no swaps would only have a 46.7% chance of being a lottery pick.

There are some other insights I'll probably add on to this over time, and I hope folks will find this interesting and comment on.

Thanks for taking the team to read this.

[Chinook]

Awesome, thread scott. Great work that will only become more interesting as we get closer to 2030. One interesting factor to me is that swaps are both voluntary and non-simultaneous. Like the Spurs aren't getting (ignoring protections), the best of SAS30, DAL30 and MIN30. They're getting the option to pick between of i)MIN30 and ii) whichever they prefer of SAS30 and DAL30. The Spurs could decide to decline a swap for something like cap reasons. Or they could agree to extinguish one of the swaps in exchange for some trade relief. As far as I know, extinguishing a swap counts as a "touch", just as altering protections does.

What I'm less sure about is what rights the other teams have in this. Let's say the Wolves in 2030 finish with the second-overall pick (so the protections don't come into play), the Spurs finish with the ninth pick and the Mavericks finish with the 30th pick. (As a quick side note, the NBA is not like the NFL. The champs don't get the last picks. It's just been the case that the last year the first-overall seed won the le). Anyway, in this scenario, could the Spurs choose to swap their pick with Dallas, getting the 30th pick, and then swap that with Minny for their second pick, basically giving Dallas a lotto pick (theoretically in exchange for compensation) while Minny gets left holding the bag. If that isn't possible (and I'd hope it wouldn't be), would it be because the NBA actually prevents if or because Minny specifically traded the rights to swap its pick with the BEST of SAS30 and DAL30? Could the Spurs extinguish their swap with Dallas while maintaining their swap with Minny? It's clear enough that the reverse should be fine, as Minny comes later in the decision tree.

This might seem trivial, and indeed to the idea of this thread, it doesn't really matter. But theoretically, the actual value a team with 29 pick swaps could command might vary tremendously depending on the order of the swaps in the decision tree relative to the picks available at each stage. Like if the Spurs added every other team to their 2030 swap collection, but Dallas finished with the first-overall pick, then then entire swap chain is broken before it starts. But if the first-overall pick lies even one more step into the chain, chaos may ensue. It'll be interesting if we ever get to see those swaps in full action.

[exstatic]

Awesome, thread scott. Great work that will only become more interesting as we get closer to 2030. One interesting factor to me is that swaps are both voluntary and non-simultaneous. Like the Spurs aren't getting (ignoring protections), the best of SAS30, DAL30 and MIN30. They're getting the option to pick between of i)MIN30 and ii) whichever they prefer of SAS30 and DAL30. The Spurs could decide to decline a swap for something like cap reasons. Or they could agree to extinguish one of the swaps in exchange for some trade relief. As far as I know, extinguishing a swap counts as a "touch", just as altering protections does.

What I'm less sure about is what rights the other teams have in this. Let's say the Wolves in 2030 finish with the second-overall pick (so the protections don't come into play), the Spurs finish with the ninth pick and the Mavericks finish with the 30th pick. (As a quick side note, the NBA is not like the NFL. The champs don't get the last picks. It's just been the case that the last year the first-overall seed won the le). Anyway, in this scenario, could the Spurs choose to swap their pick with Dallas, getting the 30th pick, and then swap that with Minny for their second pick, basically giving Dallas a lotto pick (theoretically in exchange for compensation) while Minny gets left holding the bag. If that isn't possible (and I'd hope it wouldn't be), would it be because the NBA actually prevents if or because Minny specifically traded the rights to swap its pick with the BEST of SAS30 and DAL30? Could the Spurs extinguish their swap with Dallas while maintaining their swap with Minny? It's clear enough that the reverse should be fine, as Minny comes later in the decision tree.

This might seem trivial, and indeed to the idea of this thread, it doesn't really matter. But theoretically, the actual value a team with 29 pick swaps could command might vary tremendously depending on the order of the swaps in the decision tree relative to the picks available at each stage. Like if the Spurs added every other team to their 2030 swap collection, but Dallas finished with the first-overall pick, then then entire swap chain is broken before it starts. But if the first-overall pick lies even one more step into the chain, chaos may ensue. It'll be interesting if we ever get to see those swaps in full action.

We have the option to do one swap. In your scenario, we grab Minnesota’s #2 pick.

[scott]

Thanks Chinook! Thanks for the clarification on the 30th pick, I couldn't remember and it wasn't important enough for me to look it up at the moment.

I was very curious if the swaps could be executed the way you spelled out. If the Swaps need not be executed in particular order, in theory, if you held swaps from all 29 other teams - I was curious if it effectively gave you the right to set the draft order any way you pleased (or didn't, if you were compensated not to). For example. If Team A is terrible and get's the #1 overall pick - how much extra would they be willing to compensate you to put them at the #2 pick?

My guess is the league would not allow this, not because there is an actual fear of a team acquiring 29 swaps, but because of the incremental unintended value it adds to swaps, but surely it must be written somewhere. I'll look into the CBA on swaps a little later, but this is a very fascinating wrinkle!

[scott]

We have the option to do one swap. In your scenario, we grab Minnesota’s #2 pick.

In the non-basketball world, it would all depend on how the contract is written... but since I've never worked in an NBA front office I don't know how these things are actually negotiated/done. Take the hypothetical where we are discussing acquiring a 2030 swap from Miami. I'd presume we can write this any way the two teams agree upon. Miami can give us the right to swap any pick we have... or Miami can agree to swap us with the Spurs natural pick... or Miami can agree to swap their pick with the next best of SAS/DAL/MIN? Of course... all subject to whatever rules the league has set forth.

Surely the NBA must have a written rule, right? It makes perfect sense that we would only be allowed to do one swap... but does it explicitly state that anywhere?

[Seventyniner]

My (uninformed) guess is that the first swap you get in a given year is just vanilla, though it can have protections and any further swaps have to specify how they work in relation to any swaps that already exist. We would need to see the wording of the actual trade sent to the league office to really know, and I imagine it has to exist in detailed writing in order to be enforceable later.

[exstatic]

In the non-basketball world, it would all depend on how the contract is written... but since I've never worked in an NBA front office I don't know how these things are actually negotiated/done. Take the hypothetical where we are discussing acquiring a 2030 swap from Miami. I'd presume we can write this any way the two teams agree upon. Miami can give us the right to swap any pick we have... or Miami can agree to swap us with the Spurs natural pick... or Miami can agree to swap their pick with the next best of SAS/DAL/MIN? Of course... all subject to whatever rules the league has set forth.

Surely the NBA must have a written rule, right? It makes perfect sense that we would only be allowed to do one swap... but does it explicitly state that anywhere?

We agreed to a swap with Dallas last summer, but they never agreed to swap with Minnesota, which is kind of what you’re spitballing. My thinking is that we have two swaps, but can only execute one.

[scott]

We agreed to a swap with Dallas last summer, but they never agreed to swap with Minnesota, which is kind of what you’re spitballing. My thinking is that we have two swaps, but can only execute one.

I generally agree with this, but to play devil's advocate, using Chinook's example where MIN finishes with the 2nd draft seed, SAS 9th and DAL 30th, we could execute the swap with DAL, which DAL agreed to, and #30 becomes our pick. We could then SWAP with MIN, which MIN also agreed to in practical terms, because #30 is now ours (not DAL's).

Like I said, I agree with your impression, because that seems both logical and fair, but I can find an argument for the alternative. I'm gonna scan the CBA here in a few minutes, though I'm not sure it would be contained there since it doesn't directly involve players... I wonder if there is some other NBA rule book that deals with trades and procedure somewhere.

[scott]

Well that was a quick scan... the CBA doesn't contain the word "swap" anywhere in it, so that's a dead end

I'll see if I can find trade rules somewhere. The Salary Cap FAQ here has a little discussion, but not much: http://www.cbafaq.com/salarycap.htm

[scott]

Frankly, I'm not sure that there is another example before SA30 where a team has held multiple swaps in the same year. I can't find anything where anyone has even contemplated these scenarios before.

[rankingtear]

Frankly, I'm not sure that there is another example before SA30 where a team has held multiple swaps in the same year. I can't find anything where anyone has even contemplated these scenarios before.

OKC and UTA.

[Seventyniner]

Frankly, I'm not sure that there is another example before SA30 where a team has held multiple swaps in the same year. I can't find anything where anyone has even contemplated these scenarios before.

Stacking swaps might be the next iteration of PATFO trying to be a step ahead of the league.

[scott]

OKC and UTA.

Any specific years you are referring to? The Spurs are the only team who currently have multiple swaps in a future year. Lots of teams have swaps (and there have been 30-something swaps that have come and gone in the past, about a dozen of them finishing "in the money"), but I'm unaware of a team holding multiple in one year (and data is hard to come by)

[scott]

Stacking swaps might be the next iteration of PATFO trying to be a step ahead of the league.

Yeah, I was just thinking that - especially if there are not clear rules about how they are handled and the Spurs can gain the unintended consequence of holding another team hostage so you don't jack with their draft position. Fascinating case here. I sent Keith Smith from Spotrac a note to see if he is aware of a Trade Rulebook or if he knows how these scenarios are dealt with, I'm hoping he will respond.

[rankingtear]

Any specific years you are referring to? The Spurs are the only team who currently have multiple swaps in a future year. Lots of teams have swaps (and there have been 30-something swaps that have come and gone in the past, about a dozen of them finishing "in the money"), but I'm unaware of a team holding multiple in one year (and data is hard to come by)

OKC 25, HOU & LAC. UTA 26, MIN & CLE

[Chinook]

We agreed to a swap with Dallas last summer, but they never agreed to swap with Minnesota, which is kind of what you’re spitballing. My thinking is that we have two swaps, but can only execute one.

Dallas never agreed to swap with Minny. We know that. That's why they're step one in the decision tree. But Minny's swap came after Dallas. It's definitely made with that knowledge in mind, even though it might not be truly nested. We don't know if the Spurs could trade with Dallas to extinguish their 2030 swap without affecting the Wolves. They should be able to do so if the swaps aren't considered to be dependent on each other.

That could lead to a case where the Wolves have a high pick, but the Spurs choose to swap with Dallas' lower pick to deny the Mavs a certain player. Like if Minny had 2, Dallas had 3 and SA had 30, the Spurs could take away Dallas' third-overall pick to deny them a lotto talent and allow the Wolves to keep the second pick. That seems spiteful, but Minny might be willing to toss a pick to the Spurs to extinguish their swap and tell the Spurs they don't intend to take a player SA wants.

An analogous hypothetical would be if the Spurs had swap rights to BRK24 and WSH24. The Spurs might have been able to choose to take Sheppard away from the Rockets and let the Wizards draft Sarr or Risacher in exchange for that 2029 first Portland traded them in the Avdija deal. Because the Spurs wouldn't want Sarr anyway, there's no downside to them doing so. Of course, swaps have to be executed earlier in the process, but the idea is still on the table.

As scott pointed out, there isn't much in terms of official language I found that explains how the process works. There have been opposite swaps than this, both where a team has offered swaps to multiple teams and where a team has agreed to swap multiple unprotected picks in the same year like with OKC. As far as I know, this is a new situation.

[scott]

OKC 25, HOU & LAC. UTA 26, MIN & CLE

Gotcha, I see those now. The OKC25 is a little complicated because the protections are a little more strict. Are you aware of any cir stances like this that have already passed?

[exstatic]

The Utah swap is stated as an OR. They make one swap.

The OKC one is more complicated. One of the swaps is with Houston, who has set up a further swap with BKN. Basically Houston gets to swap whatever pick they wind up with, theirs or OKCs, to BKN for a PHOENIX pick. They’re still not moving swaps around like chess pieces, though. OKC does their swap decision making OR algorithm, then after that, Houston does theirs.

[rjv]

after reading this I came to the epiphany that ST, for all its faults, has to be one of, if not the best, basketball fan sites in all the NBA. I mean, on what other site will you see someone post a dissertation on how to quantify the value of draft picks? solid post, btw.

[scott]

Thanks for the props rjv - I agree, when folks are fighting over what really just amounts to a divergence of opinion, this site does have some really sharp basketball folks and it quite a blast!

On another note, Keith Smith responded to me and said that things like this would be governed by the NBA Operations Manual, which is not public. He said that typically, when the trade is made, it will be specified how it will play out (for example, SAS and MIN may conduct a swap after SAS and DAL already has one that may explicitly state that SAS has the right to swap with the best of MIN/DAL, or it may even state that the Spurs will have the right to swap with the best of MIN/DAL and if they do so, MIN will get the 2nd best of what remains, etc.). It seems like it would be an uncommon occurrence for it to not all be specified in advance so that a team like SAS could reshuffle the order however they want at the moment.

[exstatic]

Thanks for the props rjv - I agree, when folks are fighting over what really just amounts to a divergence of opinion, this site does have some really sharp basketball folks and it quite a blast!

On another note, Keith Smith responded to me and said that things like this would be governed by the NBA Operations Manual, which is not public. He said that typically, when the trade is made, it will be specified how it will play out (for example, SAS and MIN may conduct a swap after SAS and DAL already has one that may explicitly state that SAS has the right to swap with the best of MIN/DAL, or it may even state that the Spurs will have the right to swap with the best of MIN/DAL and if they do so, MIN will get the 2nd best of what remains, etc.). It seems like it would be an uncommon occurrence for it to not all be specified in advance so that a team like SAS could reshuffle the order however they want at the moment.

It’s frustrating that realgm hasn’t updated their future picks page.. It’s almost August, for chrissakes.

[poopbox]

I would hope the point of all these future swaps is to cash them in for real star player next to Victor. If we actually end up making these selections in 2030 and 2031 something has probably gone terribly wrong.

[exstatic]

I would hope the point of all these future swaps is to cash them in for real star player next to Victor. If we actually end up making these selections in 2030 and 2031 something has probably gone terribly wrong.

Not necessarily. At that point, we may need to cash out secondary stars for younger, cheaper talent due to the second apron.

[TheChillFactor]

this is really dope Scott, and a lot of work.

i have thought for a while that the Spurs must have some sort of analysis like this that shows that with enough picks/swaps from different teams- small bets placed all over the league - there is an X% probability that one of those lands in the lottery, or the #1 pick, or top 5 or whatever.

At one point in my life I had the skills for this kind of analysis but those have been lost over time as I don't use them and I am old and have forgotten so much. You took the time and applied your knowledge to this idea and I appreciate all the work you did.

It would be interesting to apply this kind of analysis retroactively to Duncan's career. Imagine he had a top 5 pick joining the team in 2004, or lottery pick in 2006, or the #1 pick after winning a le. They have seeded Wembanyama's future with picks - you can also imagine if LeBron or Shaq or any other top level player had that kind of future mapped out for him.

This is too complex for the "Fire Brian Wright" crowd to understand. Well done.

[scott]

this is really dope Scott, and a lot of work.

i have thought for a while that the Spurs must have some sort of analysis like this that shows that with enough picks/swaps from different teams- small bets placed all over the league - there is an X% probability that one of those lands in the lottery, or the #1 pick, or top 5 or whatever.

At one point in my life I had the skills for this kind of analysis but those have been lost over time as I don't use them and I am old and have forgotten so much. You took the time and applied your knowledge to this idea and I appreciate all the work you did.

It would be interesting to apply this kind of analysis retroactively to Duncan's career. Imagine he had a top 5 pick joining the team in 2004, or lottery pick in 2006, or the #1 pick after winning a le. They have seeded Wembanyama's future with picks - you can also imagine if LeBron or Shaq or any other top level player had that kind of future mapped out for him.

This is too complex for the "Fire Brian Wright" crowd to understand. Well done.

Thanks!

I will admit, that some of my stats skills are a little rusty as well - I've found AI (I use MetaAI, because it doesn't limit your usage like the free version of ChatGPT does) quite helpful. I essentially trained the AI with prompts to understand the cir stances, then asked some probing questions on calculating some probabilities, then asked it to show me how to do it in Excel. It had been probably a decade since I've used the COMBIN function in Excel, and once I was reminded of that (and how it basically provides you with the possible outcomes for a given scenario), building the rest of the probability chart was a breeze.

While I'm confident that AI will be the end of humanity, at least it can help me with some fun analysis in the meantime