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

[TheChillFactor]

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

someday when i have time i wanna go back and do a crude analysis of who we would have had available to us to draft if we had the same picks/pick swaps for the same teams in Duncan's career.

That would make a fun article for one of these hack sites to put together.

[TeKu]

Late to this thread sorry, but did want to say thanks to scott for compiling this, great stuff.

If the FO is half as smart as you here then this would explain why the SAC swap was in 31 rather than 30 also, which I questioned at the time.

By your numbers, and additional 2030 swap (to add to MIN/DAL) adds 7.2% odds of a lottery pick (+10.5% of a top 5 pick though), while adding that swap in 2031 instead adds 25.7% odds of a lottery pick (+14.3% of top 5 pick), albeit to lower odds overall. Which might indicate what the FO is actually valuing over that timespan also (regular lottery picks over a single high pick).

Handy numbers to check back on again given Wrights love of swaps. Thanks.

[scott]

Thanks TeKu!

One note - a Jazz redditor vehemently argued with me over the tradability of acquired swaps (when coupled with team's original draft picks). I am confident that you can indeed trade swaps this way (for example, you send Team X the better of SA/ATL26, with ATL maintaining the worst of the two picks) - however I cannot find any definitive written confirmation that this is the case. The redditor argued that if SA traded it's 26 pick (for example), the swap with ATL would simply be extinguished, which makes no sense. That person's major argument that couldn't point to an example of a trade like what propose happening in the past, so it "must not" be allowed. He also argued that (for example) ATL didn't agree to swap its pick with Team X, only with the Spurs. That should be irrelevant, because ATL's results from the swap don't change, regardless of who owns the Spurs pick.

It doesn't make sense that an asset (an acquired swap) would simply vanish into thin air if you traded away another asset (your pick). Does anyone have examples of a team trading away its pick with swaps attached? If you can't do that, then swaps are significantly less valuable (because they only maintain value if you hold them), but I don't believe this to be the case.

[Mal]

I am late to this. So the conclusion is that having two swaps in same years, boost chances for lotto pick significantly ?

[scott]

I am late to this. So the conclusion is that having two swaps in same years, boost chances for lotto pick significantly ?

Basically yes, if you believe in one pretty important assumption: that team outcomes far out in the future are basically random, which tends to more or less be backed up by the data.

However, if you believe in more dynastic team results based on superstars, then having the best of a pick between teams that have Wemby, Luka and Ant may not be all that impressive.

[TeKu]

It doesn't make sense that an asset (an acquired swap) would simply vanish into thin air if you traded away another asset (your pick). Does anyone have examples of a team trading away its pick with swaps attached? If you can't do that, then swaps are significantly less valuable (because they only maintain value if you hold them), but I don't believe this to be the case.

Would think the 2028 PHO swap they traded to WAS in the Bradley beal trade is an example here? My understanding is that BKN have the first right to swap either their pick or PHI pick (which may convey that year) with PHO first, and then WAS gets the rights to swap their pick with whichever pick PHO holds at that point. I'm not 100% on that at all, but would definitely suggest that pick swaps can be included/accounted for in a trade.

[spurraider21]

Thanks TeKu!

One note - a Jazz redditor vehemently argued with me over the tradability of acquired swaps (when coupled with team's original draft picks). I am confident that you can indeed trade swaps this way (for example, you send Team X the better of SA/ATL26, with ATL maintaining the worst of the two picks) - however I cannot find any definitive written confirmation that this is the case. The redditor argued that if SA traded it's 26 pick (for example), the swap with ATL would simply be extinguished, which makes no sense. That person's major argument that couldn't point to an example of a trade like what propose happening in the past, so it "must not" be allowed. He also argued that (for example) ATL didn't agree to swap its pick with Team X, only with the Spurs. That should be irrelevant, because ATL's results from the swap don't change, regardless of who owns the Spurs pick.

It doesn't make sense that an asset (an acquired swap) would simply vanish into thin air if you traded away another asset (your pick). Does anyone have examples of a team trading away its pick with swaps attached? If you can't do that, then swaps are significantly less valuable (because they only maintain value if you hold them), but I don't believe this to be the case.

yeah, thats nonsense

we see ALL the time, when a team trades for "the most favorable" or "least favorable" of some set of picks. that is only possible if a swapped pick is being traded.

[exstatic]

Would think the 2028 PHO swap they traded to WAS in the Bradley beal trade is an example here? My understanding is that BKN have the first right to swap either their pick or PHI pick (which may convey that year) with PHO first, and then WAS gets the rights to swap their pick with whichever pick PHO holds at that point. I'm not 100% on that at all, but would definitely suggest that pick swaps can be included/accounted for in a trade.

That wasn’t all the result of one trade. Phoenix traded fractional swaps of the same pick with different protections.

[Pauleta14]

Way to take advantage of "a little bit of downtime" scott !!

[scott]

Way to take advantage of "a little bit of downtime" scott !!

Haha. I've been very fortunate in life, which allows me to do things like waste time thinking about the Spurs, collect basketball cards (I've got quite the valuable Wemby collection amassing) and do stupid stats experiments

[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?

RealGM has updated the future owed picks page. This is what they have to say.

2030 first round draft pick from Dallas or Minnesota (San Antonio outgoing to Dallas or Minnesota)
San Antonio will receive the most favorable of its 2030 1st round pick, Dallas' 2030 1st round pick and Minnesota's 2030 1st round pick protected for selection 1; Dallas will receive the less favorable of its pick and the San Antonio pick; Minnesota will receive the less favorable of (i) its pick and (ii) the more favorable of the San Antonio pick and the Dallas pick; if the Minnesota pick falls on its protected selection, then Minnesota's obligation to San Antonio will be extinguished and San Antonio will instead have the right to swap its pick for the Dallas pick (via San Antonio's right to swap for Dallas; via San Antonio's right to swap San Antonio or Dallas for Minnesota) [Boston-Dallas-San Antonio, 7/12/2023; Minnesota-San Antonio, 6/26/2024]

[Brazil]

I was vacationing when you posted this thread scott, I just saw it today.. that's some awseome work, quite interesting to understand some teams recent obsession with pick swaps

[Russ]

Stacking draft pick swaps might create a psychological high, but it doesn’t seem to change your chances of getting a good pick -- it all washes out in the end (at best).

Using your example:

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.

However, on the other hand, if you used those two draft swaps in different years you would have two 72.4% chances of getting a lottery pick or a ulative 144.8% chance over two years.

If you stack the picks you correctly point out that you have an 86.2% chance of getting a lottery pick in the stacked year but you also have only a 46.7% chance of getting a lottery pick in the other year for a lesser total two-year chance of 132.9%.

That’s not stacking assets, it seems more like diminishing returns.

Say you get really radical and you can take four swaps in one draft or one swap in each of four drafts.

According to the chart you have a 96.9% chance of getting a lottery pick in the four-stacked draft and a 46.7% in the other three. That’s a total of 237% divided by four or 59.25% per year.

On the other hand, you could simply get four years at a higher 72.4% per year if you just take one swap per year.

So the more stacking you do, the worse it gets if you just want a lottery pick (according to the chart).

Actually, the more favorable argument for stacking swaps is the chance of getting the number one pick. But even then, it’s just a statistical wash.

If you can stack two swaps in one year or one swap in each of two years, according to the chart, you get a 10% chance at the No. 1 pick in the two-stacked year and a 3% chance in the other for a 13% total.

Or two years (with one pick swap) at 6% for a 12% total.

(That’s statistically identical because the difference is due to a slight rounding error on the chart, the 3% chance of getting the 1 pick with no swaps should be 3.33% (correctly rounded to 3%), the chance with one swap should be 6.66% (slightly incorrectly rounded to 6%) and with two swaps it should 9.99% (correctly rounded to 10%).)

In the end, the sad statistics indicate a wash. No free lunches as it turns out.

Stacking draft pick swaps might create a psychological high, but it doesn’t change the math.

In fact, stacking pick swaps may be like having money for two lottery tickets and deciding to buy two today rather than one today and one tomorrow.

In the end, as we all know, it probably won’t matter.

And ultimately in the end, thanks, scott, for your thought-provoking contribution during this long off-season.

[stnick2261]

However, on the other hand, if you used those two draft swaps in different years you would have two 72.4% chances of getting a lottery pick or a ulative 144.8% chance over two years.

If you stack the picks you correctly point out that you have an 86.2% chance of getting a lottery pick in the stacked year but you also have only a 46.7% chance of getting a lottery pick in the other year for a lesser total two-year chance of 132.9%.

That’s not stacking assets, it seems more like diminishing returns.

Stacking swaps is definitely diminishing returns... however, it's also diminishing costs. Teams are more willing to trade a swap (cheaply) to a team that already has a swap because it's a lower chance of conveying.

[Russ]

Stacking swaps is definitely diminishing returns... however, it's also diminishing costs. Teams are more willing to trade a swap (cheaply) to a team that already has a swap because it's a lower chance of conveying.

Good point.

[scott]

Say you get really radical and you can take four swaps in one draft or one swap in each of four drafts.

According to the chart you have a 96.9% chance of getting a lottery pick in the four-stacked draft and a 46.7% in the other three. That’s a total of 237% divided by four or 59.25% per year.

On the other hand, you could simply get four years at a higher 72.4% per year if you just take one swap per year.

So the more stacking you do, the worse it gets if you just want a lottery pick (according to the chart).

Actually, the more favorable argument for stacking swaps is the chance of getting the number one pick. But even then, it’s just a statistical wash.

If you can stack two swaps in one year or one swap in each of two years, according to the chart, you get a 10% chance at the No. 1 pick in the two-stacked year and a 3% chance in the other for a 13% total.

Or two years (with one pick swap) at 6% for a 12% total.

(That’s statistically identical because the difference is due to a slight rounding error on the chart, the 3% chance of getting the 1 pick with no swaps should be 3.33% (correctly rounded to 3%), the chance with one swap should be 6.66% (slightly incorrectly rounded to 6%) and with two swaps it should 9.99% (correctly rounded to 10%).)

In the end, the sad statistics indicate a wash. No free lunches as it turns out.

Stacking draft pick swaps might create a psychological high, but it doesn’t change the math.

In fact, stacking pick swaps may be like having money for two lottery tickets and deciding to buy two today rather than one today and one tomorrow.

In the end, as we all know, it probably won’t matter.

And ultimately in the end, thanks, scott, for your thought-provoking contribution during this long off-season.

There are absolutely diminishing marginal returns, and of course the chart kind of points that out, but that is a great call out.

I did want to address a little bit of math that you call out here (since you can't just sum up and divide probabilities to be statistically correct, but your points all remain valid)...

If you assume natural variance and a 46.7% chance of a lottery pick in any given far future year (which is certainly debatable), then every team naturally has a 91.9% chance of at least one lottery pick over a 4 year stretch. If you had one swap each year over a 4 year stretch (meaning a 72.4% chance at a lotto pick each year over 4 years), then you would have a 99.4% chance of at least one lotto pick over 4 years (!!!).

So if your goal is to get a lotto pick over a period of time, then horizontal stacking of swaps makes more sense, but if your goal is to get a lotto pick in a certain year (maybe you want 2031 because some contracts will be expiring and that is the year you want it, or you've scouted some 11 year old, or whatever), then vertical stacking is the way to go.

Great points, Russ.

[Russ]

So if your goal is to get a lotto pick over a period of time, then horizontal stacking of swaps makes more sense, but if your goal is to get a lotto pick in a certain year (maybe you want 2031 because some contracts will be expiring and that is the year you want it, or you've scouted some 11 year old, or whatever), then vertical stacking is the way to go.

Yeah, stacking can make sense in a particular situation that would have to be gamed out with factors unique to that draft, e.g., your likely lotto position, that of your partner and the tier distribution within that draft class.

Your chart was based upon an abstract neutral distribution of draft chances, which was really the only principled way to do it for discussion.

[Dex]

Great post, scott!

Next season will be very telling for the Spurs and their direction, but for a team not expected to contend this season, we seem to be in good shape.

✔ Young superstar and potential generational player (Wemby)
✔ Several young developing players with promise on decent contracts (Vassell, KJ, Sochan, Branham, Jones, Wesley, Castle)
✔ Veteran players with expiring contracts (CP3 and Barnes)
✔ Players that are easy to dump or include in a trade if needed (Collins, Champ, Bassey, Mamu)
✔ Tons of draft assets spanning the next 6 years

This year should establish our timeline. I still think we are 2 years from being a true playoff team, but we'll see what happens.

[ZeusWillJudge]

That's really good work. Sincerely. I haven't done a dive to confirm the numbers, but it feels like I'm seeing more swaps being used in the last few years. Maybe that's because teams started getting raw over protected swaps that wind up conveying as second rounders. That's a terrible ROI for teams that actually trade away an asset, and they are so subject to manipulation. With a swap, tanking would harm your own team as much as the other one. But I still don't like them, and don't think they offer very much in the way of value. After seeing Russ's post above, I'm not going to bother saying what I was going to say. But the worst of the worst are the protected pick swaps, and I can't believe anyone would accept one of those except when the trade is really just a salary dump, and getting a swap is sort of taking a flyer that you might get to move up a couple of spots in the middle of the draft. And not for nothing, I think the biggest reason we used to see them is because of the Stepien Rule. Now they seem to be getting used more often than just that. (That's just a gut belief - I'm not going to try and run down season by season pick swaps.)

Personally, I wouldn't give them as much value as you did. I would much rather have a high second round pick than a swap that might wind up being vapor. There are often some solid players that fall just out of the first round. And even though you're taking a chance on a player that fell out of the first round, second rounders don't come with guaranteed contracts. Second round picks aren't subject to Stepien, so you could demand a second round pick for, say, 2025 or 2026 and not have to worry that the other team is going to tank, because they wouldn't damage their first round pick to try and hang onto their second rounder. There's still no guarantee that you get a high second round pick, but at least you know you get something.

I understand your math. But if you look at a swap as an asset, if you stack them in a single year you pretty much have to cut the value of each one in half because you know you can't use them both. Stacking two swaps doesn't double your chance of getting a lottery pick, so I think it's a mony loser overall. If you really want to juice your analysis, factor in EV of lottery picks (especially at the end of the lottery), guaranteed contracts, etc. Then go sell yourself as the Paul DePodesta of basketball and retire early. But get Russ to help you with it.

[scott]

Something I didn't include in my original post because it should have been obvious... but suddenly seems important to point out:

Pick swaps hold zero value when you are considerably worse than all the teams you've swapped with.

[Guru of Nothing]

Something I didn't include in my original post because it should have been obvious... but suddenly seems important to point out:

Pick swaps hold zero value when you are considerably worse than all the teams you've swapped with.

Newman!

[CorrectCrusader]

Fantastic post.