Spurs' odds of picking 1st / picking among the top 4. Scenarios

[Spursfanfromafar]

Tankathon lists the probability for each team's picks based on their current NBA standings. Here are the odds for each team in the lottery (assuming none of the picks are traded and all picks are owned) -

https://i.imgur.com/U3pNScT.png
Now the Spurs are currently picking 10th and 11th (from the Atlanta Hawks). What is the probability of the Spurs picking 1st or within the top 4 considering they have both picks? While we want to find that answer, lets also calculate the probability of picking 1st or within the top 4 if the land earlier in the lottery. Here are some possible scenarios (the most likely ones. The Spurs and Hawks will find it difficult to drop all the way down to the 6th position based on how current rankings are).

https://i.imgur.com/z5WrIao.png
In other words, the Spurs will have nearly the same probability of picking the 1st pick and within the top 4 if they land up in the 7th position and the Hawks in the 8th position, as what the teams in the worst 3 have. As things stand, they are getting the 10th & 11th picks .. which gives them a 4.9% chance to win the NBA lottery and a 22.3% chance of getting a pick in the top 4. Thats the equivalent of having the same odds as the 9th worst team.

Here's hoping that the Hawks and/or the Spurs get into a situation that they lose games enough to finish higher in the lottery if the idea is to get one of the top 4 picks in the lottery.

[rascal]

It would be great if the Spurs can land a top 4 pick this year.

Starting next year I expect the Spurs to be making the playoffs every year so this is their last shot with their own pick in the lottery.

Of course they have another Atlanta pick and the Atlanta pick swap but no guarantee those will be in the lottery.

[ffadicted]

Good post

Honestly I'm at the point where we could sit Wemby and Fox and we'd still outperform the 76ers. If you've watched any of their games it's just simply atrocious. And their pick is top 6 protected too so they're not keen to make a push for it I'd guess. Same with Chicago and Brooklyn, they're terrible. Portland should def pass us though. I think the best case scenario is:


* We get the 9th spot by portland passing us
* Atlanta lands at 11th, reasonable to think the Suns, Kings, Warriors would all have a better record.
* Atlanta doesn't make it past the play-in.


That gets us a descent ~27% chance of a top 4 pick and very likely chance of top 10, with a far off shot at #1. I just wouldn't hold my breathe, especially if we don't sit Fox.

[spurraider21]

It would be great if the Spurs can land a top 4 pick this year.

Starting next year I expect the Spurs to be making the playoffs every year so this is their last shot with their own pick in the lottery.

Of course they have another Atlanta pick and the Atlanta pick swap but no guarantee those will be in the lottery.
yeah if anything atlanta may be on the upswing as long as Trae sticks around. dyson daniels is blossoming and he's only turning 22 next month. jalen johnson is an outstanding young forward locked up for the foreseeable future. i still like risacher a lot who has started shooting the ball straight after a rough start to the year. over the last 20 games or so he's shot 48% from the field and 40% from 3. he is yet to turn 20.

theyre also finally getting off the undesirable capela contract (22 mil off the books). nance and levert are also expiring and will clear up an additional 28 mil.

while they owe us their pick this year, they are getting picks from the lakers and kings (top 12 protected, currently projected to convey)

[baseline bum]

It would be great if the Spurs can land a top 4 pick this year.

Starting next year I expect the Spurs to be making the playoffs every year so this is their last shot with their own pick in the lottery.

Of course they have another Atlanta pick and the Atlanta pick swap but no guarantee those will be in the lottery.

Got Boston (28), Dallas (30), Minnesota (30), and Sacramento (31) pick swaps too, with the only protection being top 1 from Boston in 28 and Minnesota in 30, so should be able to get another lottery pick or two out of those also.

[spurraider21]

Got Boston (28), Dallas (30), Minnesota (30), and Sacramento (31) pick swaps too, with the only protection being top 1 from Boston in 28 and Minnesota in 30, so should be able to get another lottery pick or two out of those also.
dallas one for sure. would hypothetically be after kyrie/AD's age 36/37 seasons if either is still around

and sacto... you can usually count on them to be dysfunctional in the long haul

[exstatic]

yeah if anything atlanta may be on the upswing as long as Trae sticks around. dyson daniels is blossoming and he's only turning 22 next month. jalen johnson is an outstanding young forward locked up for the foreseeable future. i still like risacher a lot who has started shooting the ball straight after a rough start to the year. over the last 20 games or so he's shot 48% from the field and 40% from 3. he is yet to turn 20.

theyre also finally getting off the undesirable capela contract (22 mil off the books). nance and levert are also expiring and will clear up an additional 28 mil.

while they owe us their pick this year, they are getting picks from the lakers and kings (top 12 protected, currently projected to convey)

Why would Trae stick around ? Their owners have proven to be extremely cheap.

[spurraider21]

Why would Trae stick around ? Their owners have proven to be extremely cheap.
because of the aforementioned young, improving roster, city thats embraced him as the franchise player

[rascal]

Got Boston (28), Dallas (30), Minnesota (30), and Sacramento (31) pick swaps too, with the only protection being top 1 from Boston in 28 and Minnesota in 30, so should be able to get another lottery pick or two out of those also.

Too far out, five six years out, to make any assumptions on those picks. I'm talking about the foreseeable future for the Spurs own picks and Atlanta picks, this is their best shot for a high lottery pick.

[rascal]

Spurs at 9 and 11 with close to a one in three chance at a top 4.

[UNT Eagles 2016]

I hate the NBA and its protected draft picks. In the NFL they don't have any of that bullshit. Carolina didn't get to have a mulligan after trading the farm for Bryce Young. Their options were, develop Bryce Young or die trying. And Bryce Young did finally improve a bit towards the end of this past season.

[exstatic]

I hate the NBA and its protected draft picks. In the NFL they don't have any of that bullshit. Carolina didn't get to have a mulligan after trading the farm for Bryce Young. Their options were, develop Bryce Young or die trying. And Bryce Young did finally improve a bit towards the end of this past season.

Neither of the picks we still own in this draft are protected.

[Spursfanfromafar]

Here's the NBA draft lottery results since the flattened odds -

https://i.imgur.com/461H59l.png

As things stand on March 3, 2025, the Spurs are getting the 9th and 11th picks (via Hawks) which combined together provide a first pick probability of 6.5% and Top 4 pick probability of 27.3%

Those are better odds than the 2024 and 2019 picks. But ideally the Spurs should aspire for at least the 7th pick for themselves and the 8th or 9th pick for the Hawks, which will give them a 13.7%/12.3% probability for the 1st pick and 51.8% and 47.3% probability for one of the top 4 picks, equivalent of the top 3 worst records/ or the 4th worst record.

So lets root for the Trailblazers, 76ers and the Bulls and improbably for the Nets and Raptors as well. And for the Spurs to tank wholeheartedly.

[John B]

Here's the NBA draft lottery results since the flattened odds -

https://i.imgur.com/461H59l.png

As things stand on March 3, 2025, the Spurs are getting the 9th and 11th picks (via Hawks) which combined together provide a first pick probability of 6.5% and Top 4 pick probability of 27.3%

Those are better odds than the 2024 and 2019 picks. But ideally the Spurs should aspire for at least the 7th pick for themselves and the 8th or 9th pick for the Hawks, which will give them a 13.7%/12.3% probability for the 1st pick and 51.8% and 47.3% probability for one of the top 4 picks, equivalent of the top 3 worst records/ or the 4th worst record.

So lets root for the Trailblazers, 76ers and the Bulls and improbably for the Nets and Raptors as well. And for the Spurs to tank wholeheartedly.

Mitch sending Zollins and Trae to Bulls to accomplish this.

[exstatic]

Here's the NBA draft lottery results since the flattened odds -

https://i.imgur.com/461H59l.png

As things stand on March 3, 2025, the Spurs are getting the 9th and 11th picks (via Hawks) which combined together provide a first pick probability of 6.5% and Top 4 pick probability of 27.3%

Those are better odds than the 2024 and 2019 picks. But ideally the Spurs should aspire for at least the 7th pick for themselves and the 8th or 9th pick for the Hawks, which will give them a 13.7%/12.3% probability for the 1st pick and 51.8% and 47.3% probability for one of the top 4 picks, equivalent of the top 3 worst records/ or the 4th worst record.

So lets root for the Trailblazers, 76ers and the Bulls and improbably for the Nets and Raptors as well. And for the Spurs to tank wholeheartedly.

If the Sixers drop out off the top 6 for any reason, OKC gets their pick.

[John B]

If the Sixers drop out off the top 6 for any reason, OKC gets their pick.

Where do you see Spurs and Hawks finishing realistically?

[exstatic]

Where do you see Spurs and Hawks finishing realistically?

9/10 or 9/11. It’s so late, it’s hard to make up ground. The only thing that might working our favor is that of the bottom 8 teams, 6 are in the east, and when they play, someone has to win.

[Spursfanfromafar]

If the Sixers drop out off the top 6 for any reason, OKC gets their pick.

Weighed against the possibility of the Spurs landing Flagg because of ATL and SAS getting better picks, OKC picking up the 7th or 8th or 9th pick seems a better outcome than the 76ers finishing higher.

[exstatic]

Weighed against the possibility of the Spurs landing Flagg because of ATL and SAS getting better picks, OKC picking up the 7th or 8th or 9th pick seems a better outcome than the 76ers finishing higher.

The best outcome, of course, is one or both of our picks jumping into the top 4. If that doesn’t happen, I absolutely don’t want OKC getting a lottery pick. We have very little chance of either of our picks finishing better than 9 in the final pre-lottery positions. There are just too many teams that have been taking from the get go. With Embiid lost for the year, and maybe more, PHI has very little chance to climb the standings any way.

[Spursfanfromafar]

The best outcome, of course, is one or both of our picks jumping into the top 4. If that doesn’t happen, I absolutely don’t want OKC getting a lottery pick. We have very little chance of either of our picks finishing better than 9 in the final pre-lottery positions. There are just too many teams that have been taking from the get go. With Embiid lost for the year, and maybe more, PHI has very little chance to climb the standings any way.

The other issue is that the pick is Top 4 protected for next year... with Embiid going through a severe injury and the Sixers' team limited by his gargantuan salary (not to mention Paul George's)...there is a good chance that the Sixers will suck again next year.. In that case it is better to convey the 7th or the 8th pick this season rather than the 5th or the 6th pick next year and particularly good for the Spurs as that increases their probability of picking in the top 4 this year.

[scott]

We're only one win ahead of CHI for the 8th pick - that slot is easily attainable with proper tank management, but it has yet to be seen if the Spurs will do that or just continue being naturally unable to win most games.

If you believe in ESPN's BPI projections, then even 5th could still be technically achievable as they have PHI finishing there with 28.3 projected wins. 28 wins for us would require a 3-20 finish though, which may just be a little too stinky for this team to stomach. 30 wins seems a more reasonable projection, which would put us right with TOR at 7th based on the projections. We have quite a few important Double-Tankathon Games left that we need to lose: 3/21 v PHI, 3/23 v TOR, 4/6 v POR, 4/11 v PHX, 4/13 v TOR in the season finale. That last game could be a huge one.

https://www.espn.com/nba/bpi/_/view/projections

I hate talking about and hoping for losing. Please let this be the last year of this shit.

[SpurSpike]

Spurs will be given the green light to play hard against good teams as this will help player development and will be yanked around against bad teams with strange lineups to better the tank.

[Mr. Body]

It's astounding how completely awful Philadelphia is, 1-9 in their last ten games. Chicago is practically begging to drop below them and can't manage it and Brooklyn is neck-and-neck.

In the end I feel like SA will end up 8 or 9 and Atlanta will wind up 10, although even six games under .500 the Hawks are still a couple wins off the pace of only needing one play-in game for the full postseason. Man that conference sucks.

[exstatic]

One of the best things going on right now is Portland. If AD returns soon to boost Dallas, and Portland continues to play hot, Sacto may get knocked back into their 1-12 pick protected zone, denying ATL their possible late lottery pick and a decent chance to improve.

[Jsmythe]

https://i.imgur.com/z5WrIao.png

Something is wrong with the combined 1st pick probability %. It should just be the two numbers from the first table added together. So 7th + 8th should be 8.2% + 6.0% = 14.2% instead of 13.7%. I think what you computed subtracted out the probability of both picks being the #1 pick, which can't happen.

As for the other column, I think the percentages there should be a bit higher than what you listed as well, for a similar reason. I think you subtracted out the probability of both picks being in the 1-4 range, but there are cases that can't happen (both picks being #1, both being #2, etc) which should be added back in. However, the correct percentage is difficult to compute because you need to know the exact odds of getting each of the four picks.

[scott]

Something is wrong with the combined 1st pick probability %. It should just be the two numbers from the first table added together. So 7th + 8th should be 8.2% + 6.0% = 14.2% instead of 13.7%. I think what you computed subtracted out the probability of both picks being the #1 pick, which can't happen.

As for the other column, I think the percentages there should be a bit higher than what you listed as well, for a similar reason. I think you subtracted out the probability of both picks being in the 1-4 range, but there are cases that can't happen (both picks being #1, both being #2, etc) which should be added back in. However, the correct percentage is difficult to compute because you need to know the exact odds of getting each of the four picks.

If you look at the Tankathon odds table, here: https://tankathon.com/pick_odds you can sum up the probabilities horizontally or vertically, but you cannot sum up both vertically and horizontally. So for example, if you had the #1 and #2 lotto seeds, adding up the Top-4 odds for each of those would give you a 104.2% chance at a Top 4 pick which is obviously incorrect (and in fact you'd have less than a 100% chance - you'd actually have around a 77% chance).

We discussed this in a thread over the summer and Ariel (https://www.spurstalk.com/forums/member.php?u=3526) made this nice table which calculates all the various possibilities if you end up with the 8th and 9th pre-lotto seeding in this post: https://www.spurstalk.com/forums/showthread.php?t=303984&p=11093167&viewfull=1#post11093167

https://i.postimg.cc/15whf9FX/t89.png

Ariel actually calculated slightly better odds of at least one Top-4 pick in this scenario (42.6% versus the 41.6% chance that OP calculated).

So yeah, OP's table is a little off... but it's close enough to give us an idea. You can calculate joint probability distributions for any combination of picks, which I'm sure we'll all be starting at for weeks between the time the regular season ends and the lottery draw takes place :lol

[scott]

ChatGPT has gotten better at these sorts of things... I got it to spit out this joint probability distribution model for where things currently sit (9th and 11th seed)

https://i.imgur.com/Jn4CEDB.png

Odds of at least one top-4 pick with 9 and 11 are 27.7%

Here are the prompts I fed into ChatGPT to get the answers (which is a hell of a lot faster than calculating stuff yourself these days :lol)

1. "Consider the following table for NBA Lottery Odds"
2. Feed in Tankathon table (literally just paste it in)
3. "Calculate a joint probability distribution if you have the #9 and #11 seed" (you can replace 9 and 11 with whatever you want)
4. Tell it to produce the full matrix when it asks you
5. Tell it to produce the heatmap visualization when prompted
6. After that you can just directly ask it "what are the odds that you get at least one top-4 pick"

[scott]

The other way to quickly do this for calculating your joint probability for at least one top for pick is just this simple formula:


P(At least one in Top 4) = 1 − P(Neither in Top 4)



P(Neither in Top 4) = P(#x not in top 4) × P(#y not in top 4)

So for picks #9 and #10 (the tankathon table updated as I was writing this as POR beat PHI... so now 9 and 10 are the current seedings), it would just be:


P(Neither in Top 4) = (.797) x (.861) = 0.686

P(At least one in Top 4) = 1 - 0.686 = .314 = 31.4% chance at a Top 4.

Slightly different than OP's table, but close enough.

[Spursfanfromafar]

Something is wrong with the combined 1st pick probability %. It should just be the two numbers from the first table added together. So 7th + 8th should be 8.2% + 6.0% = 14.2% instead of 13.7%. I think what you computed subtracted out the probability of both picks being the #1 pick, which can't happen.

As for the other column, I think the percentages there should be a bit higher than what you listed as well, for a similar reason. I think you subtracted out the probability of both picks being in the 1-4 range, but there are cases that can't happen (both picks being #1, both being #2, etc) which should be added back in. However, the correct percentage is difficult to compute because you need to know the exact odds of getting each of the four picks.

No, the probabilities aren't just an addition of the two.

The reason we don’t simply add the probabilities of two picks to calculate the combined probability is due to the principle of independent events in probability theory. Instead, we use the formula:


P(At least one wins 1st pick)=1−P(Neither pick wins 1st pick)Why Not Just Add the Probabilities?If we simply added the probabilities, we'd get an overestimated value. This is because there's a small chance that both picks could win at the same time, which isn't possible in the lottery (since only one team can get the 1st pick).
Correct Method: Using the "At Least One" FormulaSince each pick has an independent chance of winning, the correct way to calculate the combined probability is:


P(\text{Neither pick wins}) = (1 - P_1) \times (1 - P_2)P(Neither pick wins)=(1−P1​)×(1−P2​)Then:

P(\text{At least one wins}) = 1 - P(\text{Neither pick wins})P(At least one wins)=1−P(Neither pick wins)For example, for 7th & 8th picks:


7th pick chance of 1st pick = 8.2% (0.082)

8th pick chance of 1st pick = 6.0% (0.060)

Neither pick wins 1st pick:
(1−0.082)×(1−0.060)=0.918×0.940=0.863(1 - 0.082) \times (1 - 0.060) = 0.918 \times 0.940 = 0.863(1−0.082)×(1−0.060)=0.918×0.940=0.863
At least one wins:
1−0.863=0.137=13.7%1 - 0.863 = 0.137 = 13.7\%1−0.863=0.137=13.7%

Key TakeawayIf we incorrectly added the probabilities:
8.2%+6.0%=14.2%(Overestimated)8.2\% + 6.0\% = 14.2\% \quad (\text{Overestimated})8.2%+6.0%=14.2%(Overestimate d)But the correct method gives 13.7%, which is slightly lower.
This ensures that we're not double-counting cases where both picks would win simultaneously (which isn’t possible in the lottery system).

[Jsmythe]

No, the probabilities aren't just an addition of the two.

The reason we don’t simply add the probabilities of two picks to calculate the combined probability is due to the principle of independent events in probability theory. Instead, we use the formula:


The problem is that the chances of the two teams winning the #1 pick are dependent events, not independent. It's dependent because if one team wins the #1 pick, the other teams' chances go to 0%. Dependent is like rolling one six-sided dice, and there are 6 teams, and the winner is the team whose number comes up. Each team has 1/6 chance, but if you have two teams' chances, you just added up the chances and get 1/6+1/6 = 1/3. Independent would be like rolling one dice per team, and if they got their number on their roll, they'd get the pick. But with this model, it would be possible for multiple teams to get the same pick, so this isn't the correct model for the lottery.

Consider if there were only 2 teams in the league, and the chances of them winning the lottery were 60% and 40%. If you had both teams' picks, you would simply add 60+40 = 100%. With the "at least one" formula, you'd get .6 + (.4*.6) = .84 = 84% which is clearly wrong.

[scott]

The problem is that the chances of the two teams winning the #1 pick are dependent events, not independent. It's dependent because if one team wins the #1 pick, the other teams' chances go to 0%. Dependent is like rolling one six-sided dice, and there are 6 teams, and the winner is the team whose number comes up. Each team has 1/6 chance, but if you have two teams' chances, you just added up the chances and get 1/6+1/6 = 1/3. Independent would be like rolling one dice per team, and if they got their number on their roll, they'd get the pick. But with this model, it would be possible for multiple teams to get the same pick, so this isn't the correct model for the lottery.

Consider if there were only 2 teams in the league, and the chances of them winning the lottery were 60% and 40%. If you had both teams' picks, you would simply add 60+40 = 100%. With the "at least one" formula, you'd get .6 + (.4*.6) = .84 = 84% which is clearly wrong.

I agree with this, and is what I alluded to earlier where you can add up horizontally or vertically on the table, but you can't do both. If you look at all the odds for pick #1 of the various seedings (the vertical reading), they all equal 100%, and the odds for each seed add up to 100% (the horizontal reading). If you hold multiple seedings, you can just add them together for any one pick. You don't have to worry about accounting for the possibility that both end up at #1, because this is a one-shot game... there is only one roll of the dice and therefor there is no possibility of more than one outcome for a given pick.

Likewise, that's the reason you can sum up odds both vertically and horizontally simultaneously (and by that, I mean you can add the "Top 4 Odds" of one seed and the "Top 4 Odds" of another seed and get the right answer). That's because in determining multiple picks it ceases to be a one-shot game, and becomes a multiple-shot game (in this case, 4 shots). If one of the seeds lands #1, it automatically excludes it from winning #2, 3 or 4 (though supposedly the Spurs also "won" the #2 pick in the Wemby draft even though they had already got #1... that winning pull had to be thrown out). So by winning in the #1 game, you reduce your odds of winning the #2, 3, or 4 game because one of your seeds is now eliminated.

TLDR version: to get the odds of landing a specific pick, you just add the Spurs and Hawks seeds together. To get the joint odds of "at least one better than", you have to use the probability formula provided above.

[Spursfanfromafar]

Tankathon lists the probability for each team's picks based on their current NBA standings. Here are the odds for each team in the lottery (assuming none of the picks are traded and all picks are owned) -

https://i.imgur.com/U3pNScT.png
Now the Spurs are currently picking 10th and 11th (from the Atlanta Hawks). What is the probability of the Spurs picking 1st or within the top 4 considering they have both picks? While we want to find that answer, lets also calculate the probability of picking 1st or within the top 4 if the land earlier in the lottery. Here are some possible scenarios (the most likely ones. The Spurs and Hawks will find it difficult to drop all the way down to the 6th position based on how current rankings are).

https://i.imgur.com/z5WrIao.png
In other words, the Spurs will have nearly the same probability of picking the 1st pick and within the top 4 if they land up in the 7th position and the Hawks in the 8th position, as what the teams in the worst 3 have. As things stand, they are getting the 10th & 11th picks .. which gives them a 4.9% chance to win the NBA lottery and a 22.3% chance of getting a pick in the top 4. Thats the equivalent of having the same odds as the 9th worst team.

Here's hoping that the Hawks and/or the Spurs get into a situation that they lose games enough to finish higher in the lottery if the idea is to get one of the top 4 picks in the lottery.

Updated odds with other pick possibilities as well -

https://imgur.com/a/Nh158sA
https://i.imgur.com/Dne4zwp.png
https://imgur.com/MRy5f1v

As of now the Hawks are picking after 14. But there is a good chance that they might land up between 10 and 14 still.
https://imgur.com/MRy5f1v