to figure it out, we have to make some assumptions about how likely GS and cleveland are to win their remaining games, and then calculate separately the odds of the four different scenarios that result in us getting the pick:
1) GSW winning the spurs game, then not winning the lotto
2) GSW losing the spurs game, 3-way tie results in GSW 8th, then not winning the lotto
3) GSW losing the spurs game, 2-way tie results in GSW 8th, then not winning the lotto
4) GSW losing the spurs game, getting to 6th or 7th, but then getting bumped backward (which actually is comprised of three scenarios)
1) let's say they have a 1/3 chance of winning the spurs game... which in terms of accuscore predictions or vegas odds represents a pretty big underdog situation. i think that's fair. the spurs WILL be resting guys, but it's not like they'll be trying to lose. they still have homecourt in the finals to contend for. if they win, they're 8th worst with a 90% chance of staying 8-10 and not winning a top three pick. so far we're at a 30% chance of this scenario happening (.33 x .90).
2) add to that 30% odds the odds of them getting the pick with a loss, which we're saying there is a .667 chance of. to figure this we have to break it into two scenarios: GSW loses and winds up in a 3-way tie, GSW loses and winds up in a 2-way tie. so we need estimate the chances of cleveland winning out. we're talking about a .328 team who plays a home game against an inferior-but-streaking team, and then a road game against a far-superior-but-possibly-resting team. so let's say their record dictates the odds and give them a 1 in 3 chance at each game, or a .167 chance of winning both. so now there's a 66.7% chance they lose, coupled with the 16.7% chance that cleveland wins out for a 3-way tiebreaker to have a 33% chance of 8th worst where they'd have a 90% chance of keeping the pick. so this path represents an extra 3.3% (.667 x .167 x .33 x .90) chance on top of our original 30%... up to a 33.3% chance.
3) another scenario that lands us the pick is a golden state loss coupled with cleveland NOT winning out. if we assume (as we did in the last paragraphs) that GSW has a 66% chance of losing and cleveland has an 83% chance of losing at least once, then you're looking at that percentage multiplied by the resulting 50/50 coin toss with the winner of Tor/NJ, and again multiplied by the 90% chance that they don't move up from eighth. .667 x .833 x .5 x .9 = .250, so now we're up to a 58.3% chance.
4) finally, we have to account for everything going wrong and GS getting to 7th or 6th worst, but still getting bumped backward to eight or worse in the lotto. for this scenario to play out it's either:
- GS losing (.667), cleveland winning out (.167), GS wins 6 in a 3-way tiebreaker (.333) but then gets leapfrogged by two teams in the lotto (~.040). multiply all that together for a .001 chance
- GS losing (.667), cleveland winning out (.167), GS wins 7 in a 3-way tiebreaker (.333) but then gets leapfrogged by one or more team in the lotto (~.25). multiply all that together for a .009 chance.
- GS losing (.667), cleveland losing at least one (.833), GS wins 7 in a 2-way tiebreaker (.5) but then gets leapfrogged by one team in the lotto (~.25). multiply all that together for a .069 chance.
- total likelihood of GS getting to 6 or 7 but getting bumped backwards: 7.9%. our previous 58.3 plus this 7.9 means our total likelihood is 66.2%.
obviously the math changes as soon as cleveland wins/loses a game, or if we want to adjust the mathematical likelihood of GSW winning. but that's the methodology, and it says that a 2 in 3 chance is actually pretty close.