We've reached the last day of the NBA regular season and none of Boston's four potential first round picks have been slotted yet. In all four cases there are tie scenarios to consider and in the two lottery-bound picks there are also ping-pong ball odds at play.

What follows is a rundown of the draft tiebreaker and lottery procedures, followed by an accounting of the Celtics' scenarios. If you don't care about the process stuff you should just skip down, but I have to reference the process in talking about the specifics of each pick.

How the Lottery Works

The mechanics of the draft lottery are not changing this year but the allocation of odds and number of slots being drawn has. For the first time, the league will do a drawing to determine the first four picks in the draft instead of three. Additionally, the odds have been "flattened" to give the top three picks all the same odds of getting one of those top four picks, and the rest of the seeds have been adjusted to accommodate that.

At the lottery, 14 numbered balls are dropped into a "hopper" and four are drawn out. There are 24,024 unordered combinations that can be drawn (14*13*12*11) but the combination that is drawn is always put into ascending order. For example, 1-5-10-14 is the same as 14-10-5-1.

Because they are put in order, there are "only" 1,001 possible combinations that can be drawn. One thousand of these are used and combination 1,001 (11-12-13-14) is discarded. If that discarded combination is drawn, they simply reset the machine and draw again.

Each team is assigned a parcel of combinations. The odds that a team will receive the first pick determines how many combinations they receive. For example, the 1-seed (the Knicks) receive 14% of the 1,000 combinations, or 140.

Picks are drawn in order and a single seed obviously can't get more than one pick. If a team is lucky enough to get the first pick and then one of their combinations also comes out for Pick 2, the machine is reset and they keep drawing combinations until a different team's numbers come up. In 2017, the lottery began with a Celtics combination being drawn three straight times; on the fourth time it was the Lakers.

Because picks are drawn in order from 1-4, the teams with lots of combinations are more likely to pick 1st than 4th. Seeds 1-4 make up 52.5% of combinations and so #1 is likely to come from that group. Teams with lower odds are more likely to pick 4th than 1st because as higher odds teams are probably removed from the available combinations, the smaller parcel odds climb.

Draft Tiebreakers

The draft does not use the same tiebreakers as are used for playoff seedings. Instead, all record ties, other than ones where some teams are in the playoffs and others not, have their draft order determined by a blind drawing (commonly referred to as the "coin flip" though I believe it's more like names out of a hat).

This makes sense, as you wouldn't want there to be "super tanking" games where both teams are trying to lose for draft tiebreaker preference on top of record order.

If the teams are tied in the lottery they each receive the average number of combinations for the tied slots. For example, if 4 (125 combinations) and 5 (105) were tied both teams would receive 115 combinations, regardless of the result of the tiebreaker.

However, if there is an "extra" combination the team that slots higher in the tiebreaker would get that one. For example, if the 5 (105) and 6 (90) were tied they would each receive 97 combinations but there would be one left over. Whoever wins the tiebreaker to be the 5-seed would get that giving them 98 combinations and the loser in the 6-seed 97 combinations.

These same rules also apply for ties with more than two teams.

For ties outside the lottery, the tiebreaker simply determines who picks first.

In all cases of a tie, whoever ends up with the higher pick gets the lower pick in Round 2. This also includes the lottery, so if a team loses a tiebreaker in the lottery seeding but then wins a higher pick than the team they were tied with in the lottery drawing, the team that lost the initial tiebreaker would pick lower in Round 2.

Celtics Scenarios

Memphis Pick

The Celtics will receive Memphis's pick if it lands outside the top-8. If they do not receive it this year it becomes top-6 protected next year and then unprotected in 2021. By all accounts, the team does not want the pick to fall outside the top-8 and so convey this year.

There are currently four teams impacting this pick. Memphis and Washington have 32 wins; Dallas and New Orleans have 33. Washington and New Orleans have finished their seasons but Memphis and Dallas each have one game remaining.

That means that there are three possible scenarios left from the two remaining games:

1. Memphis loses --> Washington and Memphis tie for 6/7 seeds

2. Memphis win and Dallas lose --> New Orleans, Dallas, and Memphis tie for 7/8/9 seeds

3. Memphis and Dallas both win --> New Orleans and Memphis tie for 7/8 seeds

In Scenario 1, there would be a 9% chance of the pick conveying after the lottery. If Memphis win the tiebreaker that would drop to 4.1% but if they lose it would rise to 13.9%.

In Scenario 2, there would be a 44.4% chance of the pick conveying after the lottery. That would drop to 16.8% if the tiebreaker slots them 7th, 42.5% if 8th, and 73.7% if 9th.

In Scenario 3, there would be a 26.7% chance of the pick conveying after the lottery. If Memphis win the tiebreaker that would drop to 15.3% but if they lose it would rise to 38.1%.

Sacramento Pick

The Celtics will receive Sacramento's pick as long as it does not land at #1 in the lottery. If it does land #1, they will receive Philadelphia's pick instead.

There are currently four teams impacting the Kings part of this pick, each with one game left to play. Sacramento, Charlotte, and Miami all have 39 wins; Detroit has 40. Either Charlotte or Detroit will end up in the playoffs, so this can be at most a three team tie.

The scenarios are:

1. Sacramento lose, Miami and Charlotte win --> Sacramento is the 12-seed

2. Sacramento lose, one of Miami or Charlotte win --> Sacramento is in a tie with one team for the 12/13 seeds

3. Sacramento win, Miami and Charlotte lose --> Sacramento is the 14-seed

4. Sacramento win, one of Miami or Charlotte win --> Sacramento is in a tie with one team for the 13/14 seeds

5. All of Sacramento, Miami, and Charlotte get the same win/loss result --> Sacramento is in a 3-team tie for the 12/13/14 seeds

Secondarily, Philadelphia and Utah are tied at 50 wins for the 23rd and 24th pick with both teams locked into their playoff seeds. In the unlikely event that the Kings pick jumps to #1, the Celtics would get one of those two picks instead, pending their final games and possible a draft tiebreaker, while the 76ers would pick #1.

In Scenario 1, there would be a 1.5% chance of picking 23 or 24, a 5.6% chance at 2-4, and the remaining odds that the pick would be 12-14 (86.1% at 12).

In Scenario 2, there would be a 1.25% chance of picking 23 or 24, a 4.7% chance at 2-4, and the remaining odds that the pick would be 12-14. The tiebreaker would not allocate any extra combinations but would determine who is most likely to pick at 12 or 13.

In Scenario 3, there would be a 0.5% chance of picking 23 or 24, a 1.9% chance at 2-4, and a 97.6% chance at picking 14th.

In Scenario 4, there would be a 0.75% chance of picking 23 or 24, a 2.9% chance at 2-4, and the remaining odds that the pick would be 13 or 14. The tiebreaker would both allocate one extra combinations and determine who is most likely to pick at 13 or 14.

In Scenario 5, there would be a a 1.0% chance of picking 23 or 24, a 3.8% chance at 2-4, and the remaining odds that the pick would be 12-14. The tiebreaker would not allocate any extra combinations but would determine who is most likely to pick at each of 12-14.

LA Clippers Pick

The Clippers currently have 47 wins and are in a 3-team tie for the 18-20 picks0 with San Antonio and Indiana. Oklahoma City have 48 wins and are one game ahead.

This could end anywhere from the Clippers alone in the 18th slot to tied for 20/21 with OKC.

However, being alone in 18 would mean that Dallas lost to San Antonio, so if Memphis beat Golden State (who are probably going to rest everyone), Boston would prefer the Spurs to lose and slightly hurt this pick but be a big help to the more important Memphis scenarios.

Boston Pick

The Celtics are currently slotted to pick 22nd but if OKC win they will end in a tie for the 21st and 22nd picks. A drawing would be done to break that tie with the winner choosing 21st and 52nd and the loser 22nd and 51st.

The Ideal Scenario

Boston's best case scenario would be as follows...

Memphis Lose

Sacramento Lose

Miami Win

Charlotte Win

Los Angeles Lose

San Antonio Win

Indiana Win

Oklahoma City Win

Grizzlies tied for 6/7

Kings --> Celtics at 12

Clippers --> Celtics at 18

Celtics tied for 21/22

Grizzlies lose tiebreaker and drop to 7

Celtics win tiebreaker and jump to 21

Kings win 2nd pick in the lottery

Grizzlies drop one spot to 8th

Celtics pick 2, 18, 21, 52, and roll over the Grizzlies pick who add the worst possible pick for next season!