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Breaking two possible three-way ties

Ateneo and La Salle's fates for their respective goals rely on the final week of the eliminations. (file photo)
By Ivan Saldajeno

ENTERING the final week of the UAAP regular season, here are the latest developments: three teams are now assured of Final Four spots, while three others battle for the last seat. What lies ahead of these six teams?

First, the standings:

FEU 10-2
UST 10-3
Ateneo 9-4
NU 6-7
La Salle 5-7
UE 4-8

The remaining games:

Nov. 11-UST vs. Adamson, UP vs. La Salle
Nov. 14-Ateneo vs. UE, NU vs. FEU
Nov. 18-UE vs. UP, FEU vs. La Salle

The quotient rules to follow:

1. In case of a tie for first, the team with the best quotient finishes first while the other finishes second. If it's a three-way tie, the two teams with the lowest quotients will play another match for second place.

2. In case of a tie for fourth, the two teams will battle in a playoff for the said spot. If it's a three-way tie, the team with the highest quotient will take a bye and will await the winner of a playoff between the other two teams in another knockout match.

Here are the quotients of all the teams involved in the two possible three-way ties. First, the race for first:

If only FEU and UST tie, UST will automatically finish first because of its season-series sweep. If a three-way tie ensues, here are the quotients:

FEU 1.067
UST 1.049
Ateneo 0.889

1. If UST wins and FEU loses at least one of its last two games, UST will finish first.
 a. If FEU loses only one of its last two games, FEU will finish second regardless of what happens to Ateneo.
 b. If FEU loses twice and Ateneo wins, FEU and Ateneo will battle it out in a virtual best-of-three Final Four series including the playoff for second.
 c. If FEU loses twice and Ateneo loses, FEU will finish second.
2. If UST loses and FEU wins at least one of its last two games, FEU will finish first.
 a. If Ateneo loses, UST will finish second.
 b. If Ateneo wins, UST and Ateneo will face off in a best-of-three affair in the semis.
3. If UST loses and FEU loses twice...
 a. If Ateneo loses, UST will finish first and FEU will finish second.
 b. If Ateneo wins, the three-way tie ensues. Based on the quotients above, FEU will finish first, while UST and Ateneo will play in the virtual best-of-three semis.

Summary: Ateneo can only hope for a virtual best-of-three semis, while UST can finish first with a win. FEU, with a match at hand, can dictate its twice-to-beat fate.

Now, the race for fourth:

La Salle 1.04
UE 0.981
NU 0.978

1. If UE loses at least one of its last two, UE is eliminated.
 a. If NU wins and La Salle wins twice, NU and La Salle will battle for the last Final Four seat.
 b. If NU wins and La Salle loses at least one of its last two, NU will enter the Final Four outright.
 c. If NU loses and La Salle wins twice, La Salle will enter the Final Four outright.
 d. If NU loses and La Salle loses only of its last two, NU and La Salle will battle for the last Final Four seat.
 e. If NU loses and La Salle loses twice, NU will enter the Final Four outright.

2. If UE wins twice...
 a. If NU wins, then UE is eliminated.
  i. If La Salle wins twice, then NU and La Salle will battle for fourth.
  ii. If La Salle loses at least one of its last two, NU will enter the Final Four outright.
 b. If NU loses...
  i. If La Salle wins twice, La Salle will enter the Final Four outright.
  ii. If La Salle loses twice, NU and UE will battle for fourth.
  iii. If La Salle loses only one of its last two, the three-way tie ensues. Based on the quotients and the rules regarding the wildcard ties, UE and NU will battle for fifth with the winner taking on La Salle for the last Final Four seat.

Summary: One UE loss, one NU win, or two La Salle wins and UE is out. NU can assure at least a playoff for fourth with a win. La Salle, with a match at hand, can dictate its Final Four fate like what Coach Juno Sauler implied on Sunday.

Follow the writer on Twitter: @IvanSaldajeno