IV.    BYES

In order to determine the number of teams needed to emerge from the early stages of the event, it is necessary to focus on the number of “slots” taken up in the round of 16 (if held). When counting “slots” in the round of 16, teams with byes to the semi-final count as four slots, teams with byes to the quarter-final count as two slots and teams with byes to the round of 16 count as one slot. At most 12 slots can be taken up by teams with byes. At least four slots in the round of 16 are reserved for teams without byes to emerge from the field. (If no round of 16 is held, then the focus is on the teams in the quarter-final, counting the teams receiving byes to the semi-final as two slots in the quarter-final.)  Byes are given in rank order by PPs. The team with the highest number of PPs is placed ahead of teams with fewer PPs.  A team that earned PPs for a bye with an Ineligible Player on its team cannot earn more than a bye to the Round of 16.

A.    Byes to the Semi-final.  

There are two PPs thresholds to earn a bye to the semi-final: 150 PPs for one bye and at least 162 each for two byes. In addition a team needs a win in the 2008 Spingold, the 2008 Reisinger, the 2009 Vanderbilt or the 2008 Open Team Olympiad. At most two teams may earn a bye to the semi-final. If three teams have won an event and each has PPs equaling or exceeding 162, the two teams with the highest PPs totals shall earn the semi-final byes.   

Example: There are three teams with the following PPs: 150, 156 and 165 and each team has won one of the events listed above. Only the team with 165 PPs gets a bye to the semi-final, because in order for two teams to earn a bye, each would need to have at least 162 PPs.  The other two teams would have a bye to the quarter-final.

B.    Byes to the Quarter-final.

There are six PPs thresholds to earn a bye to the quarter-final: 60, 63, 67, 72, 78 and 85. Each slot taken up by a semi-final bye removes the two lowest threshold numbers above.
  
If no team has a bye to the semi-final, up to six teams may earn a bye to the quarter-final. The six PPs thresholds to earn a bye to the quarter-final are: at least 60 PPs for one bye, at least 63 PPs each for two byes, at least 67 PPs each for three byes, at least 72 PPs each for four byes, at least 78 PPs each for five byes and at least 85 PPs each for six byes.
 
If one team has a bye to the semi-final, up to four teams may earn a bye to the quarter-final. The four PPs thresholds to earn a bye to the quarter-final are: at least 67 PPs for one bye, at least 72 PPs each for two byes, at least 78 PPs each for three byes and at least 85 PPs each for four byes. 

If two teams have a bye to the semi-final, only one or two teams may earn a bye to the quarter-final. The two PPs thresholds to earn a bye to the quarter-final are at least 78 PPs for one bye and 85 PPs each for two byes. 
 
Teams that did not receive a bye to the quarter-final will usually be eligible to receive a bye to the round of 16.  See C. below.

Examples: There are six teams with the following PPs: 60, 65, 67, 69, 72, 85.
If there are 6 slots available (no bye to the semi-final), the teams with 85 PPs, 72 PPs and 69 PPs would have a bye to the quarter-final.  The team with 67 PPs could not earn a bye because giving four byes require each team to have at least 72 PPs.
If there are 4 slots available, (one bye to the semi-final), the teams with 85 PPs and 72 PPs would have a bye to the quarter-final.  The team with 69 PPs could not earn a bye because three byes require each team to have at least 78 PPs.
If there are two slots available, (two byes to the semi-final), only the team with 85 PPs would have a bye to the quarter-final. The team with 72 PPs could not earn a bye because two byes require each team to have at least 78 PPs.

C.    Byes to the Round of 16.

If there is a round of 16, at most 12 slots can be taken up by teams with byes. There are 12 PPs thresholds to earn a bye to the round of 16: 40, 40, 40, 40, 42, 44, 46, 48, 50, 52, 54, 56. Slots taken up by semi-final byes and/or quarter-final byes remove the lowest threshold numbers above.

Example: there are five teams with the following PPs: 45, 47, 52, 65, 67, and four slots are already taken up by semi-final or quarter-final byes.  
The first four PPs thresholds for byes to the round of 16 are removed (40, 40, 40, 40) because of the four slots are taken up by the semi-final and/or quarter-final byes. The eight remaining PPs thresholds for byes to the round of 16 are at least 42 for one bye, at least 44 PPs each for two byes, at least 46 PPs each for three byes, at least 48 PPs each for four byes, at least 50 PPs each for five byes, etc.  In this example, there are three teams with at least 46 PPs, but there are not four teams with at least 48 PPs. So the three teams with 67, 65 and 52 PPs would earn a bye to the round of 16.

D.    Byes to the Round of 32

When there is a Large Entry, teams with 40 or more PPs that did not earn a bye to the R16 shall have a bye to the R32 if there is a R32 KO.