Pieper HS Tournament This tournament completed October 21st, 2023.

Detailed breakdown of how Joshua's M-S-C-O tiebreaks were calculated. Tiebreaks are used to order players who finish with the same score, in the order M, then S, then C, then O. Byes have no opponent, so they are listed but not counted in the opponent-based tiebreaks.

M - Modified Mean [10.0]

The Modified Mean adds up the scores of every opponent Joshua Williams has played, then discards one of them depending on how Joshua Williams is doing.

Joshua's score (2.0 of 5.0 possible) is less than 50% of the possible points, so the highest opponent score is discarded.

Round	Opponent	Opponent's Score	Counted?
1	Joseph Tolico	4.0	Discarded
2	John Herrera	4.0	Counted
3	Jaselyn Torres	1.5	Counted
4	Jayden Galvan	2.5	Counted
5	Carson Galbreath	2.0	Counted
Modified Mean		10.0

S - Solkoff [14.0]

The Solkoff is the combined score of every opponent Joshua Williams has played, with nothing discarded. A higher Solkoff means Joshua Williams faced tougher opposition.

Round	Opponent	Opponent's Score
1	Joseph Tolico	4.0
2	John Herrera	4.0
3	Jaselyn Torres	1.5
4	Jayden Galvan	2.5
5	Carson Galbreath	2.0
Solkoff		14.0

C - Cumulative [7.0]

The Cumulative tiebreak adds together Joshua's running score after each round. Early wins count more, because they carry forward into every later round's total.

Round	Result	Score After Round
1	1.0	1.0
2	0.0	1.0
3	0.5	1.5
4	0.0	1.5
5	0.5	2.0
Cumulative		7.0

O - Opponent's Cumulative [39.5]

The Opponent's Cumulative adds together the Cumulative tiebreak of every opponent Joshua Williams has played.

Round	Opponent	Opponent's Cumulative
1	Joseph Tolico	10.0
2	John Herrera	12.0
3	Jaselyn Torres	6.5
4	Jayden Galvan	7.0
5	Carson Galbreath	4.0
Opponent's Cumulative		39.5