D-Values

NAQT computes "D-values" to issue invitations to its Intercollegiate Championship Tournament (ICT) and Community College Championship Tournament (CCCT) to teams that did not qualify automatically. The inputs to the D-values are teams’ performances at the Sectional Championship Tournaments (SCTs) and Community College Sectional Championship Tournaments (CC SCTs).

The system is based on, and named for, a proposal by NAQT writer Dwight Wynne, a quiz bowler at Capistrano Valley High School, UCLA, and UC-Irvine.

Abbreviations

The system makes use of these statistics:

  • TUPPTUH: Tossup points per tossup heard. This is found for a team by computing each game’s tossup points per tossup heard and averaging those values.
  • BHPTUH: Bonuses heard per tossup heard. This is found for a team by computing each game’s total correct tossups per tossups heard and averaging those values. Note that this computation includes overtime tossups that didn’t actually result in bonuses being heard in that particular game.
  • PPB: Bonus points per (actual) bonus heard.
  • TUPPTUHopp: The average TUPPTUH values for the team’s opponents (weighted by number of games played).
  • TUPPTUHavg: The average TUPPTUH value for every team that competed at any SCT. That is, this is a global average incorporating results from all SCTs, not just a single tournament.
  • SOS: The strength of schedule played by the team. This equals the team’s TUPPTUHopp divided by TUPPTUHavg.
  • DCT: A correction factor to TUPPTUH and BHPTUH for teams that played in combined fields on the wrong packet set. It is 0.9 for Division I teams that played on Division II questions and 1.11 for Division II teams that played on Division I questions.
  • DCB: A correction factor to PPB for teams that played in combined fields on the wrong packet set. It is 0.7 for Division I teams that played on Division II questions and 1.43 for Division II teams that played on Division I questions.
  • Adjusted TUPPTUH: The team’s adjusted TUPPTUH, as if it were playing average teams on the proper questions. This equals the team’s TUPPTUH times its SOS times its DCT.
  • Adjusted BHPTUH: The team’s adjusted BHPTUH, as if it were playing average teams on the proper questions. This equals the team’s BHPTUH times its SOS times its DCT.
  • Adjusted PPB: The team’s adjusted PPB, as if it were playing on the proper questions. This equal’s the team’s PPB times its DCB.

Method

The team’s raw D-value is computed to simulate the points it would score in a 20-tossup game against average opponents. It equals:

20 × ( Adjusted TUPPTUH + Adjusted BHPTUH × Adjusted PPB)

This computation is done separately for the Division I and Division II fields.

After the raw values are computed, they are listed in order for each SCT and a correction is applied to ensure that invitations do not break the order-of-finish at an SCT. Starting at the top of each SCT, each team is checked to see if it finished above one or more teams with higher D-values. If it did, then that team and every team between it and the lowest team with a higher D-value are given the mean D-value of that group and ranked in order by their finish.

After those order-of-finish corrections are applied for each SCT, the rankings are combined into a single list.

Invitation Process

Teams with automatic bids for winning a division or hosting an SCT will be given invitations. Then additional invitations will be issued to fill out the rest of the field in strict (corrected) D-value order.

Public Nature

Spreadsheets containing the raw data for the teams as well as the computed values referenced above will be posted on NAQT’s website.