NAQT computes “D-Values” to issue invitations to its Intercollegiate Championship Tournament (ICT) and Community College Championship Tournament (CCCT). The inputs to the D-Values are teams’ performances at the Sectional Championship Tournaments (SCTs) and Community College Sectional Championship Tournaments (CC SCTs).
D-Values are calculated to compare the performance of teams that competed at different qualifying tournaments.
The system is based on, and named for, a proposal by former NAQT writer Dwight Wynne, who played quiz bowl at Capistrano Valley High School, UCLA, and UC-Irvine.
The original D-Value system was introduced in 2010. It was used through 2017 and then also for the 2018 CC SCTs. A second version was used for the 2018 SCTs and 2019 CC SCTs. A third version (described on this page) was introduced for the 2019 four-year SCTs. Both CC SCTs and four-year SCTs will use the new (third) version in 2020. The changes are summarized here.
NAQT’s ICT qualification process strongly emphasises D-Values: The first 20 spots in the field are reserved for the teams with the highest D-Values.
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. This is an uncorrected, "raw" value that does not take into account the packet set on which the game was played.
- 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. This is also an uncorrected, raw value.
- TUPPTUHopp: The average corrected TUPPTUH values for the team’s opponents (weighted by number of games played). This average excludes games against the team for which TUPPTUHopp is being calculated. The corrected value equals the raw TUPPTUH value multiplied by the DCT correction factor.
- PPBopp: The average corrected PPB values for the team’s opponents (weighted by number of games played). This average includes all games, even those against the team for which TUPPTUHopp is being calculated. The corrected value equals the raw PPB value multiplied by the DCB correction factor.
- TUPPTUHavg: The average corrected 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.
- PPBavg: The average corrected PPB value for every team that competed at any SCT.
- SOS: The strength of schedule played by the team. This equals the sum of the team’s TUPPTUHopp and PPBopp divided by the sum of TUPPTUHavg and PPBavg. SOS cannot go below 0.75; lower values are replaced by 0.75.
- DCT: A correction factor to TUPPTUH and BHPTUH for teams that played in combined fields on the wrong packet set). It is 0.8 for Division I teams that played on Division II questions and 1.25 for Division II teams that played on Division I questions. (It is 1.0 for teams that played the appropriate packet set.)
- DCB: A correction factor to PPB for teams that played in combined fields on the wrong packet set. It is 0.82 for Division I teams that played on Division II questions and 1.22 for Division II teams that played on Division I questions. (It is 1.0 for teams that played on the appropriate packet set.)
- 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.
The team’s base 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))
After the base 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 (and, if still tied, by base D-Value).
After those order-of-finish corrections are applied for each SCT, the rankings are combined into a single list for each division.
The raw data for the teams and the computed values will be posted on NAQT’s website.