S-Value Revision Proposal
Last year, NAQT began soliciting community input on a revision of its S-value system for ranking teams that competed at its Sectional Championship Tournaments (SCTs) and Community College Sectional Championship Tournaments (CC SCTs). We've looked at a number of models, and are now presenting the one we think is most applicable for public comment.
The chosen model is based heavily on a suggestion of Dwight Wynne and, in honor of that, its results are (at least temporarily) called D-values to distinguish them from the previous S-values.
Abbreviations
The methods use of these statistics:
- TPPTH: 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.
- BHPTH: 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.
- TPPTHopp: The average TPPTH values for the team's opponents (weighted by number of games played).
- SOS: The strength of schedule played by the team. This equals the team's TPPTHopp divided by the average TPPTH for the field as a whole.
- DCT: A correction factor to TPPTH and BHPTH 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 TPPTH: The team's adjusted TPPTH, as if it were playing average teams on the proper questions. This equals the team's TPPTH times its SOS times its DCT.
- Adjusted BHPTH: The team's adjusted BHPTH, as if it were playing average teams on the proper questions. This equals the team's BHPTH 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 x ( Adjusted TPPTH + Adjusted BHPTH x 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
As before, 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 D-value order.
Public Nature
Unlike in past years, spreadsheets containing the raw data for the teams as well as the computed values referenced above will be posted on NAQT's website. Everybody will be able to see the computed D-values and know exactly where they stand in the invitation list.
Discussion
A thread for discussing this proposal has been opened. People should also feel free to send questions or concerns to NAQT at naqt@naqt.com.