# Bonus conversion

(Redirected from PPB)

Bonus conversion, or PPB, is a statistic that describes a team's proficiency at earning points on bonuses. In formats where all bonuses are worth thirty possible points, bonus conversion is computed by dividing a team's total bonus points by the total number of bonuses heard, and is expressed in points per bonus (ppb). In formats where bonuses take different maximum point values over the course of the game, bonus conversion is computed by finding the average percentage of bonus points earned (total bonus points earned/total possible bonus points), and is expressed in percent per bonus (also ppb). For whatever reason, CBI uses the former definition even though their bonuses are not all worth the same amount of points.

Formats which use bouncebacks and are connected enough to the quizbowl mainstream to report full statistics, such as the PACE NSC, will usually separate "bonus conversion" (on bonuses a team controls) from points earned on bounceback opportunities, which may be labeled "bounceback percentage," "points per bounceback," or similar.

Bonus conversion is used as a benchmark for tournament difficulty relative to attending teams. The standard for tournaments is that the best teams in the field should convert somewhere around 20 ppb, most teams should convert around 15 ppb, and the weak end of the field should convert somewhere around 10 ppb. Tournaments where many teams are converting over 20 ppb are considered too easy for the field; tournaments where many teams' ppb are in the single digits are considered too hard for the field.

## Arguments for emphasizing bonus conversion

Bonus conversion has been argued as the most fair way to break ties, as it is independent of opponent strength and roughly independent of possible variations in round-to-round question difficulty.

Many systems which use mathematical formulae to rank teams on performance across multiple sites or tournaments place a large emphasis on bonus conversion. Examples include the D-value and Groger ranks. The Fred Morlan high school team rankings relied entirely on bonus conversion numbers, and difficulty corrections derived from those numbers.

## Arguments for de-emphasizing bonus conversion

Bonus conversion is extremely sensitive to stats errors, with mistakes that may easily go unnoticed in a vacuum (such as entering a player's statline as 4 tossups instead of 3 in a blowout game) able to strongly influence the final bonus number. As bonus conversion may be used to compare teams with very close numbers for tiebreaking purposes, these errors have a meaningful chance of producing the wrong tiebreaker result. Similarly, since it is not customary to accept or resolve protests that do not affect the outcome of a game, otherwise meaningless disputes about questions can affect bonus conversion.

Answering tossups in a competitive environment with the other team is a fundamental feature of quizbowl as opposed to any question-and-answer game generally, and many people believe that removing this aspect from tiebreakers or rankings unjustifiably privileges what should be a smaller part of the game. In a related point, being "opponent-independent" is exactly the opposite of what you want when breaking ties in, e.g., a round-robin format where determining who performed better against the set of common opponents is the entire goal.

The disparaging term "cult of bonus conversion" has been used in two related senses:

• For commenters who believe that any tournament in which initial seeding or final ranking does not match bonus conversion rankings is flawed
• For those who overvalue bonus conversion at past tournaments, as contrasted with other data that may be used, when making national rankings

Bonus conversion rankings can inaccurately privilege breadth over depth in extreme situations. Most commonly, a team with very little knowledge in a major category such as science that is slightly better at all other categories than an opponent will usually win actual games against that opponent (since they will generally be expected to outbuzz the opponent on 16 out of 20 tossups) but may have lower bonus conversion (since they can expect 0 to 10 points on 20% of their bonuses).

## Tiebreakers

Bonus conversion is a convenient way to compare teams who did not play the same opponents (e.g. in selecting which teams from different prelim pools receive wild-card playoff spots, or seeding teams from different pools in the playoffs). It is not a logical way to break ties in a round-robin as compared to PPG, since PPG fully incorporates bonus conversion as well as additional commensurable data.