The theory behind this stat is somewhat similar to PATH and another stat that I've previously worked out, but a little more comprehensive. It's based on a simple measure:
Teammate buzzes are equal to the number of teammate 15s + 10s + -5s. The above measure can be conceptualized as player tossups converted when the player is playing one-on-four against the other team and the packet (the denominator is equal to opponent tossups converted plus dead tossups). I think this is a reasonable way to isolate individual performance, and it's very similar to the idea behind PATH.Equation 1) individual tossup percentage
player tossups converted / (tossups heard - teammate buzzes)
From there, I thought to compute four measures, each normalized to a twenty-tossup sample. Two are very simple: The number of points added for getting 15s, and the number of points subtracted for getting -5s (only accounting for the marginal point value of the two).
This computes the value of all of those five-point bonuses that come along with a 15.Equation 2) value of 15s
5 * (number of 15s / (tossups heard - teammate buzzes)) * 20
This computes the value of all of those five-point penalties that players incur on -5s.Equation 3) deduction of -5s
-5 * (number of -5s / (tossups heard - teammate buzzes)) * 20
The third value is also fairly simple: It simply computes the raw positive value of getting a tossup:
The logic here is that a player's buzz (with the five-point power reward already taken care of above) is worth 10 points plus the expected PPB.Equation 4) value of raw tossups
(10 + team PPB) * (player tossups converted / (tossups heard - teammate buzzes)) * 20
The final calculation measures the value of expected points taken away by a player's negs. The better a team, and the better a player's teammates, the more detrimental a player's negs are.
The four terms in this equation can basically be thought of as:Equation 5) deduction of -5 opportunity cost
(team tossups answered / (tossups heard - player buzzes)) * (number of -5s / (tossups heard - teammate buzzes)) * (10 + team PPB) * 20
The final stat sums the results of Equations 2 through 5 above to get what I would say amounts to "expected player points contributed against four average players in the field over twenty tossups, if the player in question were the only one able to buzz on his/her team but the rest of the teammates could consult on bonuses."chance that teammates get the tossup if other players don't buzz * player -5 percentage * (10 + expected PPB) * 20