Statistical Measure of Event Bombs

[Unome]

I spent some time working on a statistical measurement of event bombs, after figuring out that bidirectional measures such as standard deviation aren't quite as useful for this purpose. A description of the process I used:

Inputs - a team's ranks in each of the scored events, and a critical value between 0 and 1. Multiply the team score by the critical value to get the target value. Subtract the largest rank from the target value, and repeat this with the next largest value, etc. until doing so would bring the value below zero. Take the remainder and divide it by the next largest rank, and add the result to the number of subtractions made. Divide this value by the maximum possible value for this, which is the critical value multiplied by the number of scored events, to get the final statistic

I've attached a spreadsheet that calculates the statistic, in case anyone wants to use it/cares. It can be fairly easily replicated in most programming languages (I made an attempt with Java).

Generally, values for the weakest teams tend to range around 0.9 or so, since they're basically just finishing low in most or all of the events. Generally, I would consider anything under 0.4 or 0.35 to indicate significant event bombs. The lowest value that I found was around 0.15, for Piedmont IB Middle School at the NC State Tournament last year.

I have no idea what one would use this statistic for, but I found it interesting so I thought I would share it

[PM2017]

I spent some time working on a statistical measurement of event bombs, after figuring out that bidirectional measures such as standard deviation aren't quite as useful for this purpose. A description of the process I used:

Inputs - a team's ranks in each of the scored events, and a critical value between 0 and 1. Multiply the team score by the critical value to get the target value. Subtract the largest rank from the target value, and repeat this with the next largest value, etc. until doing so would bring the value below zero. Take the remainder and divide it by the next largest rank, and add the result to the number of subtractions made. Divide this value by the maximum possible value for this, which is the critical value multiplied by the number of scored events, to get the final statistic

I've attached a spreadsheet that calculates the statistic, in case anyone wants to use it/cares. It can be fairly easily replicated in most programming languages (I made an attempt with Java).

Generally, values for the weakest teams tend to range around 0.9 or so, since they're basically just finishing low in most or all of the events. Generally, I would consider anything under 0.4 or 0.35 to indicate significant event bombs. The lowest value that I found was around 0.15, for Piedmont IB Middle School at the NC State Tournament last year.

I have no idea what one would use this statistic for, but I found it interesting so I thought I would share it

Oh, trust me, this is useful (deciding teams, making yourself feel bad when you get crushed by Troy and other teams like CCA at states, etc.)

[y1008083]

How do you calculate the critical value?

[Unome]

How do you calculate the critical value?

It's not calculated. It's the proportion of the team score that will be counted to (so 0.5 is essentially asking, how many of the team's worst events contributed to 50% of their points, and then divides that number by the most event result, which is the critical value times team score).

[jaymaron]

Plot rank on the X axis logarithmically. The Y axis is linear, and it shows points, normalized so that the rank #1 team gets 1 point. A sensible score function is a straight line in the plot. The Science Olympiad function is goofy.

A natural point function that handles both high-ranked and low-ranked teams is:

Points = log_2(Players/Rank)

Where "Players" is the number of players in the field. This function produces a straight line in the plot. For Players=64, the function gives:

Rank Points
1 6
2 5
4 4
8 3
16 2
32 1
64 0

Expanded discussion in https:/jaymaron.com/scioly.html#score

The un-normalized point functions are:

Rank World F-1 Indy NASCAR Tennis Golf Bowling Tour de Science
Cup ski ATP PGA PBA France Olympiad

1 100 25 50 10 2000 600 7500 50 60
2 80 18 40 9 1200 330 4500 30 59
3 60 15 35 8 720 210 3450 20 58
4 50 12 32 7 720 150 2850 18 57
5 45 10 30 6 360 120 2550 16 56