# Explanations

General explanations for most of the statistics used on this webiste.

##### Skiing data

*Course Times* are used for most skiing statistics. The Course Time (or ski time) is the total race time without range and penalty time. Course Times are available since the 2001–02 season.

**Ski Rank (avg):**

` `*Course Time* rank average

**back from median (in %):**

`Arithmetic mean of percent back from each race's median `*Course Time*

**back from Top10 median (in %):**

`Arithmetic mean of percent back from each race's top 10 median `*Course Time*

**back from Top30 median (in %):**

`Arithmetic mean of percent back from each race's top 30 median `*Course Time*

**back from average (in %):**

`Arithmetic mean of percent back from each race's average `*Course Time*

**back from Top10 average (in %):**

`Arithmetic mean of percent back from each race's top 10 average `*Course Time*

**back from Top30 average (in %):**

`Arithmetic mean of percent back from each race's top 30 average `*Course Time*

**Speed (in km/h):**

` Arithmetic mean of each race's speed: (Total `*Course Length* - 170m per Shooting) ⁄ Total *Course Time*

**Z-score:**

` (Standard score) Number of standard deviations by which `*Course Times* are above or below the mean (based on *back from median* data)

##### Shooting data (hit rates)

In accourdance with IBU conventions, only shots of completed races are counted.

**back from average (in %):**

`Arithmetic mean of percent back from each race's average `*Total Hit Rate*

**back from median (in %):**

`Arithmetic mean of percent back from each race's median `*Total Hit Rate*

**Z-score:**

` (Standard score) Number of standard deviations by which the `*Total Hit Rate* is above or below the mean.

*Note*: The three values above are multiplied by −1 to keep hit rate statistics comparable to all other (time based) data.

##### Shooting Time

*Shooting Time* is the time spent on the shooting mat. Shooting Times are available since the 2001–02 season.

**Rank (avg):**

` `*Shooting Time* rank average

**back from median (in %):**

`Arithmetic mean of percent back from each race's median `*Total Shooting Time*

**Z-score:**

` (Standard score) Number of standard deviations by which the `*Total Shooting Time* is above or below the mean

##### Range Time

*Range Time* is the time between entering and exiting the shooting range. Range Times are available since the 2001–02 season.

**Rank (avg):**

` `*Range Time* rank average

**back from median (in %):**

`Arithmetic mean of percent back from each race's median `*Total Range Time*

**Z-score:**

` (Standard score) Number of standard deviations by which the `*Total Range Time* is above or below the mean

*Note*: Before 2011–12, *Range Times* included time spent in the penalty loop and are not comparable to current values.

##### Shooting Efficiency

The *Shooting Efficiency* is an overall shooting score, combining shooting accuracy and shooting time. It is the theoretical average time an athlete loses through shooting (based on hit rate, range time and potential penalty loops).

**Range Time + Penalty Time:**

`Arithmetic mean of sums of Range Time and Penalty Time `

**Time Loss Sprint:**

`(1 - `^{Hit Rate }⁄_{100} ) · 10 · *Penalty Loop* + 2 · *Range Time*

**Time Loss Pursuit/Mass Start:**

`(1 - `^{Hit Rate }⁄_{100}) · 20 · *Penalty Loop* + 4 · *Range Time*

**Time Loss Individual:**

`(1 - `^{Hit Rate }⁄_{100}) · 20 · *1 minute* + 4 · *Range Time*

For **team events** no theoretical time loss is calculated (because spare rounds do not allow a clear separation of hit rate and range time), instead the sum of *Range Time* and *Penalty Time* is used for shooting efficiency.

##### Performance Score

The *Overall Performance Score* quantifies biathlon performances solely based on ski speed, shooting percent and range time, not considering any actual race results.
The Total Performance Score is calculated by approximating the importance of skiing, hit rate and shooting pace
using the method of least squares (for more details, see here and here),
and then weighting each z-score value accordingly.

**Ski Speed Score:**

`z-score of percentage back from median `*Course Times*

**Hit Rate Score:**

`z-score of `*Total Hit Rate*

**Range Time Score:**

`z-score of `*Total Range Time*

**Total Performance Score:**

`Weighted aggregate Z-score `

**Non-Team events:**

`0.59 · Ski Speed + 0.29 · Hit Rate + 0.12 · Range Time `

**Individual:**

`0.50 · Ski Speed + 0.45 · Hit Rate + 0.05 · Range Time `

**Sprint:**

`0.65 · Ski Speed + 0.25 · Hit Rate + 0.10 · Range Time `

**Pursuit:**

`0.55 · Ski Speed + 0.32 · Hit Rate + 0.13 · Range Time `

**Mass Start:**

`0.52 · Ski Speed + 0.35 · Hit Rate + 0.13 · Range Time `

**Relays/Team events:**

`0.60 · Ski Speed + 0.16 · Hit Rate + 0.24 · Range Time `

**Non-Team (before 2014–15):**

`0.62 · Ski Speed + 0.25 · Hit Rate + 0.13 · Range Time `