Following up on my last post, the z-scores for last season’s basic statistics are also a good tool to take a more theoretical look at biathlon. One of the things which always interests me on a general level is the question: what is more important, skiing or shooting?

The two charts show the z-scores for median ski speed and shooting efficiency (a.k.a. lost time at the range) for all 2013–14 World Cup starters (arranged by World Cup rank). The men’s and women’s chart is quite similar in how skiing and shooting seemingly influences the Overall World Cup rank. Generally, the performances get worse the farther down the rankings you go (as you would expect), however, it appears the higher ranked half of the World Cup field, on average, is better at skiing, while the bottom half are better shooters than skiers (per definition, negative values are good, positive values are bad here).

In order to quantify the effect that skiing and shooting has on an athlete’s World Cup rank, I came up with the idea to interpret the three sets of data – ski speed, shooting efficiency and World Cup rank – as a **system of linear equations** (all in z-scores). I don’t want to go into too much detail, but I explained it a bit more here before.

Mathematically speaking, the system is *overdetermined*, i.e. there are more equations than unknowns, and *inconsistent*, i.e. it has no solution. However, using the method of least squares, you can find an **approximate solution**. The ratio between the least squares coefficients indicates the approximate influence of these elements (here the influence of skiing and shooting for the World Cup rank).

Men |
Women |
|||

Skiing | Shooting | Skiing | Shooting | |

Top 20 |
54.8 | 45.2 | 61.1 | 38.9 |

Top 40 |
57.9 | 42.1 | 56.3 | 43.8 |

Top 60 |
65.8 | 34.2 | 61.4 | 38.6 |

Top 100 |
61.2 | 38.8 | 65.2 | 34.8 |

All |
66.1 | 33.9 | 66.2 | 33.8 |

average |
61.2 |
38.8 |
62.0 |
38.0 |

for Overall World Cup rank (in %) |

**2013–14**

For last season, all groups I looked at, both male and female, produced pretty consistent results. On average, skiing (61%-62%) was the more important factor for the World Cup rank than shooting (38%-39%). For both genders, skiing has the biggest influences if you look at where an athlete is ranked among the entire field; shooting gets slightly more important for smaller groups (most among the men’s top20 → 45%). However, the fewer athletes (i.e. linear equations) you take into account, the less robust and more random the results get.

Taking it one step further, I split up general shooting into shooting accuracy and shooting speed (range time). This leads to a linear system with three unknowns (ski speed, shooting % and range time), and the influence of each category can again be approximated with the least squares coefficients’ ratio.

The results you get for three elements are very consistent with the results above: the influence of skiing for the World Cup rank is at about 60% (on average). The shooting accuracy is more important (about 25%) than the shooting pace (about 15%). Still, the range time is probably a lot more important than you would expect (especially compared to shooting percentage). Again the results for men and women are very similar.

Men |
Women |
|||||

Skiing | Shooting % |
Range Time |
Skiing |
Shooting% |
Range Time | |

Top 20 |
52.0 | 30.5 | 17.5 | 59.2 | 25.1 | 15.7 |

Top 40 |
60.1 | 23.8 | 16.1 | 53.8 | 24.1 | 22.1 |

Top 60 |
67.7 | 23.6 | 8.7 | 57.4 | 21.0 | 21.5 |

Top 100 |
64.3 | 23.9 | 11.8 | 60.9 | 20.6 | 18.5 |

All |
60.0 | 27.5 | 12.4 | 64.2 | 27.0 | 8.8 |

average |
60.8 |
25.9 |
13.3 |
59.1 |
23.6 |
17.3 |

for Overall World Cup rank (in %) |

**2013–14**

All of this is only a very imprecise approximation of course, based on a small sample size (no group is larger than 200 athletes). However, the fact that the results, which are highly theoretical, are quite similar across all groups and genders, might be an indication there is some merit to it. Also, using a sightly different method, I got results along the same lines in the past (then 65-35, now 60-40). Using z-scores should be methodologically more sound though.

The fact that shooting is equally important for men and women is actually surprising, because women must ski a longer penalty loop relative to their total course length. Shooting penalties should have a bigger effect in female competitions, however the larger skiing differences among women apparently compensates for that perfectly.