Crag Score Base Calculation
Introduction
Crag Score was developed by www.thecrag.com as an objective way of assessing a climber's ability relative to the climbing community as a whole. Free climbs completed by a climber are each assigned a statistically derived value, which is then summed to give a climber's Crag Score base value.
For further rating purposes additional weightings are provided taking into account style, how long ago, and repeat ascents. The additional weightings are covered in another article Crag Score Ratings. The remaider of this article covers the base calculation for Crag Score.
The benefit for climbers is they can see how they are progressing relative to the climbing community. Using a time series graph, climbers achieving higher grades will see their Crag Score increase over time.
The Crag Score provides an unbiased system for ranking climbers' performance universally, at a particular crag, or in comparison to a sub-set of climbers. It will also be a powerful tool for climbers to chart their progress through time and ultimately to plan specific and realistic training and development schedules to work towards their climbing goals.
Basis of Calculation
The methodology used to derive climb Crag Score values compares a climb's grade/rating with the overall community's ability to climb that grade. This gives rise to dynamic scores, which will change over time as the community becomes better (or worse) at climbing that grade.
Clearly higher graded climbs should attract higher scores, but by how much? Exactly how much harder is a 5.11b than a 5.11a? What about a 5.12a compared to a 5.11d? One grade harder right?
The Crag Score methodology answers this question by looking at how many climbers, within the community, climb a particular grade compared to any other grade. If twice as many climbers have done a 5.11d compared to a 5.12a then the 5.12a is assumed to be twice as hard (ie double the Crag Score).
To assess relative difficulties between climb grades the Crag Score requires knowledge of the grade profile of climbs done for all grades for the whole climbing community. Figure 1 shows a hypothetical grade profile for the climbing community using the Yosemite Decimal System (YDS) grades.
Figure 1: Grade Profile Sample for Overall Community Ticks
The Community
To determine the grade profile in Figure 1, a sample community representative of the whole community was used. For the Crag Score, the sample community is www.thecrag.com's members. Climbers of all levels subscribe to www.thecrag.com in order manage, track and chart climbs they have done. They do this by ticking climbs (ie adding climbs to their account) as they browse a comprehensive index of climbs.
Membership attracts an unbiased demographic with regards to climbing ability. It should be noted that there are geographic biases as membership tends to build up quickly around geographic areas where a comprehensive index of climbs has been installed. It is also probable that membership may skew to the younger end because by definition members are confident and competent users of the Internet. Any such biases will diminish over time as the member base expands.
Statistical Derivation
The statistical derivation of the Crag Score uses the grade profile of climbing community ticks, similar to the sample in Figure 1. This is then converted into a distribution vector. In the conversion, any grade easier than the most commonly climbed grade (eg 5.9) is assigned a constant value of 1.00, while any grade above is assigned a value in proportion to the grade profile of Figure 1.
The Distribution Vector is then converted to the Crag Score by inverting the Distribution Vector. Figure 2 shows a sample Crag Score by YDS grades.
Figure 2: Sample Crag Score
Note that in practice there are some extra steps to take into account the various grading systems around the world. Also note that the Crag Score by YDS grades shown in Figure 2 is based on hypothetical data only for the purposes of describing the derivation of Crag Score.
Dynamic Score Allocation
A climber's Crag Score is dependent on every other climb completed by climbers in the sample community. That is a climb done by a French climber will affect the Crag Score of a US climber. Practically, however, the effect of a single tick will be far too small to notice.
This means Crag Scores awarded for climbs will change over time. We intend maintaining a file of historic Crag Score data and will produce occasional reports on trends through time.
Climbing Styles
Intentionally, climbing styles (eg onsight and redpoint) are not taken into account in calculating the Crag Score. That is a climb done by top rope will get the same Crag Score as an onsighted climb.
Style independence makes the Crag Score a more valuable tool for self-appraisal based on each individual's own approach and style. It also allows climbers to compare time series Crag Scores between climb styles. Figure 3 shows an example of how a climbers time series Crag Score may look comparing onsights with top ropes.
Figure 3: Climbers Time Series Crag Score for Top Ropes and Onsights
This hypothetical example shows a climber who improved steadily for four years, climbed less for a couple of years then got back into it again, climbing relatively more top ropes as he/she climbs harder. These kind of graphs would not work if Crag Scores were different for different styles.
Example Crag Score Values
Table 1 shows some example actual Crag Score values in February 2003 and April 2006. The calculation is based on about 60,000 and 270,000 distinct climbing ticks respectively from www.thecrag.com subscribers.
Table 1: Actual Crag Score Values
| YDS Rating | Crag Score Feb 2003 | Crag Score Mar 2006 |
| 5.10a | 1.0 | 1.1 |
| 5.11a | 2.2 | 2.1 |
| 5.12a | 10.4 | 6.6 |
| 5.13a | 101.8 | 67.8 |
