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In [[numerical analysis]], a '''blossom''' is a [[functional (mathematics)|functional]] that can be applied to any [[polynomial]], but is mostly used for [[Bézier curve|Bézier]] and [[spline]] curves and surfaces.
'''Calculated Match Averages''' (CMAs or averages) are calculated for every [[motorcycle speedway]] rider.


The blossom of a polynomial ''ƒ'', often denoted <math>\mathcal{B}[f],</mathis completely characterised by the three properties:
The CMA is calculated from the following:<ref name="CMA">{{cite web | last = | first = | authorlink = | coauthors = | title = Green Sheet Averages | work = | publisher = Speedway FAQs | date = | url = http://www.speedway-faq.org/british.html#gsa | format = | doi = | accessdate = 2008-03-12 }}</ref>   
* It is a symmetric function of its arguments:
<ref name="Speedway Regulations">{{cite web | last = | first = | authorlink = | coauthors = | title = SCB Speedway Regulations | work = | publisher = Speedway Control Bureau | date = January 2007 | url = http://www.acu.org.uk/uploaded/documents/The%20SPEEDWAY%20REGULATIONS%202007%20Final%20Print%20Version.doc | format = | doi = | accessdate = 2008-03-12 }}</ref>
:: <math>\mathcal{B}[f](u_1,\dots,u_d) = \mathcal{B}[f]\big(\pi(u_1,\dots,u_d)\big),\,</math>
 
: (where ''&pi;'' is any [[permutation]] of its arguments).
<center><math>\left ( \frac{\hbox{Total points}}{\hbox{Total rides}} \right ) \times4</math></center>
* It is affine in each of its arguments:
 
:: <math>\mathcal{B}[f](\alpha u + \beta v,\dots) = \alpha\mathcal{B}[f](u,\dots) + \beta\mathcal{B}[f](v,\dots),\text{ when }\alpha + \beta = 1.\,</math>
CMAs scale from 3.00 to 12.00, any rider scoring above or below these values will be awarded the maximum. These averages are used in leagues such as the [[Speedway Elite League|British Elite League]] to identify heat-leaders for the purposes of choosing which riders to enter for each race.
* It satisfies the diagonal property:
 
:: <math>\mathcal{B}[f](u,\dots,u) = f(u).\,</math>
At the start of a season, a rider retains their last recorded CMA (or assessed CMA if they have never previously established one) until they have competed in six home and six away matches. A new CMA is then issued that comes into effect seven days later. These are subsequently updated on the 15th of every month from May onwards, and come into effect on the 1st of the next month.
 
These CMAs are used in most professional leagues and are altered or weighted depending on the league the rider gained the CMA in. A rider that has no recorded average will receive an indicative CMA for the start of the season that is assessed on their prior experience in the sport.


==References==
==References==
*{{cite paper | author=Ramshaw, Lyle | title = Blossoming: A Connect-the-Dots Approach to Splines | publisher=Digital Systems Research Center | date=1987 | url=ftp://ftp.digital.com/pub/compaq/SRC/research-reports/abstracts/src-rr-019.html | accessdate=2006-06-28}}
{{reflist}}
 
*{{cite paper | author=Casteljau, Paul de Faget de | authorlink = Paul de Casteljau | title = POLynomials, POLar Forms, and InterPOLation | date = 1992 | editor= Schumaker et al. | book = Mathematical methods in computer aided geometric design II | publisher = Academic Press Professional, Inc.}}


*{{cite book | author=Farin, Gerald | title = Curves and Surfaces for CAGD: A Practical Guide | year = 2001 | publisher = Morgan Kaufmann | edition = fifth | isbn = 1-55860-737-4 }}
[[Category:Motorcycle speedway]]


[[Category:Numerical analysis]]
[[pl:Kalkulowana średnia meczowa]]

Revision as of 16:06, 17 August 2014

Calculated Match Averages (CMAs or averages) are calculated for every motorcycle speedway rider.

The CMA is calculated from the following:[1] [2]

CMAs scale from 3.00 to 12.00, any rider scoring above or below these values will be awarded the maximum. These averages are used in leagues such as the British Elite League to identify heat-leaders for the purposes of choosing which riders to enter for each race.

At the start of a season, a rider retains their last recorded CMA (or assessed CMA if they have never previously established one) until they have competed in six home and six away matches. A new CMA is then issued that comes into effect seven days later. These are subsequently updated on the 15th of every month from May onwards, and come into effect on the 1st of the next month.

These CMAs are used in most professional leagues and are altered or weighted depending on the league the rider gained the CMA in. A rider that has no recorded average will receive an indicative CMA for the start of the season that is assessed on their prior experience in the sport.

References

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pl:Kalkulowana średnia meczowa