So far we "only" leveraged the Khmelnitsky test data, in a rather straightforward way. Let's now explore a more hazardous area: try to standardize the data, introducing the knowledge we have thanks to the Wiki-Elo-List.
As the KT results do comply with the rule of thumb (constant Elo gain per doubling), to my understanding we only need a shift in the KT score to better align with the Wiki-Elo-List (meaning: add a constant value).
Do you remember the polynomial formula displayed above? We juste need to substitute a better value to the final constant (and keep the x² and x part of the formula unchanged).
So far, the scope of the test only includes two devices for which the Wiki-Elo-List provides values: the fast MephiIIIS and the Ph.Revelation. But we have a third device with a known Elo within the list: the Ph.Revelation II. Let's use it as well, as the polynomial formula can provide an estimate for its KT Elo:
Code:
SMhz Constant-free Wiki Elo Delta Standardized KT Elo
IIIS Glasgow 7.2 0.0 1701
IIIS Glasgow 12Mhz 12 53.2 1707 1653.8 1754
Phoenix Revelation 38 165.6 1900 1734.4 1866
Phoenix Revelation II 109 259.0 1973 1714.0 1960
Phoenix Revelation II AE 196 307.2 2008
Phoenix Reflexion 1,5Ghz 244 324.4 2025
Phoenix Reflexion 1,7Ghz 272 332.8 2034
Mephisto Phoenix 480 375.3 2076
average delta: 1700.7
The "constant-free" formula is -21.3015036253151*LOG10(SMhz/7.2)^2+244.626198127018*LOG10(SMhz/7.2)
(see above formula within the graph)
The delta is the Wiki-Elo minus the constant-free value; from which an average value is calculated.
The standardized KT Elo is of course the same polynomial pattern with the average delta as a new constant: -21.3015036253151*LOG10(SMhz/7.2)^2+244.626198127018*LOG10(SMhz/7.2)+1700.7
This provides this new graph with "better" Elo values (better meaning standardized according to the Wiki-Elo-List data available so far):
'x' is still a bit of a complicated value (log of the speed ratio), so let's expand the x axis to the SMhz (speed in Mhz) value, and add a logarithmic regression curve to get a less cumbersome formula:
New formula displayed: 89.7821030247115*LN(SMhz)+1531.25499276664
or, should you prefer the log function: 206.730932042356*LOG10(SMhz)+1531,25499276664
Resulting tab, using either of the above:
Code:
IIIS Glasgow 1708
IIIS Glasgow 12Mhz 1754
Phoenix Revelation 1858
Phoenix Revelation II 1952
Phoenix Revelation II AE 2005
Phoenix Reflexion 1,5Ghz 2025
Phoenix Reflexion 1,7Ghz 2035
Mephisto Phoenix 2086