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Kazaross/Rockwell MET Formulas

Posted By: Chase
Date: Wednesday, 31 March 2010, at 2:56 a.m.

In Response To: Kazaross/Rockwell MET Formulas (Bob Glass)

I compared the results of Neil's Numbers, the Janowski, Turner, and Merrigan formulas, as well as a modified Merrigan formula (see below), to the R-K MET up to 11-point matches. I don't have anything in any kind of format that I can easily share and I'm not going to take the time to put it all together, but I can summarize what I came up with.

First, none of the formulas handle things very well when the leader is 2-away, so I ignored that line of the table. That leaves 36 relevant entries, since half the table mirrors the other. Second, I rounded off all calculations, so when I say an entry is off by one percent or two percent, it's sometimes a little less. Third, all formulas overestimate the -3/-4 entry by 2 percent, giving it as 59%, which agrees with H-W, rather than the R-K value of 57%.

Here's what I found:

* Neil's Numbers missed 10 entries by 1 percent and 1 entry by 2 percent.

* Janowski missed 6 entries by 1 percent and 1 entry by 2 percent.

* Turner missed 15 entries by 1 percent and 2 entries by 2 percent.

* Merrigan missed 23 entries by 1 percent and 2 entries by 2 percent.

* Modified Merrigan (see below) missed 13 entries by 1 percent and 0 entries by 2 percent.

* Hybrid Merrigan (see below) missed 6 entries by 1 percent and 0 entries by 2 percent.

So the Janowski formula does best overall. However, it's the most difficult to use (which is why the other formulas were derived.)

The original Merrigan formula is:

92 - D
--------- * D + 50
6 + T

where:

D = the difference between the leader and trailer.
T = the distance the trailer is away from winning the match.

What I noticed is that (for the relevant entries) the misses are always 1% too high. The formula is more accurate overall if 49 is used in the above formula rather than 50. Furthermore, the misses in this "modified Merrigan formula" tend to be highly concentrated within an area of the table -- specifically, when the leader is less than 6-away and the trailer is more than 8-away.

What this means is that the original Merrigan is very accurate within that area of the table, while the modified Merrigan is very accurate for the rest of the table. Being able to apply the appropriate version of the formula will leave you with only 6 misses, all of which are within 1 percent. (The errant 2% entry at -3/-4 mentioned above is reduced to a 1% error.)

This approach obviously isn't as elegant as having one universal formula, but if you're willing to work with an inelegant "hybrid" solution, you get a tiny bit more accuracy. The big upside, however, is that Merrigan is a lot easier to work with than Janowski for most people.

Caveat: I don't guarantee any of this, so before you commit to an approach, check it out for yourself (and please call any errors to my attention).

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