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WASTAGE AND VARIANCE

Posted By: Timothy Chow
Date: Tuesday, 19 October 2010, at 3:02 p.m.

In Response To: WASTAGE AND VARIANCE (Ray Kershaw)

The idea behind these concepts is that raw pip count alone (let's call this number P) is not enough to tell us how well we're doing in the race. Two positions may have exactly the same raw pip count yet one may bear off much more quickly than the other.

Trice championed the idea that instead of the pip count P, one should consider the number of rolls needed to bear off. Let me call this number R. The advantage of R is that it is a much more accurate measure than P of how you're doing in the race. A disadvantage, of course, is that it's far from obvious how to compute R, and if you can't compute something then it's useless for all practical purposes. A second disadvantage—or at least a complication—is that R is not a fixed, constant number; it is a random variable because of the randomness of the dice.

Wastage and variance are concepts that we use to get a handle on these difficulties. Wastage is the difference between P and the average value of R times the average number of pips in a roll. Trice (and others?) have developed ways of estimating wastage over the board. By adjusting the raw pip count P according to these wastage formulas, we get a good estimate of the average value of R. In general, high-wastage positions are those with lots of checkers bunched up on your low points. The pip count is low but the number of rolls needed to bear off is much higher than the pip count alone would indicate.

Wastage alone will get you a long way, if you get good at estimating it. However, wastage takes into account only the average value of R, and does not take into account the variance of R, meaning how much R might deviate from its average value in a particular game. If all your checkers are on your 1-point then you'll never miss and so R won't vary much from its average value. But if your checkers are far from home then the variance of R will be higher.

So back to your original question:

high-wastage low-variance: all checkers on 1 point

low-wastage high-variance: all checkers far from home

high-wastage high-variance: a big stack in the outfield and a big stack on your 1 point

low-wastage low-variance: this is harder to come up with, but some positions with just a few checkers remaining might qualify.

Messages In This Thread

• WASTAGE AND VARIANCE
  Ray Kershaw -- Tuesday, 19 October 2010, at 11:49 a.m.
  • WASTAGE AND VARIANCE
    Maik Stiebler -- Tuesday, 19 October 2010, at 1:03 p.m.
    • WASTAGE AND VARIANCE
      Bob Koca -- Tuesday, 19 October 2010, at 7:05 p.m.
      • WASTAGE AND VARIANCE
        Maik Stiebler -- Tuesday, 19 October 2010, at 7:40 p.m.
  • WASTAGE AND VARIANCE
    Tom Keith -- Tuesday, 19 October 2010, at 2:01 p.m.
    • WASTAGE AND VARIANCE
      Maik Stiebler -- Tuesday, 19 October 2010, at 2:23 p.m.
      • WASTAGE AND VARIANCE
        Tom Keith -- Tuesday, 19 October 2010, at 2:56 p.m.
  • WASTAGE AND VARIANCE
    Timothy Chow -- Tuesday, 19 October 2010, at 3:02 p.m.