perhaps this has been sufficiently explained by the above posters, but it might help to think about it explicitly in terms of how gear ratios and skid patches are related. hopefully this is helpful to some degree and not condescending or overexplanatory. people with whom i talk in person often have a hard time understanding exactly why certain ratios result in more skid patches. hopefully this is fairly comprehensive.

okay, so, when you rotate your cranks one time, the number of times that your rear wheel rotates is determined by your gear ratio. the harder the gear, the more times your wheel will rotate per crank revolution. if, for example, you have 48x16, your ratio is 3.0. that means that your rear wheel goes around exactly three times for every one time that your cranks go around once.

when you skid, you are generally most comfortable doing so with the cranks in one position (say, with the pedals at 4 and 10 o'clock). some people can skid with either foot forward, giving them two positions (and, ultimately, double the skid patches*). this explanation assumes one position.

so, as stated above, when you pedal one revolution, your wheel goes around a certain number of times. in the example given above - 48x16 - the wheel goes around exactly three times, making it so that the same part of the tire is on the ground whenever you are in a given crank position. so, when i skid on my 48x16 setup in the 4x10'oclock position, i am always sliding the same part of my tire against the pavement. that is why 48x16 gives you one skid patch. more generally, any time you have a chainring size that can be divided evenly by your cog size, you will have one skid patch.

however, when you start to have ratios that don't divide evenly, you are not always skidding on the same part of the tire. take, for example, 52x16. every time you pedal the cranks around one time, you are moving the wheel 3.25 times. so, say you skid once, rotate the cranks once, and then skid again. unlike 48x16, you will now be skidding on a different part of the tire. if you were to map out the circumference of the tire, mark a point, and then go around 3.25 times, you would be at a different spot. 52x16 ends up giving you 4 skid spots, which, while better than 48x16, isn't too great. some ratios can give as many skid patches as there are teeth on the cog (or more, if you assume that there are positions between teeth).

so, you might ask, how do you calculate the number of skid patches? well, if you noticed, when you divided 52x16, you ended up with a remainder. that is, 16 fits into 52 three times and then some. as a matter of fact, it ends up going into 52 three and one-quarter times. when you do the long division, you end up with 3 remainder 4. in order to find the number of skid patches, you take that remainder and divide the cog size by it. so, in this case, you divide 16 by 4 and get the result of 4 skid patches. if you were to take your map of the wheel and go around it 4 times, you would see that you end up where you started.

of course, not all ratios will yield a remainder that divides evenly.

<<****tt, my work day is over and i didn't get to finish this post... i'll come back and finish it later...>>

*although, once you get above 7 or so skid patches, they will start to overlap, making additional patches less effective. this is, of course, because you don't skid on a single point, but, rather, a few inches of space on your tire.