Now we come to the part of actually measuring gear size. Because we always use two gears in cycling (a chain ring and a cog), we assess gearing by the ratio between the chain ring and the cog. For instance, if we use an 11-25 cassette with a standard chain ring, our available ratios would be:
53:11 / 53:12 / 53:13 / 53:14 / 53:15 / 53:17 / 53:19 / 53:21 / 53:23 / 53:25
39:11 / 39:12 / 39:13 / 39:14 / 39:15 / 39:17 / 39:19 / 39:21 / 39:23 / 39:25
If you're thinking that this doesn't look very helpful at all, you're right. It's terribly uninformative. We know we have 20 different possible combinations, and now we've given them some ratios to identify them. So what? Ah, so what indeed. If we do some simple division on those ratios, we can express them as more easily read numbers. Take a look at what they look like when we do the conversion.
4.82 / 4.42 / 4.07 / 3.79 / 3.53 / 3.12 / 2.78 / 2.52 / 2.30 / 2.12
3.54 / 3.25 / 3.00 / 2.79 / 2.60 / 2.29 / 2.05 / 1.86 / 1.69 / 1.56
See anything interesting? It looks like some of those numbers are very close to each other. Let's highlight the similarities.
4.82 / 4.42 / 4.07 / 3.79 / 3.53 / 3.12 / 2.78 / 2.52 / 2.30 / 2.12
3.54 / 3.25 / 3.00 / 2.79 / 2.60 / 2.29 / 2.05 / 1.86 / 1.69 / 1.56
Aha! What we discover is that eight out of our 20 possible gear combinations are redundant! In other words, there's virtually no difference between 39:17 and 53:23. Why the redundancy? Well, because of the way your derailleurs align your chain, going with a 53:23 actually causes a situation known as cross-gearing, in which the chain has to bend laterally so much that it increases friction and causes unnecessary wear and tear on your drive system.
More: Intro to Bike Gears
The rule to follow is to always avoid "big-to-big" or "small-to-small." In this case, the 39:17 is the combination you want to achieve this ratio.
In fact, the design impetus to avoid cross-gearing explains the redundancy in gear ratios. Notice that the redundant combinations occur at the extreme upper end for the 53-ring and the extreme lower end for the 39-ring, which are the exact spots you would develop those undesirable "big-to-big" and "small-to-small" situations. Only one of those two ratios is the one you want.
So the next time you find yourself pedaling up a hill or into the wind and shifting between your chain rings as much as your cogs in search of a good gear, take a look and see if you're in a cross-gear situation. If so, decide on a "final answer" for which chain ring you want to use and then finesse your rear derailleur to an appropriate position. Odds are that if you get your gears straight, the rest will sort itself out with a few clicks of the shifter.
Safe (and smart) pedaling!
More: What Are the Advantages of Compact Gearing
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