Duritz,
This is where Handicapping, pricing (assigning probabilities) betting overs and winning starts.

The key to understanding handicapping is to realize that you can only get so good at handicapping.

Once I get to the point where my probabilities are ACCURATE, then there is absolutely no point in working any more to improve my handicapping. If the probs are accurate, I'm done with improving my overall handicapping skills.

The natural question is, "how do you know the probabilities are accurate?" Well, you cannot test any one race for accuracy. What you do is to handicap a lot of races, and test your overall statistical accuracy. And you do it in a way that gives you great security that the method you are using IS accurate... for EVERYTHING you are doing.

Here's how you do it. First, you use some method to handicap a fairly large number of races. Obviously, the larger the sample, the better you know the accuracy of your handicapping. For now, let's say we handicap 1,000 races. Then you pick out any ONE probability. Let's say we choose the probability that the #1 runner will finish in first place. You take your probabilities for that cell in all 1,000 races, and add up those numbers. (Like .1341 (from above) + .2341 (from the second race) + .1254 (from the third race) and so on. Just add up all 1,000 probabilities that you have calculated. You'll end up with some number, like 156.7342. What that tells you is, for those 1,000 races, according to your probabilities, the #1 runner should have won about 157 times. Then you simply add up the ACTUAL number of times the #1 runner won in those 1,000 races, and compare it to your sum of probabilities. The closer you are, the more accurate your overall handicapping.If you find this hard to grasp, think of it like this. Let's say you have a runner in a race with a 25% chance of winning. That's 0.25, right? Now let's say you have four such races, with one runner in each with a 25% chance of winning. When you add those up, it's .25+.25+.25+.25=1.00. So you would have expected, in four races, that your #1 runner would have won once, on average. (Just what you would expect from 3-1, right?) If you DID have one winner in those four races, you know you're on target, and your probability estimates are right! Cut me some slack on the small sample size. This doesn't really work well with 4 races, but it DOES work just fine with 400 or 4,000. My method is extended to measure dozens of probabilities across hundreds or thousands of races.

Now, that tells you how accurately you have built probabilities for the #1 runner winning. But you should do the same thing for EVERY ONE of the probabilities you have calculated. So I add up the probabilities I calculated for the #5 runner finishing in 8th place, and then check that number against the REAL number of times the #5 finished in 8th place. And so on. You end up with a big matrix that shows you exactly how accurate your handicapping really is.

To measure your overall accuracy, you use a statistical technique called "variance." (Check out any beginning statistics book to understand variance.) Basically, variance measures how far your probabilities are AS A GROUP IN TOTAL from the real results. (Basically, it's the square root of the sum of the squares of the differences between your expected probabilities and the observed percentages.) So you can calculate the variance of the probabilities from the actual results, and you will get some number for that calculation.

Then the exercise becomes to continually try to improve your handicapping. As you improve, the variance will go steadily down. In a perfect world you would keep working at improving your handicapping until your variance is zero, but that's not possible, of course, in the real world. So you work at it until you get to a variance that's reasonable, or until you can't find any more ways to improve your handicapping.

Now another cool part of this is that you can use the exact same technique to measure how accurate the CROWD'S handicapping is, and compare that to your own handicapping as a benchmark. Just change the post-time odds into probabilities, and use the same method! Of course you can also test different handicapping TECHNIQUES to see what works and what doesn't.
Now all this is based on the idea that you can only get so good at handicapping. After all, races are governed by probabilities, and not certainties. Every single runner that races has some real, finite chance of finishing in first place. And a chance of finishing in second, and in third, and in all places including eighth. Granted, they may have a BETTER chance of finishing in one spot or another, but they have SOME probability of finishing in any position.

Further, you must understand that no amount of handicapping can ever get you to the point where you can know perfectly how any given race will finish. You can make projections based on your handicapping, but you cannot KNOW how each race will finish. Your goal becomes to minimize your variance across a very wide range of races, and individual statistics. Once you get it to a minimum, there's no reason to continue trying to improve your handicapping.

So, how do you know when to stop? Actually, that's very easy. Probabilities are a "zero-sum" game. That is, if you look at all possible outcomes of something, their probabilities have to add up to 1.000 or 100%. Let's say you handicap a race, and assign win probabilities to all the runners. If they don't add up to 1.000, you've done something wrong!

But let's say the DO add up to 100%. Your handicapping can now be either good or poor. Let's say it's poor. You've given a runner a win probability of .33 when it SHOULD be .25. You say he'll win more often than he actually would for real. Well, because probs are a zero-sum game, if you OVERESTIMATE one runners chances, you must have UNDERESTIMATED one or more OTHER RUNNERS' chances!

Let's relate this back to the variance method above. Let's say you handicap 1000 races, and your probabilities say you should have the highest-probability runner winning 281 races. If they ACTUALLY won 241, you've overestimated their probabilities. Well, if you look at the OTHER finish positions, you'll find that one or more of them must have been UNDERESTIMATED. So to determine if your handicapping is as good as is possible, you keep working until the differences ON ALL POSSIBLE FINISHES are roughly equal. If you are off by about an equal amount on every possible probability, then you know that your handicapping CANNOT GET ANY BETTER! If, however, you have one or a few segments that show higher and lower variance than average, then you know your handicapping can still improve some.

Amen