I dont think the answer to this is as simple as all that and/or I dont think we are looking at it the right way.

At first, I was going to agree w/ Miraja, on the basis that if say there was a short field in the derby, say 4 horses, well wouldnt that make it easier to have won say both the derby and Belmont? (W-x-W) And shouldnt we factor that short field in?

But then Im thinking, well doesnt that same logic apply if a horse won only one leg of the TC? Didnt the short field help him win the derby?? A horse that went W-x-x. Isnt that data pt relevant to the question as well?

Perhaps a better way to look at it is this:

Start with a horse that wins the derby, obviously someone has to win the derby. So that doesnt eliminate any horses, we've got the entire set of Ky derby winners to start with. Second step: did this horse win the second leg? Okay so we've got say 25 horses win the second leg and 50 did not. And then we look at average field size. Third step: Take the horses that won two legs and did they win the 3rd leg? again what percentage and what field size...YOu are going to get two numbers from this process but so be it...

This way you would still be factoring those horse from the "Miraja set" i.e. those that won the first and third (Win-x-Win)...Only we would have factored them in when we did step two (the question of did they win the second leg?).

RIght? SO what is then the objection Miraja? SUrely you wont argue that we used equally horses that went W-x-x (Won-didnt-didnt) as those that went W-x-W (Win didnt Win)

You would be arguing that the data pt. of horses that won derby/Bel is more important then the horse that merely won the derby only (Won-x-x). Are you going to argue that the data set of horses that won the derby only does not matter to the question?

See? Thats the fallacy in your reasoning; you are assuming that the data set of W-x-W is more important then the data set of W-x-x. But it is not.

Why not? Because those horses that Won the derby but lost Preakness were also possible TC winners. The fact that they did not win at Belmont does not alter the fact that at one pt. they were possible TC winners.

Take Fu Peg. He won derby, lost PReakness, did not compete at BElmont. Are you saying he does not count as a data pt? WHy not? HE could have won the TC. What if the field for Preakness was only 3 horses? And say Fu Peg won? Obviously the field size of Preakness affected Fu PEg's chances.

ANd it follows, therefore that the field size of Preakness affected the TC chance of every horse that won the derby.

The entire fallacy in the reasoning is not that W-x-W is not a valid data set, it is relevant, the fallacy is in assuming that winning two races is more relevant that winning the derby only. It is not.

THe original post started with the assumption that he would only count those horses that won 2 legs of the TC. What was the reason? The poster does not say, presumably he doesnt want to deal with all the data pts. Then most of us assumed that that made sense as 2 legs are better than one.... But it's really a bad assumption.

To ask the question: HOw does field size affect TC chances? One has to look at those horses won only the derby..I.e. those that only one the first leg. Obviously field size in Preakness affects their chanes for the TC How can you argue that?

Side note: YOu will have to toss out the 1985 series as Spend a BUck did not compete in the second or third legs of the TC.