mr jfc
personally i do not think you can say that you expect horse to win 1/N without giving it 1/N chance. yes i paraphrase your words here but i think intelligent people will understand my point. in the context we talk "expect" and "chance" are related. i agree not exactly the same but related. however let us agree to disagree on this point. it is irrelevant to discussion.

you say that
this is the crux of the problem with your figures and why they are flawed. let us say we pick horse A that has 10 races and each race has field of 10. you calculate you expect it to win 1/10 for each race and therefore you expect it to have won 1 race by the end of those 10.

now. what if horse A is favorite in each race. your calculation still expect it to have won 1 race of the 10.
now. what if horse A is donkey and start at 200/1 in each race. your calculation still expect it to have won 1 race of the 10.
your calculation put Lonhro in 10 maiden races at taree and expect him to win only 1.

this is where your expected figures are flawed. using 1/N takes no account of ability of horse. extend this to a group of horses and the figure take no account of ability of that group of horses. your figure of 1/N whether you like it or no is just like a "participation rate" figure - very similar (but better calculated) than impact value.

if you really want to analyse "actual versus expected" then you need to calculate expected taking into account ability and actual chance of horse to win each race. this is what Nick do. when you do this then you will find some very interesting statistics.
Thank you. Winston.