I come back to the old adage of the books trying to balance action, especially on RL's... This means that the true runline is forgotton in the mix, in reality of course the RL is:
P (Royals +1.5) = P (Royals Win) + P (Yanks by 1 | Yanks Win) -- adjusting for totals, home advantage..
Let's try a real-world example..
The White Sox are home favourites on Sunday against the Cleveland Indians. They are favourites of the magnitude -124, or are expected to win the game 55.3571% of the time...
Pinny currently have the following:
CLE +1.5 -206
CHA -1.5 +186
In theory:
P (CLE +1.5) = P (CLE WIN) + P(CHA BY 1 | CHA WIN)
= 0.446429 + (0.29*0.553571)
= 0.446 + 0.1605
= 0.6065 (or actually 0.606964 if we went to full digits)
= -154.43
Now we have to allow for Chicago being the home team, which reduces the chance of them winning by >1 run (as they (a) wouldn't bat in the bottom of the 9th, and (b) the game would end if they go ahead by 1 in the bot 9 or extra innings)..
Stats I had to hand from DrBob indicate home teams cover 68.1% of the time, and road teams 76.5% of the time, an order of magnitude of around 112%..
So we adjust the P(CHA by 1 | CHA WIN) part accordingly..
P (CLE +1.5) = P (CLE WIN) + P(CHA BY 1 | CHA WIN)
= 0.446429 + (0.325771*0.553571)
= 0.446 + 0.180377
= 0.626337 (or actually 0.626766089 if we went to full digits)
= -167
That gives us a no juice Runline of -167/+167, or roughly a 3% edge on the Pinnacle line of betting +183... is that enough to bet it? Who knows..
The total is a bit on the low side, which may account for some of it.. but even if we push the 1-run chance up a couple of percent you still only get -173ish..
There will be better examples, but I only had one game to work with atm