It’s true that the Pick 4 payouts will rarely (if ever) be right in line with the win parlay. This is because (as RickB mentioned) the pools aren’t indexed to one another. Unless the odds of each winner in the sequence are exactly the same in the Pick 4 pool as they are in the win pool, the payout is not going to be the same.
Longer sequences like the Pick4 have wider individual variation because multiple horses with win odds out of line with the multis compound the effect. But over the long run, the payouts converge with those expected based on the takeout-adjusted win parlays.
Also keep in mind that, because you’re only getting hit with the takeout once in the Pick 4 (as Jerry noted), the Pick 4 payout should not match the win parlay anyway. At NYRA tracks, the Pick 4 should actually pay, on average, 53% more than the raw win parlay.
Looking at the results for the Dec 3 sequence, it doesn’t appear that anything nefarious was going on. My guess is that what you are seeing is emblematic of a longshot bias in the multis (longshots are overplayed in the multis vis-à-vis their win odds). The same phenomenon was discussed in the recent Bruce Jenner thread.
I did a small study a few years back on Pick 4 payouts vs. their parlays. The sample size was only 83 sequences, but it shed some light on this phenomenon.
On an overall basis, considering it was such a small sample, the payouts came surprisingly close to what was expected based on the takeout-adjusted win parlays. On average the Pick 4\'s paid approximately 60% higher than the win parlay, versus an expectation of +50% more than the parlay.
Of the 83 sequences, 34 of them paid less than the expected +50%, while 49 paid more. 13 of them (15%) paid less than the raw win parlay.
When I sorted the results by parlay size however, I found that of the 11 $2 parlays that were above $4K, 6 of them (55%(!)) paid less than the raw win parlay. This implies that the public is betting longshots at a higher rate in the Pick 4 pools than in the win pools.
The Dec 3 sequence seems to be a case in point (that sequence btw, should have paid $3,175 based on the takeout-adjusted win parlay, not the $2,080 based on the raw win parlay). The FL shipper Shangala was 27-1 in the win pool off a 15-1 ML. If you assume for a moment that the odds in the Pick 4 pool of the winners of the other 3 legs coincided with their win odds, that implies that Shangala was around 8-1 in the Pick 4 pool.
This particular situation may be less an indication of a bias by the public toward longshots in the multis than it is evidence of astute betting by sharp horseplayers. That filly had a string of solid recent figures. An argument could be made by anyone using Jerry’s figures that she should even have been the favorite. The only mystery is why she was let go at 27-1 on the board, but certainly she warranted strong play in multi-race bets.
Another thing to consider is that when dealing with longer-priced horses, it doesn’t take much in terms of variation in win probability to change the parlay estimates dramatically. Shangala’s 27-1 odds equates to a win probability of 3.0%. If she was, say, 15-1 in the Pick 4 pool, that translates to a win probability of 5.3%, only a couple of percentage points higher and so small on an absolute basis as to basically be considered noise.
If you assume that both Shangala and the winner of the first leg (Legally Bay) were around their morning lines in the Pick 4 pool (15-1 ML and 4-1 ML, respectively), the Pick 4 paid just as expected - around +50% more than the parlay.
It’s also possible that the longshot bias in the multis is partly due to the lower minimum wagers, as TheBull posited. The study I did was a few years back, on the SoCal circuit, and I don’t recall if the $.50 minimum was in place at that time. But there’s certainly a pronounced longshot bias in Gulfstream’s Rainbow 6 bet, as I discussed in another post, that may be partially due to that bet’s $.20 minimum causing players to spread deeper and to subsequently underbet favorites, as I think Jerry had suspected.
Rocky R.
