If you find yourself in used bookstores, you often run across handicapping books from decades past. Paging through them, it becomes clear that most of the material is hopelessly dated; offering strategies for a game that no longer exists. However, there is one facet of handicapping literature that hasn’t changed at all.
As far back as the 1960s, you can find books and articles detailing the favorite/longshot bias in horse racing. This is the well known tendency of bettors to over-estimate the chances of higher priced options in pari-mutuel win pools resulting in below average returns for such bets. As opposed to decades past though, betting has evolved to the point where the majority of betting at North American tracks is done in exotic pools.
Particularly popular are the serial win bets such as the Pick 3 and Pick 4, which initially
achieved popularity on the west coast and are now are staples at most major racetracks.
Much has been written on them in recent years, including Steven Crist’s excellent Exotic
Betting. In fact the Daily Racing Form has incorporated Crist’s insights into their Formulator
product, creating a tool that optimizes ticket structure.
Considerably less has been written on the efficiency of these markets, whether betting patterns follow the example of the win pool. Since many strategies rely on “singles” to carry players through high probability legs it would be interesting to know whether it would be more advantageous to follow or bet against this strategy. Knowing if longer priced horses were overbet would also affect strategy in races where a player chose to spread and cover as many possibilities as possible.
Simply put, the favorite/longshot bias or lack thereof in serial win wagers has many implications for any approach.
Weaknesses of Multiple Race Exotics
The biggest downside of betting Pick Threes is the takeout structure. Currently in New York, the takeout is 26% for Pick Threes and Pick Fours. In California, it is slightly over 20%. Add in the fact that given tax laws the successful player will have a good deal of working capital tied up in withholding taxes each year and you realize it is an extremely tough bet to beat.
Looking For Value
In this article I wanted to take a look at the bets from a value standpoint to see if there were any strategies or eliminations that might improve the viability of whatever betting strategy a player may choose to employ.
The database I used contained the results for slightly under 10,000 Pick 3’s offered at Belmont, Saratoga, and Aqueduct from the middle of 2002 until September of 2009.
In order to get a feel for “value”, I created three comparison measures. The first was simply the result of a parlay. It is just the result you would get if you could bet your entire winning stake in each successive leg. This is something most people are familiar with and the measure that is used by most racing columnists when they are examining the value of an exotic bet. (Note: A parlay will always flatter an exotic bet because it applies the track take multiple times.) In the tables that follow this measure will be abbreviated as Prem Parlay.
The second measure sought to determine a comparison value by converting the final odds of each winner into the probable win pool percentage (after adjusting for takeout) and then applying the New York Pick 3 takeout percentage. (Abbreviated in the tables as Prem FV1)
The final measure skipped applying the final takeout and sought to come closer to creating a value line based on the actual chances of having a winning combination. (Abbreviated in the tables as Prem FV NT)
In order to get a nearly perfect model for New York Pick 3’s one would have to take into account the win pool favorite/longshot bias at different odds levels and use the actual pool percentages rather than attempting to recreate them based on final odds. Given the scope of this article, I felt that the created measures would give an acceptable representation of value.
Popular Perceptions of Value
Late in this year’s Saratoga meeting, Equidaily’s Seth Merrow was a guest on Steve Byk’s daily satellite radio show and offered some advice on betting the Pick Three. He stated that if you could beat an overwhelming favorite in the first leg you generally got better payoffs. The logic behind this is that given the complexity of the bet, many players tend to single heavy choices and get creative in the following two races.
When I heard the comment my immediate thought was to look at a large number of Pick 3’s and see if he was correct. Merrow didn’t define his version of an overwhelming favorite, but I used an odds level of .70 or lower.
Looking at 1047 NYRA Pick 3’s from 2002 to 2009 in my database you get the following results.
NYRA Pick3’s 2002-2009, Favorite 0.70 to 1 or less
Total |
Prem Parlay |
Prem FV1 |
Prem FV NT |
Result |
435 |
46.32% |
19.81% |
-10.14% |
Fave Lost |
612 |
31.39% |
7.58% |
-19.31% |
Fave Won |
As you can see, based on the three measures of value we have created indeed Merrow is correct. In testing other odds levels I found that the effect was stronger at even lower odds levels, but that if you defined an overwhelming favorite as only odds on, you don’t really get a premium.
While you don’t know the odds in legs 2 or 3, it is not hard looking at a set of past performances and seeing one horse is going to take a majority of action in the exotic pools. Still, in examining these legs I found the effect was weaker.
It is important to understand something here, however. The value we are measuring is in comparison to the win pool. It has already been established that the public overestimates higher priced horses in this pool. Thus you are not saying you will get a better return if you blindly bet these situations; just that using the win pool as a yardstick sometimes you can get better odds in the exotic pool.
Odds Ranks
Looking at the premium or discount you received betting different odds ranks could answer a number of important questions. The first is whether certain odds ranks give you more for your money. Some others are whether favorites are overbet in the Pick3 and do longshots give you more for your money in this pool.
Below you will see three tables comparing the payoffs in each leg of the Pick 3, dividing the results by whether one of the top 3 betting choices won or not.
Pick 3 Results NYRA Tracks 2002-2009
Leg 1
Odds Rank |
Total |
Prem Parlay |
Prem FV1 |
Prem FV NT |
Top 3 Odds |
6994 |
35.24% |
10.74% |
-16.95% |
Rank 4+ |
2826 |
40.62% |
15.15% |
-13.64% |
Leg 2
Odds Rank |
Total |
Prem Parlay |
Prem FV1 |
Prem FV NT |
Top 3 Odds |
6981 |
37.89% |
12.91% |
-15.32% |
Rank 4+ |
2839 |
34.08% |
9.79% |
-17.66% |
Leg 3
Odds Rank |
Total |
Prem Parlay |
Prem FV1 |
Prem FV NT |
Top 3 Odds |
6788 |
39.74% |
14.42% |
-14.18% |
Rank 4+ |
3032 |
30.18% |
6.59% |
-20.05% |
As you can see the results generate a decidedly mixed bag, offering no real advantage to consistently eliminating or concentrating on specific odds levels. This would tend to suggest the Pick 3 pool is fairly efficient, mirroring the biases of the win pool.
Given these results, it would be interesting to look at how payoffs compared looking at results where only favorites or lower odds horses won, compared to cases where only higher odds animals won each leg.
Pick 3 Results NYRA Tracks 2002-2009
Category |
Total |
Prem Parlay |
Prem FV1 |
Prem FV NT |
All Faves |
431 |
53.98% |
26.08% |
-5.44% |
All Top 3 |
3504 |
35.46% |
10.92% |
-16.81% |
All Not Top 3 |
287 |
15.66% |
-5.29% |
-28.97% |
As you can see, a clear pattern emerges wherein lower odds animals offer better value when combined with horses in similar odds ranges. This would seem to suggest that if a player found an advantage betting short priced horses they could find some value in the Pick 3 pool. It would also argue for strategies focusing on key contenders.
It seems apparent that despite the vast difference in betting structure, the Pick 3 pool shows evidence of the favorite / longshot bias. The next step would be to confirm it.
Is the Favorite/ Longshot Bias Evident in Multiple Race Exotics?
It is relatively straightforward to see if the favorite/longshot bias exists in Pick 3 pools. Using a simulation you would examine the results you would get betting every single combination and then separate the results by odds level.
There are many arguments as to why the longshots might get less play in these pools. In each leg you cover, the more horses you use, the more your play costs. Still the Pick 3 is often a home run bet and as you can see in the tables below the favorite/ longshot bias is indeed evident. We compare the results of betting every horse under 2.5 -1 with ALL in the other legs with same strategy for horses going off at greater than 8-1.
Odds < 2.5 With ALL, ALL (NYRA 2002-2009)
Bet Total |
Proceeds |
ROI |
PayoffAvg |
$1,587,030.00 |
$979,957.10 |
-38.25% |
$239.95 |
Odds > 8 With ALL, ALL (NYRA 2002-2009)
Bet Total |
Proceeds |
ROI |
PayoffAvg |
$5,161,124.00 |
$2,712,916.30 |
-47.44% |
$1,706.24 |
In addition to the above tests I ran simulations where low odds horses were bet together, longshots together, as well as various mixes and matches. In almost every case blindly betting odds, the favorite/longshot bias carried through, resulting in lower pure returns for longer priced horses. Thus despite the differences in pools the pattern established over the last century at North American racetracks holds true for serial win bets.
Conclusion
In this article we examined the Pick 3 using a database of New York races. We found that although there are situations where you can get better value than you might in the win pool, the favorite/longshot bias still exerts a heavy influence in these pools. Thus a player would be advised to find the best takeout rate and key specific horses in a quest for value. Scattershot approaches employing the ALL button would seem doomed to failure, given their reliance on odds levels that offer no inherent value on their own.
