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What are the reasons for morning-line odds errors?

Morning-line odds are among the most widely discussed numbers in horse racing. They are, strictly speaking, one person’s opinion as to what the public sentiment will be for a horse in a race (ie, post-time odds).

Morning-line odds are made for every race run in the US and Canada, and these opinions, released many days before the horses run their races, are often derived by the betting public for their inaccuracy. The strength and vigor of the outrage thrust upon morning-line makers and their opinions raises obvious questions. How well do the morning-line odds serve their intended purpose: to predict horses’ true post-time odds? And perhaps more importantly, if we want to make them better, what factors influence their predictive performance?

The first question may be answered by characterizing the relationship (see figure 1) between morning-line odds and post-time odds in a nationally representative historical sample of odds covering 38 tracks that includes all race types, surfaces and surface conditions.

The strength of this relationship is best expressed in terms of the variation in the post time odds that is explained by variation in the morning-line odds (termed the Rtwo value). The relationship depicted in Figure 1 has Rtwo = 0.658, meaning across all possible confounding factors, morning-line odds describe 65.8 percent of the variance of the post-time odds. For context, this relationship is approximately the same strength as the relationship between a person’s age and the quality of their eyesight.1.

Figure1: Relationship between morning line odds and post-time odds.

Answering the second question – which factors impact this relationship? – is much more challenging. “What factors contribute to the existence of a difference (ie, error) between the morning-line odds and the post-time odds?”

  1. field size
  2. scratches
  3. race type
  4. Surface (type, condition, changes)
  5. Morning-line maker’s ability
  6. Management guidance to the morning-line maker
  7. Wagering-pool size

Using an advanced statistical model to account for the contribution of these factors both individually as well as in combination (see Methods for details) one finds that surface, scratches, weather, and pool size each significantly contribute to errors in the morning line. These are summarized in table 1. Among the factors that increase error (positive t-score), the most significant is scratches; specifically, the total probability of winning represented by the set of scratched horses.

Intuitively, scratched favorites impact error more than scratched long shots because the relatively large pool of money wagered on these horses has disproportionate leverage once it is reallocated within the pool. Moreover, other factors interact with scratches to alter its impact. Non-dirt surfaces (turf and synthetic), non-ideal surfaces (eg, soft turf or sloppy dirt), large pool sizes, and large field sizes all temper the negative impact of scratches. In contrast, going “off the turf” exacerbates the impact of scratches on error. Separately, large field sizes and large pool sizes significantly contribute to smaller (negative t-score) morning-line errors overall. However, taken together these factors increase error.

Factor class

Factor effect (or interaction)

t-score

scratches

scr_mlprob

9,303

surf:scr_mlprob

-2,110

wps_pool:scr_mlprob

-2,144

nhorses:scr_mlprob

-2,987

offturf:scr_mlprob

3,498

surf:surfcnd:scr_mlprob

2,326

surf:surfcnd:nhorses:scr_mlprob

-2,071

Field and Pool Size

nhorses

-17,237

wps_pool

-4,372

wps_pool:nhorses

3,614

Table 1: Model factor effects. Note, a colon (:) denotes multiplicative interaction between the factors; t-score denotes the magnitude, direction, and significance of the effect size. See Methods for detailed descriptions of the individual factor variables.

Next, the contributions to morning-line odds error related to the quality of the horses running in the race were explored. One would expect greater error within morning-line odds made for race types in which little is known about the horses (maiden special weight and maiden claiming races) relative to race types in which veteran horses are competing (eg, claiming races, allowance races and stake). This intuition is largely (but not completely) born out by the effects depicted in figure 2 (left), which plots each race type’s contribution to overall error. Finally, having controlled for all of the factors described above, the individual contributions to morning-line errors born by the morning-line makers themselves and track management were explored, depicted in figure 2 (right). As indicated by the relative scales of these plots, the influence of track is an order of magnitude greater than the influence of race type.

morning line error by race type
morning line error by track

Figure2: Individual race type and track contributions to morning-line odds error.

Among the large circuits, New York Racing Association tracks (AQU, SAR, BEL) generate the lowest error morning-line odds whereas Southern California tracks (SA, DMR) generate the highest. Overall, however, the large circuits produce more accurate odds than smaller circuits, despite the model having explicitly controlled for the size of the fields and the betting pools. This fact suggests that the morning-line odds provided by the large circuits are fundamentally more accurate than those provided by the smaller circuits. This finding is of direct relevance to the betting public. When incorporating morning-line odds into wagering decisions, particularly decisions relating to the later legs of horizontal exotic bets for which no tote board information is available, one must be cognizant of the track at which they are betting and explicitly compensate for potential errors.

methods

data set

The dataset used in this analysis consists of 46,590 individual morning-line predictions drawn from a nationally representative sample of 38 tracks between November 2020 and June 2022. For each morning-line odds prediction, the following data elements were extracted from the race in which the prediction was made:

  1. track
  2. Carded field size
  3. Morning-line odds for each horse
  4. List of scratched horses
  5. Surface
  6. surface condition
  7. Off-turf indicator
  8. Win-place-show pool size
  9. Post-time odds for each non-scratched horse

These variables were then manipulated to inform the analysis of the factors hypothesized to impact morning-line odds prediction performance.

Converting odds to probabilities

Morning-line odds and post-time odds were converted to their equivalent probabilities, respectively, denoted mlprob and ptprob. This was done to linearize these quantities over the range (0,1).

scratches

It is hypothesized that the impact of scratches is driven less by the number of scratched entries than by the estimated fraction of the win pool that these horses represent. A scratched favorite is more likely to induce morning-line odds prediction error than a long shot, because the money that would be placed on the favored horse must be redistributed elsewhere (assuming that scratches do not impact the pool size in the absence of other confounds) . Thus, to represent the magnitude of the impact that these scratches will have on the pool, the total probability of the win pool represented by the scratched horses was calculated. To do this, for each scratched horse, their morning-line odds were converted into probabilities of winning and then summed up, denoted scr_mlprob.

surface variations

For the purposes of this analysis, it was assumed that morning-line odds are most accurate when made for races intended to be run on fast dirt surfaces. Therefore, a set of binary flags was constructed that characterize how the race surface deviates from this assumption as a way of capturing potential errors. First, for races not on the dirt (inner and outer turf as well as synthetic) the “surface” flag was set to 1, otherwise 0. For dirt races for all surface conditions other than “fast” and for turf races for all surface conditions other than “firm,” the “surfcond” flag was set to 1, otherwise 0. For all races taken off the turf, the “offturf” flag was set to 1, otherwise 0.

Other variables

The field size, denoted “nhorses,” was scaled to the range [0,1] by first subtracting the minimum carded field size (across all ML odds predictions) and then dividing the resulting quantity by the overall maximum field size. Win-Place-Show (WPS) pool sizes accompanying each ML odds prediction, denoted wps_pool, were scaled to the range [0,1] by first thresholding all WPS pools to a maximum size of $1,000,000 and then scaling the resulting values ​​in a manner similar to the field size.

Morning-line odds prediction errorr

Morning-line odds prediction error (denoted “error”) was quantified as root-squared error between the mlprob and ptprob variables.

Statistical modeling

Morning-line odds prediction errors were modeled according to a general linear mixed-effects (GLMM) model. Random intercept effects were included to control for the effects of race type and track. The fixed effects consisted of all individual and interaction terms among the (non-race type and track) variables described above. Formally, the model may be described (in Wilkinson notation) by the equation:

error ~ surf*surfcond*offturf*wps_pool*nhorse*scr_mlprob + (1|rtype) + (1|track)

All data manipulations were coded in Python (pandas and numpy packages). The model was solved using the lmer function of the R language’s lme4two package.

endnotes

  1. https://online.stat.psu.edu/stat462/node/97/

  2. https://cran.r-project.org/web/packages/lme4/index.html

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