Weak Form Efficiency in Sports Betting Markets

May combine two claims.

The average return across all NFL bets is -4.20%, which is lower than the expected profit of -3.63% indicated by the average hold.

“the average return across all bets is -4.20% which is lower than the expected profit of -3.63% indicated by the average hold.”

May combine two claims.

For NFL, a two-sample hypothesis test on returns in bin 1 and bin 20 (biggest underdogs and biggest favorites) has a p-value of .257, too high to confidently reject the null hypothesis.

“to perform a more formal test of the longshot bias we perform a two-sample hypothesis test on the returns in bin 1 and bin 20, the biggest underdogs and biggest favorites.While there appears to be a strong difference in the graph, the p-value of this test is .257;again, too high to confidently reject the null hypothesis with confidence.”

May combine two claims.

Longshot biases exist in collegiate football, collegiate basketball, and baseball.

“longshot biases can be shown to exist in collegiate football and basketball as well as baseball”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

For NFL, a regression of predicted win probability in each bin against actual win probability failed to reject the null hypothesis that the slope is one; the 95% confidence interval is [.920, 1.03].

“This test failed to reject the null hypothesis that the slope of that line is one; the 95% confidence interval is [.920, 1.03].”

May combine two claims.

The odds for UFC have a similar distribution to football and basketball, with a bi-modal distribution of slight favorites and underdogs.

“The odds for the UFC have a similar distribution to football and basketball, with a bi-modal distribution of slight favorites and underdogs.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

The density drops sharply with a trough at 50%.

“The density drops of sharply with a trough at 50%.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

Slight underdog bets in professional football, collegiate football, and the UFC have had positive returns over an extended time frame, though they do not clear a statistical significance test.

“Slight underdog bets in professional and collegiate football and the UFC have had positive returns over an extended time frame, though they do not clear a statistical significance test.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

Even money bets are less common in college football at 0.71% of all games, and near even bets are 0.74%.

“Even money bets are even less common in college football at 0.71% of all games, near even bets are 0.74%.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

Probably not a substantial claim: may not pass S3 (load-bearing).

Odds can be a little more extreme in hockey with the density extending to nearly 80%.

“Odds can be a little more extreme in hockey with the density extending to nearly 80%.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

For NFL bin 8 (+125,+144), the test of the null hypothesis that returns are negative yields a p-value of 0.108, so the null cannot be rejected at the 5% cutoff.

“If we examine the return on the most profitable bin, bin 8 with odds of [+125,+144], and test the null hypothesis that these returns are negative, we obtain a p-value of 0.108 and we cannot reject that hypothesis using a standard cutoff of 5%.”

May combine two claims.

Odds for MLB appear quite different: the even money trough is absent and even or near even odds are common.

“Odds for professional baseball (MLB) appear quite different.The even money trough is absent and even or near even odds are common.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

Extreme odds are much less common in MLB; odds greater than 75% appear quite rare.

“Extreme odds are also much less common.Whereas football and basketball both had extreme probabilities, at or near 100%, odds greater than 75% appear quite rare in MLB.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

Strictly even odds are offered in 2.94% of MLB games and near even odds in 10.4% of games.

“Strictly even odds are offered in 2.94% of games and near even odds in 10.4% of games.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

Pick'em odds are relatively rare in UFC, although there is a small minor bump at even odds.

“Pick'em odds are relatively rare, although there is a small minor bump at even odds.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

In NFL, bin 8 (+125 to +144) has the highest long-term return and the most consistently positive returns, 12 out of 16 seasons, with an overall return of 6.5%.

“Bin 8, odds in the range of [+125-+144] has the highest long-term return and the most consistently positive returns; 12 out of 16 seasons, and an overall return of 6.5%.”

May combine two claims.

The modal odds for NFL underdogs is +170, corresponding to an implied probability of 37%.

“The modal odds for NFL underdogs is +170, corresponding to an implied probability of 37%.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

The sports betting market has some technical inefficiencies, but the level of inefficiency is small.

“While we find some minor technical inefficiencies”

• Also stated in: § INTRODUCTION · plain

  “However, the level of inefficiency is small.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

Strictly even odds are offered in 2.29% of NHL games and near even odds in 4.59% of games.

“Strictly even odds are offered in 2.29% of games and near even odds in 4.59% of games.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

Of all UFC odds quoted, 2.08% are at even money and 2.70% are at near even money.

“Of all the odds quoted, 2.08% are at even money and 2.70% are at near even money.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

The CFB graph is similar to the NFL graph: returns are uneven, and heavy longshots yield very low returns relative to other groups.

“The CFB graph is similar to the NFL graph; returns are uneven, heavy longshots yield very low returns relative to other groups.”

May combine two claims.

CFB returns in the profitable bins are sometimes positive and sometimes negative over a season, with less consistency than NFL.

“As was the case with professional football, the returns in these bins are sometimes positive and sometimes negative over the course of a season, though there is less consistency than there was for the NFL.”

May combine two claims.

The technical inefficiencies vary from sport to sport but are reasonably consistent over time.

“These inefficiencies vary from sport to sport but are reasonably consistent over time.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

The returns in the three NFL bins representing 30% of games in each season vary considerably, with each bin positive in some seasons and negative in others.

“The returns in these 3 bins, representing 30% of the games in each season, vary considerably.Each bin has positive returns in some seasons, and negative returns in others.”

May combine two claims.

For NFL, p-values on other nominally positive returns are above the cutoff: bin 7 p=0.427 and bin 18 p=0.366.

“The p value on bin 7 is 0.427, and the p value on bin 18 is 0.366.”

May combine two claims.

In college basketball, even money is 1.07% and near even money is 1.11%.

“In college basketball the figures are 1.07%for even money and 1.11% for near even money.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

The odds for NHL are similar to baseball, but with a pronounced peak near parity.

“The odds for professional hockey are similar to baseball, but with a pronounced peak near parity.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

Even odds are quoted in 0.99% of NBA games, while near even odds are stated in 1.15% of games.

“Even odds are quoted in 0.99% of NBA games, while near even odds are stated in 1.15% of games.”

• AssumptionRests on an assumption: The odds and results data collected from Sports Book Review and BestFightOdds are accurate and representative of the sports betting market.

May combine two claims.

For NHL, the p-value for an ANOVA test of the hypothesis that all returns are equal is 0.905, so the null hypothesis cannot be rejected.

“The p-value for an ANOVA test of the hypothesis that all returns are equal is 0.905, so we cannot reject the null hypothesis.”

May combine two claims.

For NHL, returns in all bins are negative, with the profit in bin 5 [+130, +139] being effectively zero at -0.003%; the p-value for the hypothesis test that returns are negative is 0.364, so the null cannot be rejected.

“The returns in all bins is negative with the profit in bin 5 [+130, +139] being effectively zero at -0.003%.The p-value with associated with the hypothesis test that the returns are negative is 0.364, so we cannot reject the null hypothesis.”

May combine two claims.

The actual average return on college basketball bets is -7.71% versus the average hold of -3.56%.

“The actual average return on college basketball bets is -7.71% vs. the average hold of -3.56%.”

May combine two claims.

For UFC, statistically significant differences exist between bins 2 and 19 (<2e-16) and 3 and 18 (3.86e-07).

“Statistically significant differences exist between bins 2 and 19 (<2e-16), 3 and 18 (3.86e-07).”

May combine two claims.

In college basketball, the longshot bias holds for bins 2-19 (p=2.51E-09), 3-18 (p=1.324E-07), 4-17 (p=2.74E-07), 5-16 (p=1.70E-06), 6-15 (p=0.0174), 7-14 (p=0.0045), and 8-13 (p=0.0086).

“The longshot bias also holds for bins 2-19 (p-value 2.51 E-09), bins 3-18 (p-value 1.324E-07), bins 4-17 (p-value 2.74E-07), bins 5-16 (p-value 1.70E-06), bins 6 and 15 (p-value 0.0174), bins 7 and 14 (p-value 0.0045), and bins 8 and 13 (p-value 0.0086).”

May combine two claims.

College basketball returns show significant variation; a formal ANOVA test confirms this with a p-value of less than 2E-16.

“The returns on best in college basketball show significant variation.A formal ANOVA test confirms this with a p-value of less than 2E-16.”

May combine two claims.

Professional hockey returns are similar to baseball in that they are all mostly negative and reasonably consistent.

“They are similar to baseball in that they are all mostly negative and reasonably consistent.”

May combine two claims.

The NBA slope is slightly greater than 1, while the CFB slope is slightly below 1.

“The NBA slope is slightly greater than 1, while the CFB slope is slightly below 1.”

May combine two claims.

Pro basketball returns are generally negative, with a very small positive return in bin 2, but the p-value of 0.417 provides very low confidence that this is a meaningfully positive return.

“Pro basketball returns are generally negative, with a very small positive return in bin 2, but the p-value of 0.417 provides very low confidence that this is a meaningfully positive return.”

May combine two claims.

For CFB, returns on bins 6-8 have been positive over an extended period, but there is limited evidence that this is a statistically significant difference; p-values are 0.289, 0.428, and 0.108 respectively.

“While the returns on bins 6-8 have been positive over an extended period of time, we have limited evidence that this is a statistically significant difference.If we test the null hypothesis that the returns are negative the p-values on these tests are 0.289, 0.428, and 0.108 respectfully.”

May combine two claims.

Bets on extreme long shots in college basketball yield very poor returns, while bets on corresponding heavy favorites also yield negative returns but these returns are significantly better.

“Bets on extreme long shots in college basketball yield very poor returns while bets on corresponding heavy favorites in college basketball also yield negative returns, but these returns are significantly better.”

May combine two claims.

For UFC, the slope of the predicted to actual win percentage line is in the interval [.983, 1.08], so no bias exists across the distribution.

“slope of the predicted to actual win percentage line is in the interval [.983, 1.08] so no bias exists across the distribution.”

May combine two claims.

The average return on UFC bets is -5.82%, less than the average hold of -4.40%.

“The average return on UFC bets is -5.82%, less than the average hold of -4.40%.”

May combine two claims.

For MLB, a longshot bias is clear: bets on the biggest underdogs yield a return of -7.32%, while the corresponding favorites yield a -0.72% return; the returns are different with a p-value of 0.017.

“A longshot bias is clear with bets on the biggest underdogs yielding a return of -7.32, with the corresponding favorites yielding a -0.72% return.The returns are different with a p-value of 0.017.”

May combine two claims.

For NHL, the slope of the predicted to actual win percentage line is in the interval [.934, 1.01], so no bias exists across the distribution.

“The slope of the predicted to actual win percentage line is in the interval [.934, 1.01] so no bias exists across the distribution.”

May combine two claims.

For UFC, very small positive profits in bins 19 and 20 (.795 and .862) have p-values of 0.30 and 0.31.

“The very small positive profits in bins 19 and 20 (.795 and .862)have p-values of 0.30 and 0.31.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

For NBA, the largest difference in complementary bin profits is between bins 2 and 19, a potential reverse longshot bias, but the p-value is .238.

“The largest difference in complementary bin profits is between bins 2 and 19, a potential reverse longshot bias, but the p-value here is .238.”

May combine two claims.

Bets on extreme underdogs in college basketball have very poor returns, and in general bets on underdogs perform significantly worse than bets on favorites.

“Bets on extreme underdogs have very poor returns, and in general bets on underdogs perform significantly worse than bets on favorites.”

May combine two claims.

For NBA, the null hypothesis that the odds are unbiased can be rejected: the slope of the regression line of actual win percentage to predicted win probability is [.938, .978], which does not include 1.

“We can also reject the null hypothesis that the odds are unbiased.The slope of the regression line of actual win percentage to predicted win probability is [.938, .978]which does not include 1.”

May combine two claims.

In college basketball, returns are negative on all bins, the biggest longshot bin has a negative return of nearly 50%, and betting on the corresponding favorite has a return of -0.2%.

“While returns are negative on all bins, the biggest longshot bin has a negative return of nearly 50%.Betting on the corresponding favorite has a return of -0.2%.”

May combine two claims.

For college basketball, the null hypothesis that the slope of the projected to actual win regression line is 1 can be rejected; the 95% confidence interval is [1.02, 1.03].

“For college basketball we can also reject the null hypothesis that the slope of the projected to actual win regression line has a slope of 1.The 95% confidence interval is [1.02, 1.03].”

May combine two claims.

For MLB, the slope of the predicted to actual win percentage line is in the interval [.963, 1.05], so no bias exists across the distribution.

“The slope of the predicted to actual win percentage line is in the interval [.963, 1.05] so no bias exists across the distribution.”

May combine two claims.

UFC returns show a significant difference across the odds distribution; the ANOVA test has an effectively 0 p-value (<2e-16).

“The UFC returns do show a significant difference across the odds distribution, the ANOVA test has an effectively 0 p-value (<2e-16).”

May combine two claims.

MLB returns generally have a negative return over time, though there is a small positive return on bets in bin 14 corresponding to odds of [-125, -132], a slight favorite; the return is 1.48%, but the p-value associated with the test that it is less than zero is 0.891.

“Returns generally have a negative return over time, though there is a small positive return on bet in bin 14 corresponding to odds of [-125, -132] a slight favorite.The return is 1.48%, but the p-value associated with the test that it less than zero is 0.891.”

May combine two claims.

For NHL, the return on the biggest longshots, bin 1 [+190, +505], is -4.13%, slightly worse than the returns on complementary odds in bin 20 [-700, -219], which are -2.91%; the null hypothesis that these returns are different cannot be rejected with a p-value of .546.

“The return on the biggest longshots, bin 1 [+190, +505] are -4.13%,slightly worse than the returns on the complementary odds in bin 20 [-700, -219] which are -2.91%.We fail to reject the null hypothesis that these returns are different with a p-value of .546.”

May combine two claims.

For NHL, bins 2 and 19 show a nominal reverse longshot bias: bin 2 returns are -2.19% and bin 19 returns are -3.28%, but the null hypothesis that these returns are different has a p-value of 0.725%.

“The returns on the set of bins 2 and 19, show a nominal reverse longshot bias.Bin 2 returns are -2.19% and bin 19 returns are -3.28%,but the null hypotheses that these returns are different is 0.725%.”

May combine two claims.

A statistically significant longshot bias exists in both college sports, MLB, and the UFC.

“A statistically significant longshot bias exists in both college sports, MLB, and the UFC.”

May combine two claims.

For UFC, long run profit is positive in bins 6 and 7 (2.44 and 2.49), but the p-values do not quite make the 5% threshold at 6.28% and 6.50%.

“The long run profit is positive in bins 6 and 7 (2.44 and 2.49), but the p-values do not quite make the 5% threshold at 6.28% and 6.50%.”

May combine two claims.

A statistically significant odds bias can be detected for professional and collegiate basketball; when actual win probability is regressed on predicted win probability, the 95% confidence interval for these sports does not contain 1.

“Finally, we can detect a statistically significant odds bias for professional and collegiate basketball; when we regress actual win probability to predicted win probability the 95% confidence interval for these sports does not contain 1.”

May combine two claims.

Slight underdog bets appear to be the best option for NFL games and have earned a small positive return over the 16 seasons in the data set, but those returns are highly variable and the null hypothesis that they are negative cannot be rejected.

“Slight underdog bets appear to be the best option for NFL games and they have earned a small positive return over the 16 seasons in our data set, those returns are highly variable and we cannot reject the null hypothesis that they are negative.”

May combine two claims.

There is evidence suggesting NFL odds are weak form inefficient, but conclusions are tentative due to variable returns, and no hypothesis that would invalidate weak form efficiency can be rejected.

“In summary there is evidence that would suggest that the odds for NFL games are weak form inefficient.While there appears to be a variation in return against different odds groups and heavy longshot bets have historically performed the worst, but these conclusions are tentative due to the variable state of the returns.”

• Also stated in: § FIGURE 9 NFL RETURNS · hedged

  “While we can observe some anomalies from the strict requirements of weak-form efficiency, we cannot reject any hypothesis that would invalidate weak form efficiency.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The general consensus has been that odds makers set odds so as to attract the appropriate level of bets on either side.

“The general consensus has been that odds makers set odds so as to attract the appropriate level of bets on either side.”

• cites Pankoff 1968 sourceNot checked — no full text of the source

May combine two claims.

While statistically significant, the odds-bias discrepancies are quite small.

“While statistically significant, these discrepancies are quite small.”

May combine two claims.

Minor inefficiencies exist in some betting markets and making money betting on sports is difficult.

“While our analysis shows that minor inefficiencies exist in some betting markets and confirms that making money betting on sports is difficult.”

May combine two claims.

While there are some nominal differences in historical NHL returns, all bins are negative and none of the differences can be shown to be the result of anything but statistical noise.

“While there are some nominal differences in the historical returns, all bins are negative and none of the differences can be shown to be the result of anything but statistical noise.”

May combine two claims.

The average returns are less than the average hold, so the bettor does worse and the abnormal return accrues to the sportsbook.

“However, it is extremely important to note that the average returns are less than the average hold so the bettor does worse and the abnormal return accrues to the sportsbook.”

May combine two claims.

While CBB odds fail the strict weak form efficiency test, there are no profitable odds ranges available to the bettor.

“While CBB odds fail the strict weak form efficiency test, there are no profitable odds ranges available to the bettor.”

May combine two claims.

The study only looked at moneyline bets and did not examine spreads, totals, or proposition bets.

“First, we only looked at moneyline bets.We did not examine the other major markets of spreads and totals, not the more exotic markets of proposition bets.”

Classified as probably not a substantial claim. May combine two claims.

The study only analyzed a strategy of placing bets based on the odds, and therefore tested for weak form efficiency.

“A further limitation of this paper is that we only analyzed a strategy of placing bets based on the odds, and therefore tested for weak form efficiency.”

May combine two claims.

Bets on slight underdogs in UFC are positive but only at the roughly 6% level.

“Bets on slight underdogs are positive but only at the roughly 6% level.”

May combine two claims.

The positive average returns detected over the long run are not consistently positive and none can be confirmed as statistically significant.

“While these returns are positive over an extended period of time, they are not consistently positive and none of them can be confirmed as statistically significant.”

May combine two claims.

Many of the differences in returns across odds ranges are statistically indistinguishable from random variation, while others are meaningful.

“But many of these differences are statistically indistinguishable from random variation, while others are meaningful.”

May combine two claims.

UFC returns are similar in some ways to football, with a slight underdog profit, but also similar to basketball with what would appear to be a significant long shot bias.

“These returns are similar in some ways to football, with a slight underdog profit.But they are also similar to basketball with what would appear to be a significant long shot bias.”

May combine two claims.

UFC odds are not strictly weak form efficient because results are not consistent across the odds distribution and a statistically significant longshot bias exists.

“We can conclude that the UFC odds are not strictly weak form efficient as the results are not consistent across the odds distribution and a statistically significant longshot bias exists.”

May combine two claims.

For NBA, a slope less than 1 indicates that actual win probability increases slightly less than the win probability projected by the odds, though the difference is very minor.

“A slope less than indicates that the actual win probability increases slightly less than the win probability projected by the odds, those this difference is very minor.”

May combine two claims.

Some bets are better, or worse, than others.

“But what our analysis does show is that some bets are better, or worse, then others.”

May combine two claims.

While one band of MLB favorite odds has a nominally positive return, these returns cannot be concluded to be non-negative at a reasonable level of statistical significance.

“While one band of favorite odds has a nominally positive return, we cannot conclude that these returns are non-negative at a reasonable level of statistical significance.”

Probably not a substantial claim: may not pass S1 (asserted).

Bookmakers systematically shade the odds on true pick-'em games to slightly favor one team and attract a disproportionate share of bets on the favorite.

“Levitt's hypothesis that bookmakers systematically shade the odds.If bookmakers shift the odds on true pick-'em games to slightly favor one team and attract a disproportionate share of bets on the favorite, it would stand to reason that betting the underdog team would be a higher expected value bet.”

• cites LevittNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Betting underdogs in general, and longshots in basketball, is in general a losing proposition.

“Betting underdogs in general, and longshots in basketball is in general a losing proposition.”