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When Do Markets Fully Process Public Information? Evidence from Real-Time Prediction Markets
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\noindentKeywords: Prediction markets; belief updating; market efficiency; liquidity; sports betting; behavioural finance; event studies; NBA.\\ JEL codes: D83, D84, G14, G41, L83.
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When do markets fully process public information? This question is central to economics because prices are often used as sufficient statistics for beliefs, expectations, and decision-relevant information. In the efficient-markets benchmark, public news should be incorporated rapidly and without predictable subsequent price movements Fama1970. Yet this benchmark need not hold when attention, information processing, and trading are costly GrossmanStiglitz1980. Models of investor sentiment, overconfidence, representativeness, and gradual information diffusion provide mechanisms for both underreaction and overreaction to news BarberisShleiferVishny1998,DanielHirshleiferSubrahmanyam1998,HongStein1999, while limited attention can delay price adjustment even when information is public DellaVignaPollet2009,HirshleiferLimTeoh2009. A persistent empirical difficulty, however, is that the econometrician rarely observes both the precise arrival of information and the asset's relevant fundamental value. This paper studies real-time belief updating in a setting where these objects can be measured unusually well. We use live National Basketball Association (NBA) event contracts traded on Kalshi, a regulated prediction market exchange. A contract pays one dollar if a specified team wins a game and zero otherwise. Its price can therefore be interpreted as a market-implied probability, subject to the usual caveats about heterogeneous beliefs, risk preferences, fees, bid--ask spreads, and market microstructure Manski2006,WolfersZitzewitz2006,GjerstadHall2005. We merge one-minute Kalshi quotes, bid--ask spreads, volume, and open interest with timestamped NBA play-by-play data. The resulting dataset allows us to observe market prices, public signals, liquidity, and final payoffs at high frequency.
The setting provides a useful laboratory for three reasons. First, public information arrives continuously and is precisely recorded: every score, turnover, foul, timeout, rebound, possession, and clock movement changes the state of the game. Second, the payoff is simple, binary, and resolved within hours. Third, liquidity varies substantially across games and within games, allowing us to ask not only whether prices update, but when updating is more or less complete. This makes it possible to distinguish two notions that are often conflated. Prices may be directionally responsive, in the sense that they move in the right direction after public news, while still failing to update efficiently, in the sense that they do not move by the correct amount. Our empirical analysis proceeds in three steps. We first examine pre-game prices. Closing pre-game prices are well calibrated and become more accurate over the final 24 hours before tipoff. The pre-game price revision is strongly predictive of final outcomes, indicating that Kalshi prices contain meaningful information before the game begins. We then study live price responses to public signals. Prices react quickly and in the expected direction: favorable scoring, made shots, opponent turnovers, lead changes, and scoring runs all increase the market-implied probability of the referenced team winning. This establishes that the market processes public information in real time. The stronger test compares price changes with changes in a benchmark win probability constructed from pre-game prices and live game states. Relative to this public-information benchmark, live prices underreact on impact. A one-minute change in benchmark win probability is associated with only about a 0.64-for-one contemporaneous change in the Kalshi midpoint. The missing adjustment predicts subsequent price drift over the next several minutes, including drift net of future changes in the benchmark probability. Thus, prices move in the right direction, but not far enough. The evidence is consistent with gradual incorporation of public information rather than instantaneous efficient updating. We then ask when this incomplete updating is most pronounced. The answer depends on the interaction between salience and liquidity. This interaction connects salience-based models of attention and choice BordaloGennaioliShleifer2012 with market-microstructure and limits-to-arbitrage mechanisms, in which trading costs and limited liquidity prevent immediate correction of price errors Kyle1985,GlostenMilgrom1985,AmihudMendelson1986,ShleiferVishny1997. Salient public signals, such as three-point shots, lead changes, and scoring runs, are incorporated relatively quickly in liquid markets. However, when salient signals arrive in thin markets, prices adjust less completely on impact. The resulting underreaction gaps predict further price drift. Illiquidity therefore does not merely raise trading costs; it shapes the speed with which public information is incorporated into prices. At the same time, the predictable midpoint drift does not translate into a simple arbitrage opportunity once bid--ask costs are imposed. The evidence is best interpreted as gradual price discovery under trading frictions.
The paper contributes to three literatures. First, it contributes to the literature on prediction markets. Existing work shows that prediction markets often aggregate information and produce accurate forecasts WolfersZitzewitz2004, while also emphasizing that prices need not mechanically equal objective probabilities Manski2006,WolfersZitzewitz2006. Calibration studies document that prediction markets can be informative but may display favorite--longshot patterns or other systematic deviations PageClemen2013,Page2012. Recent work on Kalshi shows that prices are informative and become more accurate near resolution, while also displaying pricing patterns shaped by the platform's market design BurgiDengWhelan2026. We shift the focus from static calibration to dynamic belief updating: not only whether prices are right on average, but whether they move correctly when public information arrives. Second, the paper contributes to the literature using sports betting and in-play prediction markets to test market efficiency ThalerZiemba1988,Sauer1998. Closely related work studies high-frequency price responses around salient sports events. CroxsonReade2014 exploit goals scored on the cusp of half-time in soccer and find rapid and full adjustment. AngeliniDeAngelisSingleton2022 study in-play prediction markets around first goals and document both mispricing and behavioral patterns. GauriotPage2018 show that perceived momentum in football contests can affect behavior even when its underlying predictive content is limited, while GauriotPage2026 use knife-edge public information shocks in binary options markets and find mostly rapid adjustment, with short-lived underreaction to large shocks. Related evidence from second-by-second football betting markets shows that betting volume shifts toward teams that appear to gain momentum even when this perceived momentum is not associated with better outcomes OettingDeutscherSingletonDeAngelis2025. Our setting differs because basketball generates a dense sequence of public signals within each game, and because we observe both exchange liquidity and repeated changes in the public-information state. This allows us to study not only whether prices respond to news, but how the completeness of updating varies with salience and trading conditions. Third, the paper contributes to behavioral finance research on underreaction, overreaction, attention, and limits to arbitrage. Traditional financial-market tests often face a joint-hypothesis problem because fundamental values are difficult to observe. Event contracts mitigate this problem: payoffs are binary, public signals are timestamped, and benchmark win probabilities can be estimated from comparable game states. The results show that even in a simple real-money market with transparent public information, prices may update gradually when attention and trading frictions interact.
The rest of the paper is organized as follows. Section (ref) describes Kalshi's institutional setting, the NBA contracts, and the construction of market-implied probabilities. Section (ref) presents a framework for real-time belief updating. Section (ref) studies pre-game calibration and static biases. Section (ref) studies live belief updating around public information shocks. Section (ref) investigates mechanisms, focusing on salience, liquidity, and gradual adjustment. Section (ref) concludes the paper.
We study National Basketball Association (NBA) winner contracts traded on Kalshi, a regulated event-contract exchange. A typical contract pays one dollar if the referenced team wins a specified NBA game and zero otherwise. Because payoffs are binary and resolved shortly after the game, contract prices can be interpreted as market-based forecasts of game outcomes, subject to the usual caveats regarding heterogeneous beliefs, risk preferences, trading costs, and market microstructure. Our market data consist of one-minute observations for NBA winner contracts. For each contract-minute, we observe the best YES bid, the best YES ask, trading volume, and open interest. Our main price measure is the midpoint between the best YES bid and best YES ask, \[ p_{it}=\frac{bid_{it}+ask_{it}}{2}, \] where (i) indexes contracts and (t) indexes time. We interpret ($p_{it}$) as the market-implied probability that the contract pays out. To characterize trading conditions, we measure liquidity using the bid--ask spread, \[ spread_{it}=ask_{it}-bid_{it}, \] together with minute-level trading volume and open interest. We merge the Kalshi data with NBA play-by-play records. The play-by-play feed provides a timestamped record of all publicly observable game events, including scores, turnovers, fouls, timeouts, rebounds, possessions, substitutions, and clock updates. Using these data, we reconstruct the public state of each game at every Kalshi observation. For each contract-minute, we assign the most recent observed game state and construct variables describing score margin, period, time remaining, recent scoring, made three-point shots, turnovers, lead changes, timeouts, and scoring runs. A key feature of the dataset is that all live variables are oriented toward the team referenced by the contract. Positive score margins, positive recent scoring runs, and positive event indicators always correspond to information favorable to the YES contract. This contract-oriented structure allows us to pool all contracts within a common empirical framework and interpret coefficients consistently across games and teams. The merge proceeds in two stages. We first match Kalshi contracts to NBA games using event dates, team identifiers, and NBA game identifiers. We then merge each contract's one-minute price series with the corresponding play-by-play file. The resulting dataset contains one observation per contract-minute and combines market prices, liquidity measures, public-information variables, and realized outcomes. Table (ref) summarizes the final sample. The cleaned dataset contains 1,438 NBA games, 2,876 team-level contracts, and 409,512 contract-minute observations. The pre-game analysis uses 2,839 contracts from 1,421 games for which both the 24-hour pre-game price and the closing pre-game price are observed.
The dataset offers several advantages for studying market efficiency and belief updating. First, the traded claim has a transparent binary payoff. Second, public information arrives continuously and is observed at high frequency through the play-by-play feed. Third, prices and liquidity measures are observed at the same frequency as the information flow. Finally, outcomes are realized within hours rather than months or years. This combination allows us to study not only whether prediction market prices are informative, but also how rapidly and completely they incorporate public information in real time.
This section develops a simple framework for interpreting the empirical analysis. The objective is not to estimate a structural model of trading, but to discipline the distinction between three objects: the statistical content of public information, the market price response, and subsequent price correction. Consider a binary contract \(i\) that pays one dollar if the referenced team wins the game and zero otherwise. Let \(Y_i\in\{0,1\}\) denote the terminal payoff. At time \(t\), market participants observe a public information set \(\mathcal I_{it}\), which includes pre-game information and the live game state. The public-information benchmark is
This is the probability of winning implied by the observed state of the game. It is not observed by the econometrician, but can be approximated using a win-probability model estimated from historical game states. Let \(p_{it}\) denote the Kalshi midpoint, interpreted as the market-implied probability that the contract pays out. The efficient-updating benchmark is
where \(\varepsilon_{it}\) is an unpredictable pricing error. In levels, this implies calibration. In changes, it implies one-for-one updating:
where \[ \Delta p_{it}=p_{it}-p_{i,t-1}, \qquad \Delta q_{it}=q_{it}-q_{i,t-1}. \] Under efficient updating, public information should be incorporated immediately, and the residual component \(\eta_{it}\) should not predict future price changes. We allow for the possibility that prices incorporate public information gradually or with behavioral distortions. Let
denote mispricing relative to the public-information benchmark. A parsimonious updating equation is
The parameter \(\lambda_{it}\) captures the contemporaneous intensity of updating. If \(\lambda_{it}=1\), prices move one-for-one with the benchmark probability. If \(\lambda_{it}<1\), prices underreact on impact. If \(\lambda_{it}>1\), prices overreact. The parameter $(\rho)$ captures correction or persistence of previous mispricing. If prices gradually correct past underreaction, lagged mispricing should predict subsequent price movements. We allow updating intensity to depend on signal and market characteristics:
Salience captures whether the public signal is especially visible or attention-grabbing, such as a made three-point shot, a lead change, a large scoring run, or a late-game event. Illiquidity captures the cost of trading and is measured using bid--ask spreads, recent trading volume, and open interest. Substituting into the updating equation gives
This equation nests the efficient benchmark. Efficient real-time updating requires one-for-one incorporation of \(\Delta q_{it}\), no systematic dependence of the response on salience or liquidity, and no predictable subsequent drift. Deviations from these restrictions generate the empirical Hypothesis below.
\paragraph{Hypothesis 1: Pre-game informativeness.} If prices aggregate information before the game, pre-game prices should predict realized outcomes. In particular, $\mathbb E[Y_i\mid p_{i,0}]$ should be increasing in \(p_{i,0}\), and calibration implies an intercept close to zero and a slope close to one in regressions of \(Y_i\) on \(p_{i,0}\).
\paragraph{Hypothesis 2: Directional live updating.} If live prices respond to public information, favorable benchmark innovations should increase prices and unfavorable innovations should decrease them: \[ \mathbb E[\Delta p_{it}\mid \Delta q_{it}>0]>0, \qquad \mathbb E[\Delta p_{it}\mid \Delta q_{it}<0]<0. \] This is a weak form of information aggregation: prices move in the right direction, but not necessarily by the right amount.
\paragraph{Hypothesis 3: Efficient live updating.} Efficient updating requires (ref). We test this prediction using
where \(X_{it}\) contains state and market controls. Under efficient updating, market prices should move one-for-one with changes in the benchmark probability, implying $\beta=1$. Values of \(\beta<1\) indicate underreaction, while values of \(\beta>1\) indicate overreaction.
\paragraph{Hypothesis 4: Gradual correction of updating errors.} If prices do not fully incorporate public information on impact, either because of underreaction or overreaction, the resulting pricing error should predict subsequent corrections. Define the updating gap as
A positive gap indicates underreaction, while a negative gap indicates overreaction. If prices gradually converge toward the benchmark probability, then future price changes should be related to the size and sign of the gap:
Under gradual correction, the prediction is $\rho>0$. A positive coefficient implies that positive gaps (underreaction) are followed by upward price adjustments, whereas negative gaps (overreaction) are followed by downward price adjustments.
A stronger test nets out subsequent changes in the benchmark probability:
A positive value of \(\rho\) in this specification indicates that pricing errors are corrected over time, beyond the arrival of new public information.
\paragraph{Hypothesis 5: Salience affects the completeness of updating.} If salient signals attract attention or distort beliefs, the price response should differ systematically following salient public information. In the updating equation (ref), this corresponds to $\alpha_S \neq 0$.
A non-zero value of \(\alpha_S\) implies that salience affects the sensitivity of prices to benchmark probability changes. Positive values indicate stronger updating, whereas negative values indicate weaker updating relative to non-salient events.
\paragraph{Hypothesis 6: Liquidity disciplines real-time updating.} If trading frictions affect price adjustment, deviations from efficient updating should be more pronounced when markets are illiquid. The key hypothesis is that the effect of salience depends on liquidity: $\alpha_{SL}\neq 0$ in (ref). A non-zero interaction effect implies that liquidity moderates the impact of salient information on price updating. In particular, salient events may generate larger deviations from efficient updating when market liquidity is low.
These Hypotheses organize the empirical analysis. Section (ref) tests whether pre-game prices provide an informative prior. Section (ref) tests whether live prices move in the right direction and whether they update one-for-one with benchmark win-probability changes. Section (ref) studies whether incomplete updating is concentrated in salient and illiquid states and whether updating errors predict subsequent price corrections.
We begin by studying pre-game prices. This exercise provides a baseline for the live analysis. If pre-game prices were uninformative, subsequent tests of real-time updating would be difficult to interpret. Conversely, if pre-game prices are calibrated and become more accurate before tipoff, live price movements can be interpreted as updates from a meaningful market prior. We define two pre-game prices. The first, \(p_{i,-24h}\), is the last observed Kalshi midpoint at least 24 hours before game start. The second, \(p_{i,0}\), is the last observed midpoint before the first NBA play-by-play event. The 24-hour revision is \[ \Delta p_i^{24h}=p_{i,0}-p_{i,-24h}. \] Our 24-hour pre-game sample contains 2,839 contracts from 1,421 games. Figure (ref) reports calibration plots for prices observed 24 hours before tipoff and for closing pre-game prices. Contracts are grouped into five-percentage-point price bins, and the figure compares the average market-implied probability in each bin with the realized win frequency. Prices are informative at both horizons, and closing prices lie close to the 45-degree line.
Table (ref) shows that forecast accuracy improves over the final 24 hours before the game. The mean Brier score falls from 0.204 at the 24-hour horizon to 0.199 at the close. The improvement of 0.0046 is statistically significant, with standard errors clustered by game. The mean absolute error also declines, from 0.406 to 0.397. These magnitudes are economically modest but statistically precise, consistent with gradual information aggregation as tipoff approaches.
The pre-game revision is itself informative. Column 3 of Table (ref) estimates
The coefficient on the revision is 1.29 and highly statistically significant. Conditional on the 24-hour price, upward revisions predict higher realized win probabilities and downward revisions predict lower realized win probabilities. A 10 percentage point increase in the pre-game revision is associated with a roughly 13 percentage point increase in the probability that the contract pays out. The evidence does not point to large static mispricing. The calibration regressions show intercepts close to zero and slopes close to one at both horizons. Bin-level excess payoffs display some variation across the price distribution, especially in sparsely populated extreme bins, but the dominant pattern is that prices are informative and become more accurate as the market approaches game start. This result establishes the starting point for the live analysis. Kalshi prices provide a meaningful pre-game prior. The central question is therefore not whether the market has information before the game starts, but whether it updates this prior efficiently when public information begins to arrive in real time.
Having established that pre-game prices are informative, we next study how prices respond once public information begins to arrive during the game. This section tests the weakest implication of real-time information aggregation: favorable public signals should increase the price of the contract, while unfavorable signals should decrease it. This test does not require a benchmark win-probability model and does not ask whether the response is of the correct magnitude. It asks only whether live prices move in the right direction. We first provide descriptive evidence on live calibration. Figure (ref) plots realized win frequencies across bins of the Kalshi live midpoint and game-clock minutes remaining. The figure pools contract-minutes across games and does not condition on the full game state, so it should be interpreted descriptively. Nevertheless, live prices are strongly informative throughout the game: higher prices correspond to higher realized win frequencies, and the relationship becomes sharper as the game approaches resolution.
To study directional updating, we construct signed public-signal variables. All signals are oriented toward the team referenced by the contract. For example, \(signed\_points\_1m\) equals points scored by the contract team over the previous minute minus points scored by the opponent. Similarly, \(signed\_3pt\) equals one if the contract team made a three-point shot in the previous minute and minus one if the opponent did. For turnovers, the sign is reversed: an opponent turnover is good news for the contract team, while a turnover by the contract team is bad news. Thus, positive values always correspond to information favorable to the YES contract. The outcome is the one-minute change in the Kalshi midpoint, $\Delta p_{it}$. Table (ref) reports mean price changes by signal direction. The pattern is highly symmetric. When the contract team outscores the opponent in the previous minute, the price rises by 2.8 percentage points on average; when the opponent outscores the contract team, the price falls by 2.8 percentage points. A made three-point shot by the contract team is associated with an increase of 3.7 percentage points, while an opponent three-point shot is associated with a decline of 3.8 percentage points. Lead changes generate even larger directional movements, around 4.5 percentage points in the expected direction. Sustained scoring runs also convey economically meaningful information. An 8--0 run is associated with an average price change of about 2.5 percentage points, increasing to 2.8 percentage points for a 10--0 run, with nearly identical effects of opposite sign when the run is achieved by the opposing team.
We next estimate regressions of the form
where \(X_{it}\) includes the lagged midpoint, score margin, absolute score margin, game-clock minutes remaining, bid--ask spread, recent volume, and open interest. Standard errors are clustered by game. Table (ref) confirms the descriptive evidence. Recent scoring by the contract team predicts immediate price increases. One net point scored in the previous minute raises the Kalshi midpoint by 1.22 percentage points. Event-level signals also move prices in the expected direction: made three-point shots, made two-point shots, opponent turnovers, and lead changes all generate positive and statistically significant responses. Salient events, including lead changes, made three-point shots, 8--0 scoring runs, and the signed salience index, also predict immediate price movements in the expected direction.
The estimates show that live prices are not detached from the game state. Traders process public information quickly, and prices move sharply in the expected direction after favorable and unfavorable signals. This supports directional live updating. However, directional responsiveness is not the same as efficient updating. A market can move in the right direction and still move too little or too much relative to the signal's statistical content. To test whether prices move by the right amount, the next section compares Kalshi price changes with changes in a benchmark win probability implied by the public game state.
The evidence above shows that live prices move in the right direction after public signals. Directional updating, however, is only a weak requirement for efficiency. A market can respond positively to favorable news and still move too little or too much relative to the news' statistical content. We therefore compare Kalshi price changes with changes in a benchmark win probability implied by the public game state.
Following Section (ref), we estimate the benchmark probability $q_{it}$ using a logit model of the final payoff on pre-game and live game-state variables, including the pre-game closing price, score margin, absolute score margin, game-clock time remaining, period indicators, home status, recent net scoring, and nonlinear interactions between score margin and time remaining. The benchmark excludes the contemporaneous Kalshi live price. This ensures that we compare market prices with an independent public-information benchmark rather than with a model that mechanically embeds the market price. To reduce overfitting, we estimate the benchmark out of sample using five-fold cross-fitting at the game level. All observations from a given game are assigned to the same fold. For each fold, the model is estimated on the remaining games and used to predict \(q_{it}\) for the held-out games. This procedure produces an out-of-sample benchmark probability for every contract-minute. The benchmark is well calibrated. Its Brier score is 0.164, compared with 0.164 for the Kalshi live midpoint and 0.211 for the pre-game closing price. Figure (ref) shows that realized win frequencies closely track benchmark probabilities across the distribution. The benchmark therefore provides a useful proxy for the public-information component of win probability.
We next test the efficient-updating condition in Equation (ref) using the empirical specification in Equation (ref). Table (ref) reports the results. Column 1 estimates the relationship between Kalshi price changes and benchmark probability changes without additional controls. Column 2 adds the control variables \(X_{it}\), which include the lagged Kalshi midpoint, the lagged benchmark probability, score margin, absolute score margin, game-clock minutes remaining, bid--ask spread, recent volume, and open interest.
Column 1 shows the raw relationship between Kalshi price changes and benchmark probability changes. The coefficient on \(\Delta q_{it}\) is 0.630. Column 2 adds controls and yields a similar estimate of 0.638. In both cases, the coefficient is precisely estimated and statistically different from one. Thus, a 10 percentage point increase in benchmark win probability is associated with only about a 6.4 percentage point contemporaneous increase in the Kalshi midpoint. The evidence therefore points to incomplete incorporation of public information on impact.
A natural concern is that measurement error in the benchmark probability could attenuate the estimated coefficient on benchmark probability changes. We therefore examine whether the updating gap defined in Equation (ref) predicts subsequent price adjustments. Following Hypothesis 4, we estimate Equations (ref) and (ref) for horizons \(h=1,2,5,10,\) and \(15\) minutes. As in the updating regressions, the control variables include the lagged midpoint, lagged benchmark probability, score margin, absolute score margin, game-clock minutes remaining, bid--ask spread, recent volume, and open interest. Table (ref) reports the results. The coefficient on the updating gap is positive and highly statistically significant at every horizon. At the five-minute horizon, a 10 percentage point initial updating gap predicts a 2.0 percentage point subsequent price change and a 4.6 percentage point price change net of benchmark updates. At the fifteen-minute horizon, the corresponding effects are 2.4 and 4.8 percentage points. These results indicate that deviations from efficient updating are subsequently corrected rather than permanently incorporated into prices.
Figure (ref) summarizes the drift coefficients. The effect appears immediately and persists over the following fifteen minutes. The net-of-benchmark specification is especially informative: when the benchmark indicates that the contemporaneous price response was smaller than the benchmark-implied probability change, subsequent prices continue to move in the benchmark direction even after accounting for future public-information changes. This strengthens the interpretation that the one-minute response in Table (ref) reflects gradual incorporation of public information rather than only noise in the estimated benchmark.
(ref) shows that the result is robust to alternative benchmark win-probability models, including parsimonious, flexible, no-recent-scoring, and chronological-holdout specifications. (ref) shows that the result is also robust to microstructure-related sample restrictions. The coefficient on benchmark probability changes remains well below one in samples with positive trading volume, narrow spreads, non-stale quotes, and high-quality quote observations. The updating gap also continues to predict five-minute drift net of future benchmark changes. However, executable-style returns that buy at the ask and sell at the bid are negative, indicating that the predictable midpoint drift is largely absorbed by trading costs. Taken together, the evidence supports a gradual-adjustment interpretation. Live prices respond strongly to public-information shocks, but the response is incomplete on impact. The initial updating gap predicts subsequent drift, including drift relative to future changes in the benchmark probability. The next section asks whether this incomplete updating is uniform, or whether it is concentrated after salient public signals and in thin markets. (ref) shows that incomplete updating is present throughout the game and is especially pronounced in clutch situations, where the coefficient on benchmark probability changes falls to approximately 0.51.
The previous section shows that live prices respond strongly to public information but fail to incorporate it fully on impact. Price changes move in the same direction as benchmark win-probability changes, yet the contemporaneous response is substantially below one-for-one, and the resulting updating gap predicts future price drift. We now ask whether this incomplete updating is uniform across public signals and market states. The framework in Section (ref) highlights two forces that may shape the speed of price discovery. First, some public signals are more salient than others. A made three-point shot, a lead change, or a large scoring run is likely to attract attention and may therefore be processed more rapidly than less visible information. Second, even when information is recognized, incorporating it into prices may be costly when liquidity is limited. Attention and liquidity therefore need not have the same effect: salient signals may be easier to notice, while liquidity determines how fully they are incorporated into prices. To study these mechanisms, we use the updating gap defined in Equation (ref). A positive gap indicates that the benchmark probability increased more than the Kalshi price. To treat positive and negative benchmark innovations symmetrically, we define directional underreaction as \[ UR_{it} = \operatorname{sign}(\Delta q_{it}) \left(\Delta q_{it}-\Delta p_{it}\right). \] Thus, ($UR_{it}>0$) indicates that the price moved too little in the benchmark-implied direction, while ($UR_{it}<0$) indicates that the price moved too much. We restrict attention to economically meaningful benchmark innovations, ($|\Delta q_{it}|\geq 0.0025$), to avoid classifying negligible probability changes as directional shocks. We measure salience using a standardized index constructed from highly visible game events, including made three-point shots, lead changes, scoring runs, and the event-level salience score derived from the play-by-play data. Illiquidity is measured using a standardized index that increases with bid--ask spreads and decreases with recent trading volume and open interest. Both indices are standardized to have mean zero and unit variance. We estimate a reduced-form version of Equation (ref) in which the dependent variable is directional underreaction, \[ UR_{it} = \alpha + \beta Salience_{it} + \gamma Illiquidity_{it} + \theta Salience_{it}\cdot Illiquidity_{it} + \Gamma X_{it} + \varepsilon_{it}, \] where $X_{it}$ includes the absolute benchmark innovation, lagged market and benchmark probabilities, score margin, absolute score margin, game-clock minutes remaining, and close-game and clutch indicators. Standard errors are clustered by game. Table (ref) reports the results. Column 1 uses the composite salience index. Illiquidity is associated with greater directional underreaction: when markets are thinner, prices move less completely in the direction implied by the benchmark. By contrast, the coefficient on salience is negative. Salient events are associated with smaller underreaction gaps, suggesting that highly visible information is incorporated more rapidly when trading conditions are favorable. The interaction between salience and illiquidity is positive and highly significant. The effect of salience therefore depends on market conditions. In liquid markets, salient information is incorporated relatively quickly. In illiquid markets, however, the same salient signals are associated with larger underreaction gaps. Salience appears to improve recognition of public information, while liquidity determines whether that information is fully incorporated into prices.
Column 2 confirms this pattern using individual event indicators. Three-point shots, turnovers, lead changes, and large scoring runs are all associated with smaller underreaction gaps on average. These events attract attention and appear to facilitate immediate information processing. However, the interaction with illiquidity is positive for three-point shots, lead changes, and scoring runs. The effect is largest for lead changes. A lead change is among the most visible events in a game, yet in a thin market it is not fully incorporated on impact. This result is important because it rejects a simple salience-as-bias interpretation. In our data, salient information is not systematically overreacted to. Instead, salience appears to improve immediate recognition of information, while liquidity determines whether that information is completely reflected in prices. Figure (ref) illustrates the interaction. It plots the marginal effect of salience on directional underreaction,
The marginal effect is negative when markets are relatively liquid, implying that salient signals are incorporated more completely. As illiquidity increases, the effect becomes less negative and eventually turns positive. The same public signal can therefore be incorporated rapidly in a liquid market but only partially in a thin market.
We next examine whether the gradual adjustment documented in Section (ref) also depends on salience and liquidity. To do so, we augment Equation (ref) with interactions between the updating gap, salience, and illiquidity. Specifically, we estimate \[ \left(p_{i,t+h}-p_{it}\right) - \left(q_{i,t+h}-q_{it}\right) = \alpha + \rho Gap_{it} + \phi Gap_{it}\cdot Illiquidity_{it} + \psi Gap_{it}\cdot Salience_{it} + \Gamma X_{it} + \varepsilon_{i,t+h}. \] The dependent variable is future price drift net of future benchmark changes. The coefficient \(\rho\) captures the average correction of the initial updating gap. The interaction terms test whether this correction differs across salient and illiquid states. Table (ref) reports the results for horizons of 5, 10, and 15 minutes. The updating gap strongly predicts subsequent drift at all horizons, confirming the gradual-adjustment result from the previous section. More importantly, the interaction with salience is positive and statistically significant throughout. Underreaction gaps associated with more salient states are followed by larger subsequent corrections. Salient information that is not fully incorporated immediately continues to enter prices over the following minutes. The interaction with illiquidity is not positive in the drift regressions. If anything, the coefficient becomes negative at longer horizons. This suggests that illiquidity increases the initial failure to incorporate information but does not accelerate subsequent correction. Instead, the same trading frictions that slow adjustment on impact may also slow convergence afterward. Taken together, the evidence points to gradual price discovery shaped by the interaction between attention and trading frictions. Salient public signals are not ignored: in liquid markets they are incorporated relatively quickly. However, when salient information arrives in thin markets, prices adjust less completely on impact and continue to drift in the benchmark direction over subsequent minutes. The mechanism is therefore neither simple inattention nor systematic overreaction. Rather, real-time markets appear to recognize salient public information, while liquidity determines how fully that information is incorporated into prices. This interaction between behavioral attention and market microstructure helps explain why even simple binary contracts with transparent public signals can exhibit predictable short-horizon drift.
Prediction markets are increasingly used as real-time measures of collective beliefs. Their usefulness depends not only on whether prices are calibrated on average, but also on whether they update efficiently when public information arrives. This paper studies that question using live NBA event contracts traded on Kalshi and merged with high-frequency play-by-play data. The setting allows us to observe market prices, liquidity, public signals, and terminal payoffs at high frequency, and to compare price changes with changes in a public-information benchmark win probability. The evidence supports a nuanced view of prediction market efficiency. Kalshi prices are highly informative. Pre-game prices are well calibrated, become more accurate as game time approaches, and provide a meaningful prior for the live market. During games, prices respond rapidly to public information: favorable scoring, made shots, opponent turnovers, lead changes, and scoring runs all move prices in the expected direction. In this sense, the market processes public information in real time. However, directional responsiveness is not the same as efficient updating. Relative to an out-of-sample benchmark win-probability model, live prices underreact on impact. A one-minute change in benchmark win probability is associated with only about a 0.64-for-one contemporaneous change in the Kalshi midpoint. The missing adjustment predicts future price drift over the next several minutes, including drift net of subsequent changes in the benchmark probability. Prices therefore move in the right direction, but not far enough. The mechanism analysis shows that incomplete updating is shaped by both attention and trading frictions. Salient events are incorporated relatively quickly in liquid markets, suggesting that visible public signals attract attention and are processed rapidly. But when salient information arrives in thin markets, prices adjust less completely on impact and continue to drift in the benchmark direction. Salience alone does not imply bias, and liquidity alone does not determine efficiency. The failure arises from their interaction: markets appear to recognize salient public information, while liquidity determines how fully that information is incorporated into prices. These findings have implications for how prediction market prices should be interpreted. Prediction markets can provide useful and timely forecasts, and our evidence confirms that their prices contain substantial information. But informativeness is not instantaneous efficiency. When public information arrives rapidly, especially in low-liquidity states, market-implied probabilities may be directionally correct yet temporarily incomplete. This distinction matters for researchers, firms, and policymakers who use prediction market prices as measures of beliefs. More broadly, the paper shows that live prediction markets are valuable laboratories for studying belief updating. They combine binary payoffs, precisely timed public signals, real money, and endogenous liquidity. This environment makes it possible to study not only whether markets aggregate information, but when and why the aggregation process is incomplete. The evidence suggests that real-time markets process public information quickly, but not always fully: price discovery is gradual and predictably shaped by the interaction of attention and trading frictions.