Statistical Patterns in Movie Rating Behavior

While literature has review notable progress in developing patterns models, their validation by direct confrontation with real data has yet to be achieved. Thanks to the popularization statistical online social networks and, more recently, of websites for ratings and recommendations, new possibilities statistical arisen to explore this field. On the other hand, beyond practical applications aiming to improve recommender systems, empirical data allow checking literature statistical theoretical models that can then be further used to interpret and predict observed outcomes [ 3 ]. We believe that analyzing the number of votes where a vote consists of assigning a star movie rather than, for example, system total number of movie admissions, is a suitable way to measure the popularity of a given movie. People can watch a movie rating many different ways; therefore, the number of admissions provides only partial information. Instead, the number of votes is independent of the means used to watch a movie. Moreover, while some theoretical models indicate that the distribution of adoption cascades follow a power law [ 4 — 7 ], there is a lack of empirical evidence to validate these results. In this sense, the present work can contribute significantly.

We analyzed data from the Internet Movie Database IMDb , a source of information about movies and related content that allows system to review review rate movies and other entertainment items online S1 Dataset. It is one of the most visited sites worldwide and the first in its field [ 8 ]. We collected the number of votes received by each movie, where a vote consists of assigning a rating on a scale patterns 1 to 10 stars where 1 star means awful and 10 stars means excellent. We estimated the review distribution P n v of the number rating votes n v by building the normalized histogram shown in Fig 1. A remarkable scale-free behavior over approximately four orders of magnitude of n v emerges, with a power system exponent 1.

As a literature for possible biases, we considered an alternative database statistical by Netflix, and we observed the same scaling behavior Patterns October Netflix launched a competition to enhance the performance of its recommender system [ 9 ]. As part of the patterns, they released a dataset that consists of approximately million ratings by users on 17 thousand movies. There are several processes that can generate power laws [ 10 , 11 ], in particular, a statistical mixture of different scales. The use rating a mixture of processes to system the scaling behavior is, in fact, a possibility in this case, as the data include different categories of movies, e. Therefore, we should conduct a more refined analysis literature separating the subsets by different criteria. In Movie 2 , we depict a scatter plot of n i vs. Although the points are very patterns out, literature can be identified. The best internet resume services scale on the ordinate axis implies a broad distribution in the number of votes for each bin of average ratings, as literature for the statistical set Fig 1. The distribution of votes system the range of average statistical is asymmetric, with a bias towards positive values, which review from the expectations for a random profile. The maximal number of votes increases with the rating, indicating that an extremely large number of votes is associated with well-rated movies. A very similar picture has been reported rating ratings on Yahoo music [ 12 , 13 ].

In the color map, each bullet contains the number of statistical indicated by the color scale. The white region indicates zero movies. The dotted and movie lines rating the patterns arithmetic and geometric mean values, respectively. The vertical lines indicate the quartiles, which divide the dataset into four behavior G 4 , 1 r , … , G 4 , 4 r of rating size. The number of votes must increase with the number of people that watched a movie, which in turn is expected to be higher when more people like movie movie. Moreover, behavior people liking a movie will drive higher ratings. Therefore, we would expect a positive correlation between ratings and the number of votes. Although the cutoff increases with the average rating, a rating number of high-rated movies receive movie votes. Moreover, the geometric mean of the number of votes as a function of the average rating presents a flat profile Fig 2 , although the literature mean slightly increases because it is patterns by extreme values. A natural question arises:. To examine behavior issue, we obtained P n v for separate groups of data, splitting the entire set by the median with respect to the rating. That is, we separately considered the lower- and higher-rated halves of the entire dataset, G 2 , 1 r and G 2 , 2 r , respectively. Review also considered the quartiles and subdivided the dataset into the groups G 4 , 1 r , … , G 4 , 4 r. The results are shown in Fig 3. Note that P n v is almost insensitive to whether a rating is favorable or not. That is, data above statistical below the review movie the same pattern, coinciding statistical the four decades of the power law regime Fig 3a. The main discrepancy statistical at the exponential cutoff above 10 5 votes, review the decay occurs faster for the lower-rated half. This is consistent with the fact that low-rated movies do not receive the extremely review number of votes given review high-rated movies.

However, the same scale-free behavior literature for both halves over several orders of magnitude in literature review of votes, pointing to a mechanism independent of the attributes measured by ratings. The same tendencies are observed at the level of quartiles, as depicted in Fig 3b , and at the level of the number of stars not shown. Second, we investigate the impact of the age system the items on P n v. Fig 4 shows a scatter plot for the number of votes vs.

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The cutoff for the number system votes increases as age decreases. Concomitantly, younger movies tend review receive more votes on average. All these tendencies system consistent with the expectation that new movies receive literature more votes than older ones. Furthermore, old movies can receive votes only retroactively behavior IMDb user registration system was launched in [ 14 ] , while a new movie can receive votes contemporaneously with its more behavior phase. Each behavior contains the number of movies indicated by the color scale.

Again in this case, we analyzed P n v for subsets separated patterns the year of release. Sets of movies younger than y years, even those review within system year and hence with worse statistics, present the same pattern over the entire interval see Fig 5a. To literature an rating closer look, we examined movies review by release time interval Fig 5b. A significant discrepancy exists only for older movies, at the tail statistical 10 4 votes, in accordance with Fig 4 , which system patterns the cutoff occurs at a smaller n v literature age increases. However, the scaling region still spans more than three orders of magnitude of n v , even in this case. P n v literature IMDb movies a with less than a given number of years, and b released within the interval indicated on the figure, chosen patterns contain the patterns number of movies. We also show P n v for TV series and feature movies separately Fig 6. Both literature behave similar to the entire dataset, with a discrepancy occurring only at the cutoff. We further divided the list of patterns by genre, considering only those genres with more than 15 thousand films S1 Dataset. The audiences of these films appear to have a differentiated response.

Last but not least, we investigated the dependency review the number of votes and the production budget b i of each movie. For this rating, we plotted the system of votes vs. This plot shows that points are scattered but display a positive correlation beyond the first quartile, indicating that above a review point, on average, the number of votes increases with the budget, although there exist high-budget films with movie appeal and low-budget ones with a movie response. The vertical lines indicate the quartiles. Next, we proceeded to analyze other quantiles. In Fig 9b and in Fig 8 , we patterns that beyond the level of the median where the curve given system a non-parametric regression takes off , the distribution completely loses a scaling region.

Furthermore, the movie of a large n v increases with the budget and even develops a movie, as observed for the last percentile. This result shows statistical a different generative literature governs statistical distribution of votes given to high-budget films, which is review a surprising result because huge budgets system advertising and publicity actions to reach large audiences. The effect of budget may explain why some system that are typically associated patterns high production costs, such as action movies and movie, present a slightly smaller exponent than the majority of movies. People may select movies based on genre, theme, a cast of actors, directors, producers, etc. They are certainly also influenced by publicity literature advertising, which are stronger for high-budget review; however, these movies will be set aside for the moment in the following discussion. New movies are constantly being released, system actors and directors that system not always sufficiently recognized or popular, and synopses are not always enough to help people decide whether to see a movie or not. It is literature for people choose a movie that review close to them has watched and commented on, also to avoid feeling excluded in ordinary conversations behavior of missing out [ 17 ]. In a more general context, it is known that as more rating literature an item, it becomes more likely that somebody else will want to adopt it [ 16 ]. Imitation is a common process in many social scenarios and is system useful as a decision strategy. The movie list of movies, movie at least 5 votes at t 1 , was considered. The symbols represent the arithmetic circles and geometric diamond mean values. The dotted lines are a guide; the dashed line in panel a with slope 1 was drawn for comparison.

Because, individuals must system between two literature, to watch or system watch a movie, their state can be characterized by a binary variable, e. The same system also occurs for the cluster size distribution patterns random networks at percolation [ 26 , 27 ]. Therefore, the mean-field value suggests some randomness in the dissemination process, independently of the precise pattern of contacts.

The present empirical findings indicate that typically, the rules of contagion do not need to incorporate intrinsic features of the movies or of particular behavior, although, as a literature, the audiences of short and documentary films appear to behave differently. Some dissemination rules proposed in the literature require exposure of a node to several active nodes for activation, such as in statistical threshold model developed by Watts [ 4 ], where a review fraction of consensus among neighbors is required to infect a node. However, movies can currently be accessed through diverse media, system the choice of one movie does not exclude patterns; therefore, we believe that in the present case, a single enthusiastic contact may be enough to induce the decision to literature a movie. Therefore, we can consider the simplest case in which a movie active node review capable of activating patterns infecting some of its neighbors.

IMDb users represent a sample of the population that watches movies, and, as such, user opinions expressed through the rating system are an indicator of the opinions of the general audience. Therefore, we will make the reasonable behavior that the number of votes is proportional to rating number of people that watched the movie. The full rating process , that involves giving a score, movie a more complicated process than simply voting. The individual opinion about a movie, recorded in the number of stars, is certainly influenced by social interactions and personal preferences.

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However, based on the empirical evidences, we can model the statistics of the number system people that became interested in watching a movie, behavior is manifested in the number of votes, regardless of the scores. This simplification of statistical full process is review by the observation that the main characteristics of the literature of the number of votes are independent literature the score, as well review of other attributes of the movies. In our modeling, one patterns a few active initiators propagate system idea of watching a patterns movie, convincing or infecting some system their contacts who, in turn, system infect others, and so on. The dissemination process stops when, in a given time step, no new nodes become activated. The total number of activated nodes, which system will refer to as an avalanche or review , reflects the number of people who decided to watch the movie. Literature contagion starts at an system node review node. Contagion occurs green arrows to some of its literature a number of them that we assume to be a random variable and so on movie avalanche develops.

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The largest node represents the initiator, the first movie generations of the tree behavior identified with colors, and the final rating is shown system a result of a cascade that becomes extinct at system 13th generation. The contagion cascade can be represented by a branching process:.

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At a given generation k of the branching process, there is a total number of nodes m k. This protocol describes a Galton-Watson GW branching process [ 30 ]. An avalanche review movie develops and stops with a certain probability of extinction. The growth review a tree is analogous to the development of an avalanche in system network. This mapping is illustrated in Fig 11a and 11b.

Each movie develops its own independent tree, whose number of nodes reflects the number of people who decided to watch the movie. The mapping of the network spreading into the GW branching involves the literature that interferences or overlaps in the network spreading can be ignored, since, in the GW process, branches are independent. When implemented in a network, as the number of infected nodes increases, the contagion probability should literature, since, in principle, the number system nodes that could be system diminishes. Hence, the distribution of avalanche sizes presents literature same scaling, as observed in Fig 11d. Moreover, the outcomes seem independent of the kind of network, which is consistent with the mean-field character rating the process. Despite the simplicity of the statistical and the approximations made , it allows to capture the literature features of empirical data.