In this work, we present an arti cial neural network-based prediction model for underdog teams in NBA matches (ANNUT). We describe the steps of our supervised algorithm, starting from data acquisition to prediction selection. We talk about prediction selection because the nal stage of our model is represented by a ltration phase. In this phase, the outputs returned from the neural network are evaluated according to how the events are quoted on one of the most famous bookmakers. Experimental results prove that the model is able to select with a certain accuracy winning teams. In particular, it reaches excellent results when we restrict the selection among underdogs (teams which probably will not win). Furthermore, we show that a signi cant sports prediction model cannot ignore bookmaker's odds.
The world of sports betting is a real jungle. There exists a huge number of bookmakers and prediction model for every sport. In this paper, we deal with predictions of outcome for basketball events. We consider the most famous basketball league, the National Basketball Association (NBA) played in North America. The worth of NBA is its incredible amount of matches. In fact, during the regular season, each team plays 82 games, 41 each home and away. Furthermore, most of those matches end with a small winning gap, this makes the NBA league one of the most exciting league in all sports. Due to this success, bookmakers and bettors follow NBA with extreme interest. These are some reasons why we choose NBA, in addition, we can count on a well-updated statistics database provided directly by NBA.
In this work, we present a prediction model based on training and application of arti cial neural networks (ANNs) with the nal aim to predict if home or away team is going to win the match. In detail, we see why all the predictions are not the same. In fact, we add another ingredient: bookmaker's odd. We describe all needed steps of analysis and the experimental results. Using classical techniques, we train the ANN with data related to the last regular season ended in April 2017 and we show its performance. Moreover, we test our ANNUT model on data concerning the last part of the NBA regular season showing its worth also in practice i.e., money gained by betting on these predictions. We show how our model, according to experimental results, is able to select underdog teams which have an underestimated odd (according to the ANN output).
The paper is organized in the following way, in Section II, we report a brief background dealing with neural network and machine learning in general. Furthermore, we provide a description of sports betting. In Section III, we describe the state of art and similar works. In Section IV, we explain in details the phase of our analysis starting from data acquisition to outputs. In Section V, we present the experimental results applying our prediction model to matches of the last part of the regular season. Finally, in Section VI, we conclude the paper also with some possible future works. 2
In this section, we are going to introduce brie y what is machine learning, in particular, data classi cation. Furthermore, we provide a description of the main actors involved in a betting scenario. 2.1
Machine learning [
Arti cial neural networks (ANNs) [
In particular, a feed-forward neural network is an arti cial neural network wherein
connections between the units do not form a cycle. In this network, the
information moves in only one direction, forward, from the input nodes, through the
hidden nodes (if any) and to the output nodes. It is common to use a
backpropagation method [
Sports betting is the activity of predicting sports results and placing a wager on the outcome. The frequency of sports bet upon varies by culture, with the vast majority of bets being placed on association football, American football, basketball, baseball, hockey, track cycling, auto racing, mixed martial arts and boxing at both the amateur and professional levels. Sports betting can also extend to non-athletic events, such as reality show contests and political elections, and non-human contests such as horse racing, greyhound racing and illegal, underground dog ghting.
The bookmaker functions as a market maker for sports wagers, most of which have a binary outcome: a team either wins or loses. The bookmaker accepts both wagers and maintains a spread which will ensure a pro t regardless of the outcome of the wager (bookmaker's fee). In other words, bookmakers have a xed income for every event, in fact, they underestimate every possible outcome of the event, i.e. they calculate the odd according to a higher probability than the expected one, meaning a lower odd for the outcome.
Odds for di erent outcomes in single bet are presented either in European format (decimal odds), UK format (fractional odds), or American format (moneyline odds). European format (decimal odds) are used in continental Europe, Canada, and Australia. They are the ratio of the full payout to the stake, in a decimal format. Decimal odds of 2.00 are an even bet with a theoretical implied probability of 50% (without considering bookmaker's fee). 3
In the state of art concerning NBA prediction models we can nd several works,
for instance in [
In [
GP W
L WIN%
MIN FGM FGA FG% 3PM 3PA 3P% FTM FTA
In the following section, we describe the analysis process ow. Our model is essentially composed of four phases. First of all, we have to collect data. Then, in the ltering phase, we process this raw dataset by removing irrelevant features. After that, we train the ANN deploying the resulting dataset as training source and we evaluate the performance of the generated network. Finally, we compare the ANN output, computed on a new input set of data referring to future events, to the bookmaker's odd of those events. In Fig. 2 we present a diagram describing the ANNUT model.
FT%
REB
AST
TOV
STL
BLK
PF
PFD
PTS
+/In our model, every record represents a match. In every row, we insert home team
statistics and road (away) team statistics. Statistics refer to previous matches
played during the season until the day of the match. It is important to note
that we take into account only home matches for the home team and only away
matches for the away team. This is because we assume that teams have a slighltly
di erent behaviour playing home or away. Data are extracted directly from the
o cial NBA site [
The NBA calendar is full of matches and it is common to have that two teams have a di erent number of played matches in the season. For this reason, to have a balanced dataset we normalize our data according to the actual played minutes, considering in this way also overtime periods. Thus, we have values per minute, for instance: points scored per minute. The two chosen categories for classi cation are win home and win road, they are boolean variables set to 1 if home team or road team won the match. Data refer to the second half of the season allowing us to have a set of data based on a signi cant amount of already played matches. 4.2
Once prepared the raw dataset, the next step is the ltering phase. We decided to select a subset of available variables. In details, we select ten features which describe almost completely the characteristics of a team. The selected features are shown in Tab. 2. We choose to remove rst of all the statistics concerning win or loss matches because they do not describe playing styles of teams. Then, we remove the number of shots, we evaluate that having the success shot percentage and the points scored it is su cient to have a consistent description of how much and how a team scores points. Furthermore, we remove foul statistics because they do not improve the network performances. Finally, we consider other variables (as the number of turnovers, blocks, etc.) giving information on the ability of teams mostly concerning defence playing. We get records composed of twenty elds, ten elds for each team.
PTS FG% FT% REB
AST
BLK
Our ANNUT model is based on the deployment of an ANN for pattern
recognition. Our aim is to predict which team will probably win the match, home
or road. In order to build the network, we deploy the "Neural Network" tool
provided by Matlab [
In order to evaluate the performance of the generated network, we show the
receiver operating characteristic (ROC) curve presented in Fig. 1. By looking
at the area under the curve ROC (AUROC) of Tab.3 (computed constructing
trapezoids under the curve), we have a measure of the predictive accuracy of the
model. We can see that the neural network has good prediction capabilities, in
fact, we have to consider that we are into a non-deterministic context (sports
events) in which we have a huge amount of involved variables. Our AUROC
values are compared in Tab. 3 with classi ers presented in [
1 q c (1) where q is the bookmaker's odd for that event and c is a xed parameter indicating the bookmaker's commission (the average bookmaker's gain). The value p should return the implied probability computed by the bookmaker, i.e. the bookmaker's expectation on that outcome. For this reason, we consider also bookmaker's commission c. Once computed the value p for the event, we compare it to the normalized ANN output o. If the di erence between values p and o exceeds a prede ned threshold t, we choose this prediction. In other words, it means that our expectation of that event is greater at least of a factor t than the bookmaker's one.
We are now able to present the experimental results. We build the network with
a dataset composed of 566 matches extracted from the o cial NBA database
and odds are extracted from one of the most famous bookmakers, Bet365 [
Accuracy = number of correct predictions number of predictions 100 (2) In the Tab. 4, we expose our results according to our prediction schema. In the rst row, we consider every range of odd and we collect 69 event predictions over 117 considered matches, their winning rate, average odd and the balance (computed assuming that we bet one unit per prediction). In next rows, we restrict the selected predictions according to the odd, for instance in the second row we consider only events listed with an odd greater than 1:99. The winning percentage must be evaluated considering that our model selects events with high odds, i.e., low probability but high pro tability. In order to better show the performance of our model, we compute also the implied probability according to the odds of the selected matches. The implied probability is exactly the value p computed by Eq.1 with c = 1:041 and q is the average odd. Tab. 4 shows that the accuracy of our model has a good margin over the implied probability, especially in the case of odds greater than 2:99 where we have a signi cant percentage of correct predictions with respect to the implied probability.
In the last two rows, we can see a consistent gain in units. We can interpret this result as the capability of our model to predict the win of an underdog team. Considering only odds between 3:00 and 10:00, our model selects 26 events with an average odd of 4:63. 10 out of 26 events are winning predictions with a winning average odd of 4:89. Assuming to bet one unit for each event, we have a total balance of +22:89 units. Taking into account matches referring to the last row of Tab. 4 and assuming that we have a base bet amount of 10:00 e on each match, in Fig. 3 we present the trend of our balance.
Odd no restrictions In conclusion, in this paper, we describe the ANNUT model showing its profitability on real events. The ANNUT model reveals good performance in term of ANN ROC curve but also concerning the selection of winning underdog teams which lead us to interesting money earnings showing his e ectiveness into practice.
The interpretation of the success of our framework can be related to the consensus phenomenon which shows what percentage of the general betting public is on each side of the game. Thus, in order to balance the market, bookmakers change odds according to the sentiment of bettors. Considering this scenario, our ANNUT model shows its ability in spotting undervalued teams. There are several future works whom we can add, for instance, we can make an additional analysis on how to choose the threshold t. Furthermore, one weak point is represented by the fact that the model does not consider missing players. This can lead to a wrong prediction if one or more relevant players will not probably play the game because odd will very high for that team.