*Alexander Stroud*

For two years, FiveThirtyEight.com has published NBA predictions featuring win probabilities and point spreads using their CARM-Elo team ratings (2015-16 predictions and 2016-17 predictions). The win probabilities are interesting, but across an NBA season, there aren’t enough games for any individual percentage value to have a sufficient sample size for analysis. Additionally, the point spreads published by Las Vegas sports books are the models to which all amateur and professional NBA gambling predictions are compared. I consequently decided to collect a full regular season’s worth of FiveThirtyEight point spread projections, Vegas spreads (taken from the betting lines shown in the Yahoo! Sports app), and game results, and evaluated how well Nate Silver and crew could do.

I used the FiveThirtyEight line to decide which team to hypothetically place a bet on to beat the spread. Taking the first game of the 2016-17 NBA season as an example, the Vegas spread has Cleveland favored over New York by 9.5 points, while the FiveThirtyEight model gives the Cavaliers 11 points over the Knicks. Since FiveThirtyEight favors the Cavaliers by a greater amount than Vegas, a hypothetical bet would be placed on the Cavaliers to beat the spread. Incidentally, Cleveland won that game 117-88, so the FiveThirtyEight model started off the season well. Across the entire regular season, the FiveThirtyEight model had a different spread than that posted by Vegas in 1136 of the 1230 games, and of those games this FiveThirtyEight betting strategy had 559 wins and 560 losses, with 17 pushes: indistinguishable from the performance expected by simply flipping a coin to choose which team to bet on every game.

This simplest strategy is not able to make any money, so I turned to potential factors available to refine predictions. The first of these is the discrepancy between the respective spreads given by FiveThirtyEight and Vegas. Perhaps FiveThirtyEight performs better when betting on the Vegas favorite, or when its posted spread is close to the given Vegas value?

### Investigating the Discrepancy between the FiveThirtyEight and Vegas Spreads

The discrepancy between the FiveThirtyEight spreads and the Vegas spreads is calculated as the simple arithmetic difference between the two values. A positive disecrepancy signifies that FiveThirtyEight predicts that the Vegas underdog will outperform the spread, and a negative result signifies that FiveThirtyEight thinks the Vegas favorite will outperform the spread. FiveThirtyEight’s predictions are published daily; after the completion of the previous night’s games, team ratings are updated and 50,000 new simulations are run to give the next day’s spreads. As a result, the FiveThirtyEight model is not sensitive to late-breaking developments such as players resting or sitting out their first game after suffering an injury. Since the Vegas spread data was collected after games ended (and thus reflected the final value of the point spread before tipoff, accounting for news just hours before a game), injuries and players resting could cause large discrepancies between the two spread values. The FiveThirtyEight model seems more likely to be less accurate than Vegas in these large-discrepancy situations, so I might want to avoid placing bets. Examining the games where the absolute value of the discrepancy between the two spreads is 10 or greater, I saw that the assumed situation did occur:

In all six games, the team that FiveThirtyEight overfavored was missing at least one star player, and often the team was missing another star or quality starter as well. It appears likely that FiveThirtyEight’s spreads assume those players would instead be playing.

Other player-related moves that might affect the accuracy of FiveThirtyEight’s projections involve the trades of high-profile free-agents. While the CARMELO player performance projections would account for a star switching teams, each team’s Elo rating would not catch up until that player’s impact is manifested on the court in terms of wins and losses.

In their first five games after the DeMarcus Cousins trade, FiveThirtyEight overfavored the Sacramento Kings against Vegas by 9, 8, 7, 7.5, and 8.5 points, compared to only 7, 5, 1, 2, and 2 points in the five games before the Kings dealt their star center. The New Orleans Pelicans also saw discrepancy jumps right after the trade: their seven games immediately preceding all featured discrepancies between -1.5 and 0.5, with an average of 0.5, and only two of the seven games after acquiring Cousins had FiveThirtyEight-Vegas discrepancies closer to zero than -3.5, with an average across those games of -3.6 and a maximum of -7. These differences would be statistically significant (p < .05), except the five games for the Kings and seven for the Pelicans were chosen after looking at the data to emphasize the before/after discrepancy splits. Additionally, there is no way to discern a priori the number of games the CARM-Elo ratings will need to properly account for such a blockbuster trade. But regardless of statistical significance, the evidence is strong enough to warrant an examination of the FiveThirtyEight betting strategy’s performance at different discrepancy values.

### FiveThirtyEight Model Success by Discrepancy with the Vegas Spread

All discrepancy values with at least ten games played are pictured in the plot above.

Although the plot is pretty scattered, it seems that the FiveThirtyEight betting strategy had more success when projecting the Vegas underdog to beat the spread by 1 to 3.5 points. Across those discrepancy values, placed bets saw a 52.3% win rate, with 22 more wins than losses over 478 games (ignoring those where bets pushed). Using a tighter bound and considering only discrepancies from 1 to 2.5, placed bets saw a 53.1% win rate, with 22 more wins than losses over 352 games. However, this success rate is not significantly different from 50% (p ≥ .12), nor is any win rate on this chart. The 1 to 3.5 range just happens to contain a cluster of the discrepancies that ended up with a greater than 50% betting win rate.

### FiveThirtyEight Model Success by Date

Date is also a parameter I could potentially use to refine predictions. Given the roster shuffles at the trade deadline and the potential model inaccuracies noted earlier from those swaps, perhaps refraining from bets for a few weeks post-deadline would eliminate losing days. Or, maybe the FiveThirtyEight model will be inaccurate at the start of the season until it has some amount of game data on which to base every team’s rating. Below is a scatter plot of the FiveThirtyEight betting strategy’s win percentage for each of the 162 gamedays of the NBA season:

Unsurprisingly, the plot is very highly scattered. Games are hard to predict! The trendline indicates an improvement in prediction quality as the season progresses, but the coefficient of the slope is not significantly different from zero (p=0.22). To attempt to look beyond the noise, I applied smoothing, using a seven-day moving average (blue) and a fourteen-day moving average (red) of bet win percentage in the plots below.

The first, dark green vertical line corresponds to Christmas (Gameday 60), and the second, light green line is the day of the NBA trade deadline, February 23 (Gameday 114).

The weekly moving average chart is still quite volatile, again underscoring the unpredictability of the results of a single NBA game (only about 50 to 60 games are played each week). However, in the 14-Day moving average chart, the curve is smoother, revealing that the model performs quite poorly to start the season, with the average staying below 50% until early December. During the middle part of the season, between Christmas and the trade deadline, the moving average of win percentage stays mostly above 50%, and then after the trade deadline the average declines steadily before fluctuating again at the end of the season. I chose Christmas and the trade deadline as benchmarks because they roughly split the season in thirds, and because both are important dates for the NBA. Christmas is a showcase with high-profile games, and is often the date around when casual fans start tuning into the NBA, as football winds down. An increase in casual viewers could lead to an increase in bets placed in Vegas, which might affect the spreads posted by the sports books. The trade deadline, as previously mentioned, features a roster shuffle, which could impact the accuracy of the FiveThirtyEight model. While these reasons are simply speculation, the two landmark dates chosen do occur around gamedays where the 14-Day moving average of win percentage changes.

The results of the FiveThirtyEight betting strategy in each of the three sections are as follows:

Again, while the stretch of time between Christmas and the trade deadline is unequivocally the best for the FiveThirtyEight betting strategy of the three stretches considered, it still is not significantly different from 50% (p ≥ .29). Even if I combine the two best strategies, and only bet on those games where the discrepancy is between 1 and 3.5 and the date is between Christmas and the trade deadline, results are not promising. With those rules applied, the FiveThirtyEight betting strategy has a 55.1% win rate, with 17 more wins than losses over 167 games. This is the best win rate yet, but the model has been reduced to betting on only 13-14% of NBA games. It also still fails to see a statistically significant difference from the 50% benchmark (p > .09), even before accounting for the fact that the best-performing of all the strategies has been chosen, which alters the distribution of p-values.

### Conclusions

While there are stretches of time and clusters of discrepancies where the FiveThirtyEight betting strategy will outperform Vegas, and I was able to formulate potential explanations for their success, they are not statistically different from the expected output of flipping a coin to decide which team to bet on. The main lesson is that Vegas knows what they’re doing with their models, and it will be almost impossible to beat them. However, I was not surprised that I could not find extended success. If a model published online, like FiveThirtyEight’s, was able to consistently make money against the Vegas spreads, eventually enough people would use it to bet against Vegas that the oddsmakers would take note and adjust the point spreads accordingly.

If FiveThirtyEight keeps their model the same and the betting strategies that proved more successful this year (discrepancy between 1 and 3.5 points, from Christmas to the trade deadline) show the same positive results next year, I might consider placing down some money on the FiveThirtyEight side of the Vegas spread in the future. The small volume of games that fit these criteria means that earning potential from such a strategy is limited to a little extra money on the side, unless a bettor is willing to risk large sums on individual games. Ultimately, the best way to make money in Vegas is to own the casino.

*Contact Alexander at astroud ‘at’ stanford.edu*