Time of day importance for games

Ever notice that it seems like the Seahawks really struggle in morning games, but are nearly unbeatable in evening games? It's not just your imagination. Football Outsiders had a really good post explaining the phenomenon here:

The post is two months old, but if you haven't read it yet, it's worth reading the whole thing.

Unfortunately, if you're using NFL numbers, you inevitably end up with small sample sizes. But that got me thinking: if time of day affects performance in football games, surely it should affect other sports, too.

The NBA plays most of its games in the evening, largely because there are plenty of people available to watch an evening game, but far fewer for a mid-afternoon game, except on weekends. And while most NFL games are played on weekends, most NBA games are not. For example NBA finals game 6 started at 9 pm local time in Cleveland.

If Football Outsiders' thesis is correct, this should provide an advantage to west coast teams. The NBA conveniently breaks into conferences by geography, so one would expect western conference teams to tend to do better than eastern conference teams. Fortunately, there is a wealth of data on this.

For example, this last regular season, there were 450 games that pitted a west team against an east team. The west was 232-218 in those games. Therefore, the west has an advantage. Done?

Well, no. There's always the question of whether this could have happened by random chance. With 450 games, if all games were 50/50 propositions, you'd expect an average record of 225-225, with a standard deviation in the number of wins of sqrt(450)/2 ~ 10.6066. Thus, the west did 0.6128 standard deviations better than expected. Using a normal approximation, one can compute that the west wins at least 231.5 games (you need the half game for discreteness reasons) is about 27%. One can ditch the normal approximation and do explicit computations with a binomial distribution and get about the same 27% probability. That's readily explainable by random chance.

But the east actually did better this year than most. Out of the last 13 years, there were only 3 in which the west didn't perform at least 2.49 standard deviations better than expected. The probability of that happening in a given year is about 0.6%, which really isn't so explainable by random chance.

In 2013-2014, the west was 284-166 against the east, or more than 5.5 standard deviations better than expected. By a normal approximation, the probability of the west winning at least 284 cross-conference games by random chance is about 1 in 57 million. This is actually far enough off into the tail that a normal approximation isn't very good, as the probability of winning exactly 284 games would be about 70% higher than the probability of winning exactly 285. With an explicit binomial distribution, we get a probability of less than 1 in 68 million. Did that happen by random chance? No. Those are lottery odds.

But once we've got a lot of data, why not just add it all together? Over the last 13 seasons, the west is 3212-2428 against the east, or more than 10.4 standard deviations away from average. Calc's erf() function unhelpfully reports the probability of this happening as 0. Fortunately, we can still fall back to a binomial distribution and get a probability of about 7.9026E-026, or about than 1 in 12.7 septillion. Yes, "septillion" is a real number, and that 12.7 septillion is about 21 moles. Did that happen by random chance? Definitely not.

In the NBA, western teams are favored over eastern teams by about 4 games per year, or 2 games per year over neutral. Some western and eastern teams are actually in the same time zone (e.g., Dallas and Chicago are both central), so it's likely a smaller effect for teams near the center of the country and larger on the coasts. Dear NBA owners: want to win more games? Try moving your franchise to Seattle.

So what about the Seahawks? Well, sometimes you measure things because they're easy to measure, which is why I went with NBA numbers. In the NFL, per Football Outsiders' analysis, it looks like west coast teams are disfavored by about 0.4 wins per season, i.e., an average quality west coast team should expect to win 7.6 games per year, while an average quality east coast team would expect 8.1 wins.

If the NFL wanted to improve competitive balance, getting rid of the morning games for west coast teams would be a good way to do it. It's not like everyone is busy on Sunday afternoons. With church customarily on Sunday mornings, you'd think this would improve ratings, not hurt them.

Thankfully, the playoffs have a much smaller proportion of morning games than the regular season. Of course, that's little comfort when both of the morning games in this last playoffs featured the Seahawks.