Hello, P&Ters! About a month ago, we learned, thanks to the diligent work of poooooo that our beloved Knickerbockers appear to lose a great deal more on Fridays. I took it upon myself to determine whether this conclusion was statistically significant; my question is, do the Knicks have a significantly lower winning percentage on Friday, as compared to other days of the week?
Take the jump to find out.
Here we have the two previous seasons (updated as of last nights game). Wins, Losses, Total number of games, then the respective winning percentages are what each column represents. To the left of each we have the totals of Monday-Sunday (minus Friday), and to the right we have the totals of Friday. (Again, thanks to poooooo for the initial compilation of data). Also included are the total winning percentages, as well as the mean winning percentages.
Here are the total winning percentages and means taking into account both seasons.
Now, for something to be "statistically significant", it means that the differences between two groups are unlikely to be attributed to chance. The 0.521 mean winning percentage appears to be different from the 0.333, of course, but I've seen for more "different looking" sets of data actually end up being insignificantly different. So let's venture into the word of (relativelybasic) statistics!
The first statistics test I will run is the "Student's T-Test". It is a very basic, and very common test that is used to compare to arrays of data that measure the same thing - and determines the probability that the differences between the two can be attributed to chance. This is a "p" value.
A sample T-Test equation, which takes into account both sets of data, their respective means, and their standard deviations to compare the differences
I compared the entire array of data in two seasons that represented the win percentage for every day of the week except Friday, to the win percentage that was on Friday. I made the test "heteroscedastic", because we have two samples with unequal variance; 6 days of the week as opposed to one.
The p value = 0.00623. This means that there is a 0.6 % chance that the differences between the data sets can be attributed to chance. If a p value is < 0.05, the result is said to be statistically significant.
Okay, interesting. So the other test I conducted is slightly more complicated, probably more accurate for comparing this set of data: a Chi Square analysis. Chi square compares observed values to expected values, and determines the probability that the differences are due to chance.
I used the mean winning percentage for every other day of the week as a baseline for comparison; my hypothesis would be that the winning percentage for six days of the week would not be significantly different that the winning percentage of the seventh day of the week; Friday. The observed values were the wins/losses on Fridays, the expected values were what the wins/losses should have been based on the mean win % for every other day
My chi-square value was = 0.2879
This lies somewhere in between the p-values of 0.05 and 0.025, making the differences statistically significant
So, what does this mean? It means that it's not just superstition; the Knicks have been statistically more likely to lose on a Friday as compared to other days. This would be an acceptable hypothesis in scientific literature, assuming I ran everything correctly. While I'm keen on blaming Robert Randolph, there are certainly other factors that could contribute to losses being more likely on Friday.
Just to be safe, though, get out your scimitars, folks!
Let's look at some more data, shall we?
Here I've gathered some more detailed information (my goodness it was painful to look back at some of these losses). Particularly notable off the bat is the nine consecutive losses we had on Friday in 2010-2011. Absolutely ridiculous - this set is likely the primary contributor to the significance I discovered above.
In the comments below (thanks for the kind words, by the way) a few of you have brought up whether some the Friday futility may have to due with the strength of schedule - the hypothesis being that Friday may include some marquee difficult matchups between the Knicks and upper echelon teams. A contrary hypothesis is that a majority of these losses are "let down" losses against inferior competition that the Knicks simply overlooked.However, studying the Friday win % seems to indicate that this is not the case. The difference between the Friday Opponent Win % and the Win % of teams across the NBA is entirely negligible; the difference is not significant (p= 0.24221).
Here, for your viewing convenience, is a breakdown of these Friday losses. 75% of games against plus .500 teams were lost, as opposed to 63% of games against sub .500 teams. While we have played more sub .500 teams on FNK, the data set as well as the corresponding percentages indicate that this has no significance.
My conclusions based upon the above data are that (1) The schedule is not significantly stronger or weaker on Fridays and (2) The Knicks are not significantly more likely to win or lose against either a plus .500 or sub .500 team; that is, there is no correlation between opponent record and whether the Knicks will win or lose the proceeding game.
Now that opponent win % is confirmed to not be a factor, what else could be? Perhaps either the offense or defense is suffering? Please scroll back up for a second - look at the points per game, points allowed per game on Friday Night Knicks as opposed to the season stats.
According to successive T-Tests, the p-values comparing values comparing this data are 0.54821 (Points Scored Per Game) and 0.67443 (Points Given Up Per Game). While PF/PA are not clear indications of offensive or defensive efficiency (I'm not going into extreme detail to look at FG%, turnovers, etc) I believe it is a useful enough benchmark to test the hypothesis - which is completely shattered. Check out those p-values. Huge! On average, the Knicks do not score nor give up more points on Fridays than they do throughout the season.
So what's going on? We've discounted the usual suspects that would be explanations for our losses on Fridays. The only viable explanation thus far, whose significance cannot be tested, is that this is a curse.