Kevin Durant has been doing this sort of thing quite a lot recently:
But what’s that got to do with Kennett’s curse?
Any footy fan can tell you about Kennett’s curse: from 2009 to 2013, Geelong beat Hawthorn 12 times in a row, and it was kinda awesome to watch (unless you barrack for Hawthorn). And I’m sure that the overwhelming majority of true footy fans can tell you what Kennett’s curse is: a run of 12 consecutive successes in 12 Bernoulli trials.
And, as they’re lining up for an incredibly expensive beer at Docklands, they’ll start giving you the subtleties of the Curse: was it really 12 trials? Or was it actually 13 trials, going back to their previous match. Or 15, stretching back to previous seasons? Or 150 trials? It depends when the experiment actually started – choosing the starting point after the experiment has already started – selective endpointing – is a frequent trick, or error, to frame numbers in a way that suits your narrative.
The good news on this is that fans of the AFL, and the AFL itself, are not alone in seeing significance where it doesn’t exist. The NBA have joined the party, with their, ahem, stellar article on the scoring streak of the Oklahoma City Thunder’s Kevin Durant. Durant has been kind enough to score 30+ points for 11 straight games, delighting Thunder fans and causing considerable relief for Brian Martin, who now has something to fill the no-doubt endless blank screens which would otherwise fill NBA.com.
(Not that we can be too smug down here in Victoria. Our contributed ads are decorated with little flourishes like this by the interns… Would you prefer to meet Aussie NBA star Patty Mills, or would you like to meet “Patty Mills”… if that is your real name?)
Moving on: the article is titled “Comparing the Scoring Streaks”, in the same way you’d title an article “Comparing the Five Parts of TS Elliot’s The Waste Land”, if all you intended to do was count the number of words in each and mention the various fonts. Martin recalls similar scoring streaks by (in order of famousness in non-basketbally circles) Michael Jordan, Shaquille O’Neal, Kobe Bryant and Tracy McGrady), noting who was the oldest and youngest, who had lots of 3-pointers, who also surpassed 40 points or more, etc etc… and including such random factoid gems as:
And, concerning who averaged the most points per shooting attempt in open play:
… which seems to be a stuff up. Aren’t free throws and field goal attempts mutually exclusive? If so, why are free-throw points and attempts included in the calculation of points per field goal attempt in the first table? And, as an aside – if Martin is trying to establish accuracy or shooting efficiency or some other (unspecified) metric, there are many more sophisticated ways than just subtracting the free throws (don’t you earn them by getting fouled or some such chicanery? which is presumably another way of being effective player).
All of which is just a distraction from the main game: why does anyone care about streaks?
Sharp-eyed readers will have already made the connection between the Kennett curse and Kevin’s streak. They both involve an attempt to achieve something which has a yes-no result: did Hawthorn win? Did Durant score 30 points? And the probability of a streak of yeses (or nos) can be calculated using what is possibly my most favouritest formula in the whole mathematical world, courtesy of Ask a Mathematician:
Ridiculously complex, isn’t it? I like to display it in eerie colours for added impressiveness. And yet, pretty easy to work with in Excel, because there are only 3 variables:
p = the probability of a “yes” (Hawthorn win / Durant scores 30 points… the probability of a “no” is represented by q, which is simply = 1 – p)
N = the total number of “trials” (how many of Hawthorn’s / Durant’s games are we looking at)
K = the length of streak are we looking out for
In the case of Hawthorn, two of the variables are debatable. What was Hawthorn’s true probability of winning each of their games? Perhaps the betting odds would have been a reasonable guide (an idea there for a future post). And how many total matches are we looking at (see para 2 of this post)?
In the case of Durant, the same two variables are debatable for the same reasons – but why not look at his whole career, and his career frequency of 30+ point games?
Incidentally… you can critique NBA.com all you like – I already have – but no-one can say they don’t give you plenty of stats to play with. It’s so cute that they publish them in a table without an export option but think no-one will be able to – or want to? – work out a way around it. And, below, they offer such helpful interactive hints for the uninitiated (although I personally think that if you don’t know how points are scored in basketball, manipulating Kobe Bryant’s career game log stats would come a distant second priority behind, say, watching a game).
Back to Mr Durant. He has played 510 games, including 192 30-point games. Running these numbers through the ridiculously complex formula, his streak should occur 0.67% of the time – 67 times in 10,000. Experimenting with the variables, but keeping it as an 11-game streak, yields…
So, where does this sit in the great streaks pantheon?
McGrady’s streak, on this measure, is off-the-charts weird – 4 in 10 million! The low probability is driven by his apparent inability to score 30 points on a regular basis (and is a good answer to the earlier rhetorical question, why not just use career stats?). A much more sensible suggestion would be that, for a period surrounding and including his streak, his true proportion of 30+ point games was significantly higher – and the same goes for all his colleagues in this table.
The exception, of course, is Jordan, who has a Bradman-like knack of ruining any analysis. Whilst everyone else’s streaks are at less than 1% probability, his is about as surprising as a dull article on NBA.com.
Just for fun (redundant phrase – everyone knows that all of this is fun already), I’ve reverse-engineered the ridiculous formula to find out what length of streak would returned a 1% probability for Jordan: a streak of 19 games would have him right next to Durant in this table, at 0.64%.
Durant’s data also needs an asterix – we’re cherry picking by making the calculation now, and not when his career has finished (or at some random point, as with Bryant – we’re assessing his in-progress career at a point totally unrelated to anything he’s just done). The 0.67% should drop a little if he gets near 1,000 games like his colleagues.
NBA.com tells us that in 30 seasons, there have been only 5 streaks like Durant’s. In 30 seasons, could the NBA have seen hundreds of players as good as those in the list (Jordon excluded… grumble grumble)? If there were 500 “good” players, you’d expect 500 x 0.01 = 5 of them to achieve this rare feat – but that’s moving on to binomials, and a whole other conversation.
Sadly, NBA.com articles make no provision for reader comments, presumably because we’re far too enthralled, amazed or disappointed by the content to make a contribution – so I can’t let Brian Martin and his readers in on all these findings. Perhaps if I find him on Twitter and suggest that he read this and make some amendments, there’s a 0.00004%, or “McGrady’s chance”, that he might do it?Follow @newstatsman