## when did the Jazz turn the corner? mathmeckily speaking, of course..

Amar recently posted a really nice graph of net margin of victory for the year, reproduced without permission here.

based on the graph, Amar stated, and we all agree, that the Jazz have "turned a corner". i've been thinking about what it means to turn a corner and decided to write up my thoughts and share a few more graphs.

first of all, how would you characterize turning a corner? KC_Jones postulated in the comments section that it has to do with keeping a positive margin:

Where the slope of the fitted curve becomes positive.

Jazzbeetle suggested that it has to do with obtaining a positive net (cumulative) margin.

[Where] it appears to be going from net negative to net positive.

and i suggested that it might also have something to do with having a positive change in margin. so, we have three candidates for what it means to turn a corner.

1. when the net margin function is positive. (Jazzbeetle)
2. when the net margin function has positive slope. (KC_Jones)
3. when the net margin function has postive concavity. (lol)

everything is entitled to its opinion, so i'll put mine in here: i think all 3 have merit, lol. if you've thought about calculus or physics or whatever recently, you might make a (lame) comparison to distance, speed, and acceleration.

1. the first measurement tells us when the Jazz finally overcame the terrible start to their season, i.e., when the wins overcame the losses. it means that they became good enough for long enough to essentially undo their poor play record early on. the net margin is like the distance traveled. the first part of the season had the Jazz traveling in the wrong direction. their net margin becoming positive means they finally made it back to where they started so that they could continue in the right direction.
2. the second measurement tells us when the Jazz started to string together wins. this is when their hard work began to pay visible dividends in the win/loss column. the margin is like the velocity. the margin becoming positive means that the Jazz turned their bus around and started to drive in the right direction.
3. the third measurement tells us when the Jazz started to actually improve toward winning. it tells us when the margin of error became less negative, i.e., when the Jazz started losing by less and less. the change in margin is like the acceleration. when the margin is negative but has a positive change, it means the Jazz hit the breaks in an attempt to turn it around.

okay, now we got all the hokey analogies out of the way, so let's focus on trying to answer all 3 questions, since the answers each contain some valuable information.

a quick semi-technical note first: since a single game is a volatile statistic, i decided that a good way to fit a curve that isn't too reactionary to single games was to smooth out the data by looking at averages over spans of games. this made sense to me because "turning a corner" is about trends, and trends establish themselves over a span of a few or many games. i decided to replace values of net margin, margin, and change in margin at a specific game with an average including a few games prior and after the game in question. i used four different averages: the naive average over the span, and three averages using standard approximations to integrals. i won't bother to label which average is which. i figure that showing all four together gives a good indication of a trend. however, i will mention that the approximation which uses a trapezoidal approximation to integration seems to fit the data quite well, so a line amidst the data will represent a "trapezoidal" averaging. furthermore, because accumulation functions are always more well-behaved, there's a sort of double averaging happening where i use the net margin averages to help alleviate the noise in margin and change in margin data.

Net Margin

i averaged out net margin over the surrounding +/- 2 games and used the "trapezoidal" average over +/- 3 games to fit a curve, as seen in this graph.

and here is the graph of the fitted curve along with the original net margin data.

the conclusion? the Jazz got and kept a positive net margin for the season around game 75, which we could have seen without the fitted curve, lol.

Margin

the original margin data is a mess, lol. it's the nature of basketball. here it is, for your enjoyment.

i averaged out the margin data over +/- 4 games and used the "trapezoidal" average (on some sanitized margin data) to fit a curve, as seen in this graph.

the conclusion? the margin is hanging close to 0 from games 43 to 49, and then stays largely positive for the rest of the season. note the approximate margin flirting with 0 and negative values between games 68 and 72. no surprise here, since the losing streak happened during games 69-72.

in my mind, the Jazz were competitive from game 43 on, roughly half the season. fwiw, game 43 was the win in Milwaukee on 22 January. game 51 was the win against Sacramento on 7 February. the point is that the post all-star winning streak didn't surprise us as much as it did national writers, because we saw a sort of pre-streak materializing in the games leading up to the all-star break and the Kanter trade.

Change in Margin

the change in margin data is even worse. i won't even bother posting it here. it's essentially all noise. i smoothed out the change in margin data and averaged it over spans like in the other cases, then a curve was fitted using some "trapezoidal" approximations. the result is the following graph.

the conclusion? the Jazz improved from games 18 to 32 (game 18 is halfway through the 9 game losing streak), regressed a bit from 32 to 40, improved from 40 to 62, regressed a bit from 62 to 72, and improved from 72 on.

around game 40 (the win versus Los Angeles on 16 January), the Jazz really applied the breaks to their losing season, so they could turn it around at game 43. in the games (62-68) leading up to the 4-game skid, the Jazz had one really great performance (vs Charlotte), but on average were winning closer games than in the previous spans of games. in other words, the regression here still meant winning, but they were getting closer to losing, i.e., slowing down or something.

anyways...

the Jazz turned lots of corners this season. it was a fun one to be a part of and hopefully this corner-turning leads to more fun ahead. also, i'm sort of a bandwagon gal, so i'll join the rest of the commenters here in a shout-out to the writing staff at SLCdunk for putting out great stuff and putting up with an annoying audience (i.e., me) lol.

All comments are the opinion of the commenter and not necessarily that of SLC Dunk or SB Nation.