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by Gabe Farkas | permalink | trackback | comments |
When the NBA announced it was bringing in a new ball for this season, I was pretty surprised. There were many questions running through my mind. What was wrong with the old ball? Was it just a marketing gimmick? Would it affect play? Well, even before the season was underway, many players complained about the new ball. They said it was too slippery, or that it caused cuts on their hands. Big names like Shaq, Tracy McGrady, Dirk Nowitzki, and yes, even Steve Nash were all opposed. Eventually, the league bowed to pressure and agreed to bring back the old. With all the hoopla surrounding the introduction (and now subsequent removal) of the new ball in the NBA this year, I decided to investigate what kind of effect, if any, it had on the players' ability to play the game. The first steps were to figure out how to measure any possible effect, and to collect appropriate data to make these comparisons. Background To tease out any effect the new ball may have had, I wanted to look at what I call "hands factors" – things that are affected by how the players' hands interact with the ball. The two most obvious ones I came up with were turnovers (TO) per possession, and field goal percent (FG%). I reasoned that if the ball was more slippery, and a player had a harder time keeping a good grip on it while dribbling, this might lead to more frequent turnovers. The other time a player needs good hand-ball contact is when he shoots the ball. The easiest, most straight-forward measure of that is FGM/FGA (aka FG%). As for the data, the venerable Knickerblogger was able to provide me with team-by-team data for previous seasons. On the morning of January 1st, while everyone else was recovering from the previous night's partying, I downloaded the same data for the current season to-date from his trusty stats page, since December 31st marked the last day the new ball was used. The Numbers In the 2005 and 2006 seasons, there were a total of 227983 and 227252 possessions, respectively. I calculated this with the usual APBRmetric formula of Possessions = FGA + 0.4*FTA - 1.07*(ORB / (ORB + Opp DRB))*(FGA - FG) + TO Of these, there were 35677 TOs in the 2005 season and 35459 in the 2006 season. Also, in the 2005 season there were a total of 197626 attempted field goals, of which 88435 were made baskets. In the 2006 season, there were 194315 FGA and 88166 FGM. For the purposes of this discussion, I pooled the 2005 and 2006 data together and called this the "Old Ball" data. The numbers then come out to: Possessions(Old Ball) = 455235 Looking at the same data for the 2007 season through games played on December 31st, these numbers were: Possessions(New Ball) = 85894 Methods Now that I had all the data I needed, I wanted to examine if there was an association between my "hands factors" and the New Ball. Were players more prone to TOs with the new ball? Would their ability to shoot the ball also be affected? There are well-defined methods to compare two categories of variables like these, and the frequency with which each occurs. One of the most well-known of these is a two-by-two contingency table. It's a lot simpler than it sounds. For turnovers, our two categories for types of possessions would be "no turnover" and "turnover"; our two cases would be all possessions using the old ball, versus all possessions using the new ball. This table ends up looking like:
And for field goals, where our two categories are FG Made and FG Missed, the contingency table becomes:
With these tables in place, I used the Pearson chi-squared statistic, χ-squared, which measures how close the numbers inside the table are to what one might theoretically expect them to be if there was no difference between the two cases (the Old Ball and the New Ball). If the two cases would give exactly the same proportion of outcomes, then χ-squared equals 0. The bigger χ-squared is, the stronger the evidence there's a difference between the Old Ball and the New Ball. As a general rule, anything below 1 and you're still in pretty good shape. The Results When looking at TOs, χ-squared comes out to over 47! I was hoping to see a little bit of difference between the Old Ball and the New Ball, but this was a really, really big difference. For anyone familiar with P-values, P< .0001 for this test. I went back and checked my calculations, but indeed there was a very strong association between turnovers and the type of ball used. For field goal shooting, χ-squared came out to a little under 8. This was still rather strong evidence (P=.0051) of a difference in how well players were shooting the ball with the New Ball versus the Old Ball. Now that we know an association exists between my "hands factors" and the type of ball used, it's time to look at the specific nature of that association. To do this, we use the Odds Ratio (OR). The OR is simply a measure of the odds that something in one row of the table will end up in the first column, compared to the odds that something in the other row will end up in the second column. In other words, it's a way of comparing the difference in odds that something will happen between each case. For TOs, we get OR = 1.072. This means for any given possession there's a 7.2% higher chance of turning the ball over if you're using the New Ball compared to the Old Ball. That seems to make sense given the players' complaints that the New Ball was generally harder to handle. For FGs, we get a different story: OR = 1.023, meaning there's a slightly greater chance of a made basket (2.3% greater, to be exact) when shooting with the New Ball compared to the Old Ball. This was surprising, since it suggested that, despite their relative unfamiliarity with it, players were shooting slightly better with the New Ball. One might argue that more TOs but higher FG% is a mixed bag. But, with so many other variables in play during a typical NBA game, seeing a statistically significant difference in both TOs and FG% is proof enough for me that the return to the Old Ball was the right move for Stern & Co. Published on Saturday, January 6th, 2007 at 5:51 pm 6 Responses
Pedro Souza said on January 6th, 2007 at 10:50 pm :
Nice post. I was looking forward to reading something like this. I have a few points though: a) At least theoretically we can't isolate the new ball variable when it comes to turnovers and field goals %. I think it'd be necessary to check the TO/game for each team to see, for instance, if teams that have completely rebuilt their rosters are or are not more prone to TOs. If this is true and if in this season more teams were rebuilt from scratch than in the previous years, this could be an influence. It's a long shot and I have no clue about it, but it could be tested. b) We should also take into account that there were rule changes a few years ago that greatly benefitted slashing guards. Last year was the big "new rule awareness" season, with Kobe dropping 200 pts, Wade dominating the finals etc. So we could wonder whether or not a considerable number of teams and players changed their style to fit the rules; this could influence the TO's and FG%'s. c) A derivation of the question above could be related to small-ball run'n'gun line-ups. Given the Suns' success this past season, a lot of teams tried to follow their path - right now I can think of the Raps and the Nuggets. We'd have to compare FGA/game for most teams to see if they're playing at a faster pace, I guess. d) I'm not sure about this, but, anyway, as far as I knew the chi-square statistic does not tell us exactly about the strength of the correlation, but rather inform us of the probability of rejection of the null hypothesis of independence. From what I've read, we can safely discard the null hypothesis. Gotta take into account the degrees of freedom as well (not sure if you it was done) Maybe you should try to run Yule's Q test - the standard (bc - ad)/(bc + ad) formula. Again, I'm no expert in statistics, so maybe you've done all that and I didn't even realise.. cheers"! pedro Kevin Pelton said on January 7th, 2007 at 1:12 am :
Gabe, I think using total turnovers is too general a measure to isolate the impact of the new ball. When Hollinger did a comparison earlier this season, he found that dribbling turnovers were down but this was offset by an increase in violation turnovers — likely because the NBA has attempted to crack down on traveling. (The numbers, from 82games, also showed an enormous increase in "other" turnovers, but I'm not sure what those are.) Gabe Farkas said on January 7th, 2007 at 2:06 am :
Pedro - thanks for reading and for your well-thought-out response. Regarding your first point, by aggregating over the entire league, my intention was to try to absorb any blips that may have occured from teams rebuilding their rosters, or other outliers like that. Of course, there are a plethora of other variables in play besides just the new ball, so the results should definitely be taken with a grain of salt. As for any possible change in pace, in 2005 there were 92 possessions per 48 minutes (over the entire league season). In 2006, there were 91.6 poss/48. In the data set that I looked at for 2007 so far, there were 93.5. This is a change, but I think it's a small one. I didn't investigate if it was a significant difference, but I suspect it may not be. Lastly, you're correct that chi-square is a test to reject the null hypothesis of independence. In this case, the null hypothesis is that there was no difference in TO/poss or FGM/FGA for the New Ball compared to the Old Ball. I don't think we can safely discard that automatically; in fact, that's what I wanted to find out. The results of the Pearson's test indicated that we should reject this null hypothesis. Also, for a 2×2 contingency table, the degrees of freedom is (I - 1)(J - 1) = 1. Thanks again for your feedback! Pedro Souza said on January 7th, 2007 at 12:41 pm :
hello gabe, thanks for your kind words. Kevin Pelton, in the comment just below mine, raised a very important issue, namely the disagregation of TO's. I'm not sure if it's possible to do that with the data you collected. Anyway, you're absolutely right regarding the degrees of freedom. My bad, doh! Did you try to run Yule's Q test though? You've already shown we can reject the null hypothesis, which is already a big deal, now it'd be interesting to check the strength of association, especially because if the new ball affected mostly turnovers but not FG%, then I'd guess we could interpret that as being a consequence of the 2006 crackdown on travelling/carrying, and not really the new ball. Also, there's a further point which might escape all attempts at statistical analysis: I think it's possible that, given the players' difficulties with handling the new ball, they've sort of adjusted their game to avoid committing turnovers. In other words, that could mean players weren't so keen on pulling dribbling stunts with the new ball, that they might have gotten less aggressive with ballhandling. That could've kept dribbling turnovers down. I'm not sure how one could possibly measure that - it's a big counter-factual hypothesis. cheers Gabe Farkas said on January 8th, 2007 at 5:36 pm :
Kevin and Pedro, Overall I agree that there are myriad factors to consider when looking at a year-over-year difference like this, and the new ball is just one of them, so it's tough to make definitive conclusions here. Lastly, Pedro, I apologize but I'm too familiar with Yule's Q. However, after researching it a bit, it seems like it's applied to ordinal data or matched pairs data? I would agree that performing an ordinal test is stronger, but didn't see the need in this case. Also, for a 2-by-2 table, it seems it would be equivalent to calculating the gamma (http://www2.chass.ncsu.edu/garson/pa765/assoc2×2.h...). For matched pairs, my inclination would be towards McNemar's Test for a dataset like this. However, I don't see how these could be set up as matched pairs. Stephen said on January 15th, 2007 at 3:27 am :
Pedro,Tracy McGrady of the Rockets made a comment to effect that he could not handle the new ball like the old ball and that he welcomed back the old ball as it would allow him to do more on the court. Suggests you are right that the ball did cause at least some players to adjust the way they played. Leave a Reply
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