*Update (1/05/12 2:10 PM EST): Added Andris Biedrins, Shaquille O'Neal, and Jermaine O'Neal to list.*

Yesterday, over at Weak Side Awareness (a great NBA stats blog that you should check out, btw), "wiLQ" (@Exploring_NBA on twitter) posted jump ball data for the last 4 seasons:

New blog post where you can finally find out... who did win and attempt most jump balls in each of last 4 years weaksideawareness.wordpress.com/2012/01/04/jum…

— Mike wiLQ (@Exploring_NBA) January 4, 2012

I thought this was really neat, so I asked him for the raw matchup data, so that I could calculate an "Adjusted Jump" probability or odds ratio. Without going into too much technical detail, I set it up the way I do my football ratings, except instead of margin of victory, the result of each jump ball is simply a "1" or a "0". For each jump, one player is arbitrarily assigned an indicator of +1 and the other -1. Trust me, it all works out. (Ok, in general, you should be leary of people who say "trust me", so go check this for yourself, if you don't actually trust me.) I then imported the data into R (my favorite statistical programming language) and ran a multiple logistic regression. There were 552 players in the data set, but I only used a small subset of players (46) who had a large number of jump ball opportunities last season as factors in the model. My thought is that if all 552 players were used, there would be a lot more noise and less significance.

Here is the function call in R (in case you might be interested in doing similar analysis):

Call: glm(formula = RESULT ~ Brook.Lopez + Dwight.Howard + Amare.Stoudemire + Marc.Gasol + Al.Jefferson + Spencer.Hawes + Tim.Duncan + Josh.Smith + Nene.Hilario + Darko.Milicic + JaVale.McGee + Tyson.Chandler + Andrew.Bogut + Emeka.Okafor + DeAndre.Jordan + Andrea.Bargnani + Luis.Scola + Robin.Lopez + Nenad.Krstic + Serge.Ibaka + Joakim.Noah + Kwame.Brown + David.Lee + DeMarcus.Cousins + Ben.Wallace + Marcus.Camby + Samuel.Dalembert + Zydrunas.Ilgauskas + Josh.McRoberts + Andrew.Bynum + Pau.Gasol + LaMarcus.Aldridge + Roy.Hibbert + Kurt.Thomas + Anderson.Varejao + Nazr.Mohammed + Marcin.Gortat + Erick.Dampier + Amir.Johnson + Chris.Wilcox + Channing.Frye + Ryan.Hollins + Chris.Kaman + Andris.Biedrins + Blake.Griffin + Joel.Anthony, family = binomial(link = "logit"), ' data = jumpballs_R)

The output of such a calculation is the log odds ratio, which I have turned into the odds ratio (ODDS). I also give the "Adjusted Win %" (50% is average, of course). The CODE column denotes whether the coefficient was statistically significant (more *** are more highly significant). If a player does not have any *, then he is arguably an average jump baller, even if his numbers appear slightly above or below 50%. Here is the full list:

### Discussion

The results at the top are not super surprising, but it's nice to see a confirmation of what we already believe. Bynum and Howard are the best. I'm a little surprised to see Dalembert that high. And also Ben Wallace. My guess is that the reasons for success in getting the jump ball have to do with timing and quickness of leaping as much as length and reach. If we turn to the bottom of the list, I am not at all surprised to see David Lee dwelling there. Most of those must have been from his NYK days, because I can't even recall him jumping a ball in GSW.

Once again, I'd like to thank wiLQ for making these data available - and be sure to check out his blog!

So (almost) all the below-average jumpers are in the other 500 players? I would have guessed based on opening jump balls alone that more centers would be below average just by going against other centers.

That wouldn't be that surprising to me considering this list contains most of the "quality" starting centers over the past few seasons.