Friday, April 27, 2007

Shady Whistles: Running Some Numbers

Because I've been beating on the "conspiracy" drum for the past two nights, I figured I should run some fairly basic numbers to see if I have a valid point. My eyes are telling me that the teams the NBA would like to see win are being allowed to mug the opposition, but I need to see if the free throw attempt stats back any of this up. For these purposes, I am taking four contests in which there seemed to be an obvious "desirable" winner to the league, which I will call "games of interest." They are: Game Two of Mavs-Warriors, Game Two of Spurs-Nuggets, Game Three of Suns-Lakers, and, as a control, Game Three of Bulls-Heat tomorrow night.

I will be listing each team's free throw attempt differentials from the regular season (I tried to incorporate home and away, but couldn't find a data source that offers a "FTA allowed" home/road split), then looking at how that played out in the game(s) preceding the "game of interest," and then comparing the results. My hypothesis is that in the first game of the Mavs-Warriors and Spurs-Nuggets series and the first and second games of Suns-Lakers and Bulls-Heat, when the NBA - and therefore the officials - weren't overly concerned with the outcome, the numbers should play out pretty close to what we might anticipate, with any large advantages going to the teams with the better differentials during the season. The second half of the hypothesis is that the "game of interest" will see something completely out of whack with the predictive model.

Okay, let's see what we've got.

Mavericks - #24 in the league in FT differential (-2.1)
Warriors - #30 (-3.7)

This is obviously pretty rudimentary, but based on those per game differentials, we can expect the Mavs to have the slight edge (+1.6) in free throw attempts in most games of this series.

Game One: things played out as expected with Dallas getting 25 attempts to 22 for the Warriors.
Actual Difference: Dallas +3
Projected-to-actual gap: +1.4

Game Two ("game of interest"): enormous gap here. Dallas got a whopping 43 free throws. For the purposes of this exercise, I will pull out the three technical shots which leaves 40 for the Mavs and just 27 for the Warriors.
Actual Difference: Dallas +13
Projected-to-actual gap: +11.4

Spurs - #6 (+2.8)
Nuggets - #1 (+6.2)

The Nuggets have by far the best differential in the league, which comes with having the #4 (Iverson) and #6 (Anthony) players in the league in free throw attempts per game. One could expect Denver to get approximately 3.4 more free throw attempts per game in the series.

Game One: They did much better than that in Game One, getting 25 freebies to the Spurs' 10. Part of this can be attributed to San Antonio jacking up too many threes, but mainly it reflects season-long trends, albeit exaggerated trends.
Actual Difference: Denver +15
Projected-to-actual gap: +11.8*
(Note that the Nuggets see a huge "gap" score here, but since we assume Game One was a game in which the league was unconcerned with the outcome, there is nothing to take away from that number, other than to note the extreme turnaround three nights later.)

Game Two ("game of interest"): Allen Iverson took 25 shots but did not attempt a free throw. The Spurs got 23 attempts from the stripe, while Denver took just 17, which is almost 13 below their season average.
Actual Difference: San Antonio +6
Projected-to-actual gap: +9.4

Suns - #15 (-0.9)
Lakers - #19 (-1.2)

We should expect very little free throw disparity in the series (0.3 advantage for Phoenix), with perhaps a slight edge going to the home team in each game.

Games One and Two: The Suns got more attempts in the first game and the Lakers in the second, with Phoenix netting 43 total and L.A. taking 35 free throws.
Actual Difference (over two games): Suns +8
Projected-to-actual gap: +7.4

Game Three ("game of interest"): The Suns managed just 12 attempts from the line, two of which came from illegal defense calls. The Lakers, meanwhile, nearly matched their total from the first two games combined with 28.
Actual Difference: Lakers +16
Projected-to-actual gap: +16.3

Bulls - #22 (-1.7)
Heat - #13 (-0.3)

Another fairly narrow margin, but the Heat should expect a couple of extra attempts per game, maybe even more since Wade wasn't in the lineup for the full season. The number we are working with is +1.4 for Miami.

Games One and Two: It was a draw in game one with both teams getting 27 attempts, but the Heat took eight more in the second contest.
Actual Difference (over two games): Miami +8
Projected-to-actual gap: +5.2

Game Three ("game of interest"): ?


It will be interesting to see what happens in the Bulls-Heat game tomorrow night. But if the other three games are an indicator, we should see a massive advantage for Miami. In the three "games of interest" in which the NBA would have a vested interest in seeing the home team win - either to tighten up a series, keep a favorite alive, or squeeze a few more contests out of a big star - the "gaps" have been +11.4, +9.4, and +16.3. Obviously, the desperation of the home team (leading to more aggressive play on offense), the excitement of the crowd, and other factors play a role. But those gaps are enormous. On average, the home team of interest got 12.4 more free throw attempts than 82 games worth of data would project.

That's a whole lot.

And if that keeps up, it means that Miami's expected 1.4 free throw attempt advantage will swell to almost 14 tomorrow night. I, for one, will be watching very carefully to see where the final number comes in. And honestly, I hope it is the Bulls that shoot more free throws and that my whole theory is shot to pieces, because in this case, I so very badly want to be wrong.


Jim said...

Thanks for the numbers. At least I'm not the only one that feels the same way!

Anonymous said...

The stats are overly simplistic and equate to no really argument to stand on. To get a true analysis of free throw disparity you need to use
 season averages (not differentials)
 you need to calculate in home/away differentials (home teams often shoot more free throws)
 you need to statistically weight for shot attempts in the paint (most fouls, occur in the paint)
 you also need to statistically weight for intentional fouls (teams in the lead often shoot a significant % of their free throws in the last 5 minutes of the game)
 Finally you have to control for the three official which is rather complex statistically

When you can do this then I buy the free throw thing as an example of a conspiracy. Better examples of a conspiracy are quick ticky-tack fouls on a key player, by the same official, in a quarter (or as we have seen in the past several weeks the use of technicals and ejections).

Kevin said...

That's something that I had thought was true just while watching, wouldn't it change everything if it were true.

Anonymous said...

Oh, my. Tim Duncan got to shoot six whole free throws on 17 shot attempts while being pounded by Nini. What a blatant attempt by the refs to control the game -not to mention that four of the supposedly excessive FTs came in the last sixteen seconds on intentional Nuggets fouls. So the "disparity" is then 19-17 - stop the presses !!

GMAFB with your "analysis." Home teams always get more calls in the NBA and you seem to have neglected that minor factor as well.

Adam Hoff said...

To the first "anonymous," good points. I admitted in the post that it was a rudimentary method. It doesn't really prove anything, but at least it somewhat confirms what I was seeing with my own two eyes. As for home/away differentials, I mentioned in the post that I wanted to use those, but couldn't find any information on "FTA allowed" home/road splits.

To the second "anonymous," see above in regard to the home team aspect. And also to the "rudimentary" comment. I'm not making claims of perfection; just running some numbers. As for taking out the last four free throws, it still doesn't explain how Denver shoots just 17 free throws when they normally shoot 30 a game. The issue I was having with the officials in those games is that they were swallowing their whistles for the road team and refusing to call fouls, while still calling the usual amount of fouls for the home team.

The number of attempts for the road teams were: 27 (Golden State), 17 (Denver), and 12 (Phoenix). The reason I used differentials instead of just raw numbers is that by looking at the other team, you get a better idea of how many they should have expected to shoot. For instance, 27 is actually above Golden State's season average, but when you compare them to Dallas, it changes things.

That said, I don't expect everyone to agree with me and appreciate the comments either way.

Anonymous said...

While I do think that the NBA is highly suspect, this analysis is embarrassing.

As there is a hugh lack of it, I will provide some Suns/Lakers context. Take a look at the FT differentials for the 07 reg. season and the 06 post season:

Victor, Differential

Suns, +8 Suns
Lakers, +1 Lakers
L, +6 L
L, +16 L
S, +7 S
S, +1 L
L, +7 L
S, +7 S
S, +13 S
S, +8 S

Not shockingly 16 FT differential was not unprecedented. Think the NBA wanted the Lakers to go up 3-1 on the Suns that day? Guess the refs didn't get the memo that all of Canada, Brazil, and Nation-of-Kobe-Haters were watching.

Anonymous said...

Interesting figures. I'd also like to note that maybe more weight should be placed on those teams' head-to-head matchup FT disparities as well. You could draw +14 FT/game on all teams for the whole season, but in head-to-head matchups, maybe you're only +3 because that team plays you better or something like that. Just a thought I had.

Kent said...

To the last comment: why would you even factor in last year's series? Neither team even resembles its old self. I was watching the game last night and it was obvious the refs were influenced by something. Barbosa was getting slammed around like a pinball. The only fouls they would call on the Lakers were when Luke Walton would fall down and trip somebody. I'll take the analysis in the post over a series from last year with totally different players.

Kent said...

Sorry, not to the last comment - to the one before that.

Anonymous said...

Oh, and also, I wouldn't count out the factor of desparation from the team that is trailing in a series. When your desparate, you will work harder to get in the paint and get some buckets. You may fight a little harder to get down there and draw some fouls. Let's put it this way, a lot of times, the more aggressive team gets more calls even if they aren't drawing more fouls than the seemingly less aggressive team. The Lakers were more aggressive yesterday, so they were rewarded with more calls. That's the way the refs always work.

Adam Hoff said...

It seems that the combination of Henry discussing this on True Hoop, the controversial nature of the topic, and the (admittedly) flimsy numbers is generating some chatter.

First, let me say that any disdain for the methodology is perfectly acceptable. It was far from a perfect science. However, it isn't as if I'm on a Senate committee here. I just wanted to randomly pick a stat and see if it backed up what appeared to be happening. And it did. I suppose we could compare based on specific officials, past playoff series, and all the rest, but really, who has time for all that?

And if Miami shoots 35 free throws tonight and the Bulls shoot 10? What then? I think it means something. Now, as Buffalo Springfield once sang, what it is ain't exactly clear. It could mean the playoffs are scripted (highly doubtful) or just that refs are very easily swayed by desperate home teams and home crowds. But it seems like something is going on.

I do see merit in the home/road differentials, but as I've mentioned a few times, I can't seem to track down any splits for "opponents" stats. If anyone knows of a source, please let me know. I also see merit in the team matchups (although we are getting into an even smaller sample size and run the risk of players being absent).

Adam Hoff said...

The desperation point is a very good one. I do think that explains some of the discrepency. However, as I said in the original post, while it may account for some of the difference, it doesn't seem to explain all of it.

The Frozen Envelope said...

Conspiracy theories! I love 'em! I totally agree that the refs made sure to knot up the Denver and Dallas series, to get longer series. And it was obvious they wanted more Kobe. But who could blame them? He was sick last night. The Lakers-Suns is a great draw for the NBA as a first round series, of course they would want more games. I think LA will get a little less love the next time out and then none at all in Phoenix. That is just how the NBA always rolls. Yeah, the numbers are a little weak, but at least you didn't just scream conspiracy without at least providing something to back it up.

BTW, if you want conspiracies, just wait until the Wolves somehow get a top two pick to pair Oden or Durant with KG. No way Stern lets one of his five most marketable players continue to play for a sub 500 team. Just watch. And with West leaving, Memphis is going to get screwed. Boston will get the other top pick.

Anonymous said...

How do you explain the Pistons winning last night or the Rockets getting more free throws? And should we expect the Wizards to get the royal treatment next?

Anonymous said...

"How do you explain the Pistons winning last night or the Rockets getting more free throws? And should we expect the Wizards to get the royal treatment next?"

Who cares about Orlando or Washington? We're talking about the big dogs here, the Spurs, Mavs, Heat haha.

Adam Hoff said...

Personally, I think any series that gets bumped to NBA TV doesn't constitute a "game of interest." I doubt the league is losing sleep if the Magic or Wizards get swept. The Rockets-Jazz and Nets-Raptors are kind of tweeners. I'm not sure if I should be looking at them or not. So I'll choose not.

Adam Hoff said...

At the behest of one of the comments, I went and ran the differentials based on matchup. These are pretty tiny sample sizes, and I have a feeling that key players missed action in a lot of these games, so I simply don't trust them. But I'll run them anyway and let you make up your own mind. The Spurs actually had a 23-17 advantage on average in the season (in three games), which is exactly the numbers from Game Two. The other three all reinforce the original theory. Here they are:

Warriors-Mavs (3 games) - Warriors +2.3
Lakers-Suns (4 games) - Suns +5.3
Miami-Chicago (4 games) - Bulls +15
Spurs-Nuggets (3 games) - Spurs +6

Again, it is hard to take too much from this. For instance, Melo missed two of the games against the Spurs, Kobe missed the first game against Phoenix, Wade played just 81 (of a possible 192) minutes against the Bulls this year, and so on. But there you have it.

Adam Hoff said...

And for the home/road splits, the best I could do was look to see if teams got more free throws and were called for less personal fouls at home, while road teams got less free throws and were whistled for more fouls.

Here are the numbers (I ran home and away for LA, PHX, MIA, and CHI, since the analysis includes games in both locations):

Mavs (home) +0.6 FTA, -0.6 fouls
Warriors (away) -1.7 FTA, -0.1 fouls
Net FTA: Mavs +2.3

Phoenix (home) -0.1 FTA, -0.9 fouls
Lakers (away) -0.8 FTA, +0.6 fouls
Net FTA: Suns +0.7

Phoenix (away) +0.1 FTA, +0.9 fouls
Lakers (home) +0.8 FTA, -0.6 fouls
Net FTA: Lakers +0.7

Spurs (home) +0.9 FTA, -0.4 fouls
Nuggets (away) -1.4 FTA, -0.4 fouls
Net FTA: Spurs +2.3

Chicago (home) +0.1 FTA, -1.4 fouls
Miami (away) -0.2 FTA, +1.0 fouls
Net FTA: Miami +0.1

Chicago (away) -0.1 FTA, +1.4 fouls
Miami (home) - +0.2 FTA, -1.0 fouls
Net FTA: Chicago +0.1

Now, these numbers can make your head hurt if you look at them for too long. I can't really just fold them into the previous differential numbers, because the personal foul stats don't truly tell us what the FTA allowed look like. But if you just take home FTA and road FTA for the respective teams and link them, then link the personal fouls, it tells a bit of a story.

For instance, in the Mavs-Warriors series, it looks like Dallas gets .6 additional FTs at home, while G-State shoots 1.7 less. So Dallas could conceivably enjoy an additional +2.3 projected FTA throughout the series. However, those same numbers tell us that Golden State actually fouls a fraction less on the road than at home, so maybe Dallas' bump would be more like 0.3. Who knows? But it does seem to reflect the widely-held belief that home court does indeed increase free throw attempts. Just not by much.

The biggest swings here are that the Nuggets and Warriors both shoot 1-2 less free throws a game on the road (thus swinging the numbers toward SA and Dallas), that the Bulls and Heat both get away with an extra foul in home games, and, well, that's about it.

Running these numbers tells me that either home court becomes a MUCH bigger influence on officials in the postseason or that it isn't the whole reason this is happening. I'm perfectly willing to consider the former, but isn't that a problem in and of itself?

I will probably get this posted on the front page at some point, but wanted to include it here for the time being.

Anonymous said...

Well, those numbers to seem to cut against the arguments just a little. It looks like that Dallas-GSW game would be a +9 "gap" as you call it. Denver-SA would have been a +7.1, and PHX-LA a +15.6. First, I realize what you are saying about it not being a straight forward addition because you were working with differentials while these are just net home/road free throw numbers. But second, even if the home court aspect does in fact drop those numbers to the ones I just listed, that is still pretty bogus. I definitely think the refs are swayed, whether by the coaches, the fans, or the league office. If it happens again in Miami tonight, as you predict, I will be convinced that something is amiss.