Play-by-play theater: Revisiting consecutive fouls
01.10.12
Play-by-play theater is a feature (that I just started) where I use the comprehensive play-by-play archive from the past three seasons to hunt for extreme, and possibly silly, events that have occurred in a college basketball game. And who doesn’t like extreme, and possibly silly, events? I do! I mean, I don’t! I don’t not like extreme, and possibly silly, events!
On Saturday, “BigH1313” of twitter fame, wondered which game listed in Friday’s consecutive foul table featured ten consecutive fouls by the same team to start the game. The answer: Whoops! There actually wasn’t such a game.
Thanks to BigH1313, though, I was forced to recheck my work which determined that the logic used to produce Friday’s table was a bit off. It turns out the forces working against consecutive fouls being called on the same team are even stronger than shown last week. Here’s the corrected table which includes the 200+ additional play-by-plays from games over the weekend.
Probability of (x+1)th foul being called on Team A when first x fouls of game have been called on Team A
x n n(a) Chc(a) 1 13326 6158 46.2 2 6158 2683 43.6 3 2683 1057 39.4 4 1057 386 36.5 5 386 129 33.4 6 129 37 28.7 7 37 8 21.6 8 8 1 12.5 9 1 0 0.0
x: number of consecutive fouls called against Team A since beginning of game
n: total number of cases
n(a): number of cases where Team A was called for the next foul
Chc(a): percentage of cases where Team A was called for the next foul
Instead of there being a single game with the first ten fouls called against one team, there’s actually only one nine-foul game since the beginning of the 2009-10 season. That one-in-13,326 event took place on December 3, 2010 when UMBC committed the first nine fouls of a game at UConn before Donnell Beverley was whistled with 5:55 remaining in the half. The final foul count in the game was UMBC 17, UConn 12.
For reference, if you assumed a sequence of fouls was completely random, with either team having a 50% chance of getting the next call, you would have expected 52 cases of a nine-foul game in a sample of this size. You even would have expected one game with 15 consecutive fouls against the same team to start the game. Imagine the riot that would ensue in that case!
As I alluded to Friday, there are other forces at work here besides officials trying to avoid a full-blown riot. It figures that teams that have committed a string of fouls might try harder to avoid them on the following possessions and teams that aren’t committing fouls might get a little more frisky. It seems like that’s not enough to completely explain this effect, but I’m not sure how one would isolate the influence of pure officiating on the data. Anyone?
On Wisconsin: The FAQ
01.09.12
As you may have noticed, Wisconsin inhabits the #2 spot in my ratings this morning despite having lost five of its first 17 games, including a home game to Iowa and a lopsided loss to Michigan in the past week alone.
This is an issue that is not going to go away this season. Even in a worst-case scenario for the Badgers, they are going to be highly ranked on this web site the rest of the season. This bothers many people and in order to manage the increasing number of inquiries into the matter, I have established what the tech geeks call a “FAQ document” for handy reference. What follows is that document. Please share with all parties you deem relevant to the matter.
Q: Why do you think Wisconsin is #2?
A: I actually don’t think this. Please stop assuming that I, Ken Pomeroy, personally believe every team is properly ranked. No system can do this. Even if you somehow had the time to rank all 345 teams, by the time you were done with this exercise, you would find some things that you didn’t agree with in the rankings you had just made. For fun, spend some time just try ranking the top 50. Through some miracle, if you’re happy with the position of each team when you’re done, just let the results of games come in for the next 2-3 days and then see if you’re still happy.
The bottom line is that is impossible to rank 345 teams that will make any particular individual happy. There are always going to be some outliers in a system. Wisconsin is perhaps the biggest outlier ever in my system. And it’s only going to get worse, because they are going to lose more games and not drop very far because most of the teams they play the rest of the season are very good. But to get back to the question, I don’t believe they’re the second-best team in the country. Something like #20 sounds about right.
Q: Who has Wisconsin beaten to deserve to be #2?
A: As a reminder, the ratings are not meant to have any relation to the polls. (The first paragraph on the ratings explanation page is worth reading if you haven’t seen it before.) I don’t care who “deserves” to be #2. The #2 team in my system should be the second-best in the country. It is theoretically possible to be the second-best team in the nation without having beaten anyone of prominence.
As an example, in 2010, Duke went 1-3 against teams ranked better than 20th in my system during the regular season. Then in the tournament they went 5-0 against such teams! It was crazy, but not completely surprising. The point is, for predictive purposes, simply looking at who a team has beaten or lost to is short-sighted. Obviously this methodology has not worked well in predicting the Badgers’ recent performance. Duly noted. In bulk, though, simply rating teams by the quality of their wins and losses is not going to make for a good predictive system.
Q: The fact that Wisconsin is #2 invalidates all of your work. (More of a comment, really.)
I disagree. Let’s say you are very good at performing some task. For the next 345 times you perform this task, I will judge you based on your worst effort. I don’t think you would feel like this is a fair way to measure your ability to perform the task. Because it isn’t.
If you are going to trash the entire system based on the biggest outlier over the last six years, I suspect you had no desire to use the system in the first place. Either that, or your team is ranked lower than you think it should be.
Q. When are you going to fix this?
First off, I’m not sure it can be fixed. I mean, sure I can fix it so Wisconsin is ranked more reasonably. I could add some code to my algorithm like this…
if Wisconsin: do something to fix Wisconsin else: do normal calculations
But that really isn’t a good way to solve the problem. Needless to say, I’d like to fix it. However, fixing Wisconsin can result in messing things up for others. Plus, there are a lot of other ratings systems already doing cool things, and I’m not in the game of copying others’ work, so that doesn’t leave a lot on the table for me to pursue. That doesn’t mean improvements aren’t possible, but regardless of what I come up with, I can promise you there will still be teams that you feel are mis-rated.
For instance, one of the most respected ratings systems in the nerd world is the LRMC ratings. They had Wisconsin fifth before yesterday’s games. Last year, heading into the tournament, they had Belmont fourth, and their system outperforms mine! The Sagarin predictor, also deservedly respected, had Wisconsin second heading into yesterday’s games.
If you would simply remove Wisconsin from the planet, the ratings on my page would look fine to me. I guess you could ignore the entire system based on the worst outlier, but I don’t think that makes a lot of sense. There’s still some insight gained from the teams that differ from the polls. (See: Saint Louis, New Mexico, UConn, Mississippi State, among others.)
Q: Your work is flawed. (Not really a Q, either, I guess, but I get this all the time.)
A: Ugh, I hate it when people say this. Of course it’s flawed. The thing is, your knowledge is flawed, too. If you are ignoring potentially useful tools because of a single issue, then your judgment is flawed as well. And I’m guessing you’ve never tracked the quality of your knowledge so you don’t even know how flawed it is. If you’re like most people, you think you’re knowledge is great because you remember the predictions you made that worked out and you forget about the ones that didn’t. It’s human nature.
The difference between your flawed knowledge and my flawed system is that I am tracking the results of my system so you can identify all of the flaws for yourself. Ten years from now, you’ll be able to look at my site and see that Wisconsin was like 21-13 at the end of the 2012 season and ranked #5. Whereas the time you made some crazy prediction that didn’t pan out is quickly forgotten.
I would say there’s still enough value in the work here to provide a useful reality check on your own knowledge. Used together, your flawed knowledge and my flawed tools can be more powerful than used separately.
Q: Anything else we need to know?
A: Well, since you asked, you might as well know that Ohio State will almost surely be the #1 team the rest of the season. Also, they will probably finish with more losses than Kentucky or UNC or Syracuse, because they will play a tougher collection of teams the rest of the season. Just to reiterate, if you are looking for a ranking of teams by wins and losses, a la the AP poll or the RPI, then you’ll be more fulfilled consulting the AP poll or RPI for your ranking needs as the season continues. (Sagarin and Massey actually have better systems for this purpose, though.) However, I believe you will be less enlightened by ignoring the work of predictive systems.
Note also, that this does not mean I think Ohio State is the best team in the country, nor do I expect you to think that! (Although right now, I actually do believe the Buckeyes are the best, but I may change my mind as upcoming events warrant.) I didn’t think Duke was the best team two years ago, even after the tournament. But by the time the season ended, it was hard to argue they weren’t one of the best teams in the country, and were significantly underrated by the folks who take a resume approach to evaluating teams at the expense of all other information. And basically, I don’t think the Wisconsin situation invalidates the predictive methods used on this site, except in cases involving Wisconsin.
The untrained eye: Washington State vs. Utah
01.06.12
Utah beat Washington State 62-60 in a 60 possession, overtime game on Thursday night. I was there. This is was I saw.
Imperfection denied
Heading into last night, no team in the nation had a better shot at going winless in conference than Utah. Their inaugural Pac-12 contest was a 40-point loss to Colorado, who is (despite now leading the conference at 2-0) probably somewhere between the 7th and 11th best team in the conference. By the end of the night, the Utes were off the hook. As was the third-most likely team, Grambling who beat Alabama A&M 60-55. The bottom line is that it’s very difficult to go through a conference slate winless, no matter how bleak the situation looks after non-conference play. The onus is now on Towson, who has a 29% chance of losing their last 15 CAA games. Despite being on a 34-game losing streak, I have the Tigers’ back. They will win a game in conference.
Upsets require breaks
As one might have expected in a Utah win, the Utes played better than normal. The ran a crisp offense in the first half and only committed three turnovers while racking up 29 points in 27 possessions. It also helped that the normally sloppy Utes encountered a zone during the entire half. This allowed Utah to take better care of the ball and also take the air out of it. The game ended with just 60 possessions in 45 minutes which undoubtedly boosted Utah’s chances as well. Furthermore, Washington State made just 10 of their 22 free throw attempts. The Utes played better than usual, and the Cougars (except for Brock Motum) played worse than usual, and that’s how these things happen. It should happen to Towson before the end of the season, too.
Utah probably can’t be considered the worst power-conference team of all time
I mean, for history’s sake, with the win they have become just a historical footnote. But for scoring-margin aficionados like myself, the remaining 16 conference games for Utah will determine whether this game was completely improbable or merely slightly unusual. Keep in mind, in two conference games the Utes have been outscored by 38 points. If Utah finished the season with an average scoring margin of -19, then yeah, this game is going to look out of place.
Fun with play-by-play data
At the under-12 media time out in the second half, Utah had committed eight fouls to Washington State’s one. Being obsessed with probabilities, I contemplated the chances that the next foul would be called against Washington State. You might be aware of this study, which showed that officials prefer to avoid lopsided foul counts. Not only was the foul count unbalanced at this point, but there were three other things going for a high chance of a Wazzu foul – 1) Utah would have the ball coming out of the break; 2) the game was at Utah, so the crowd was rather ornery to this point; and 3) Utah was trailing. It turned out Washington State would pick up two fouls on the ensuing possession.
The study referenced above looked at a 365-game sample. I went back and looked at every play-by-play for the last three seasons and came up with the following data demonstrating the tendency for officials to even up the foul count.
Probability of (x+1)th foul being called on Team A when first x fouls of game have been called on Team A
x n n(a) Chc(a) 1 13084 7030 53.7 2 7030 3410 48.5 3 3410 1604 47.0 4 1604 662 41.3 5 662 253 38.2 6 253 89 35.2 7 89 28 31.5 8 28 7 25.0 9 7 1 14.3 10 1 0 0.0
x: number of consecutive fouls called against Team A since beginning of game
n: total number of cases
n(a): number of cases where Team A was called for the next foul
Chc(a): percentage of cases where Team A was called for the next foul
With over 13000 play-by-plays, we have enough of a sample to produce a smooth curve without any massaging of the data. The conclusion is obvious: After each consecutive foul on one team it becomes more likely that the other team will get whistled.
There are other factors contributing to this trend besides refs just giving into a coach’s complaints. Just how much of this is the result of a ref’s fragile psyche is up for debate. Nonetheless, the next time you see a lopsided foul count, you should expect the next call to go against the team that has been benefitting from the calls to that point.