Thursday, February 28, 2013

I'm Calling It

Watching that game last night, I kept waiting for the Cats to get a couple of stops.  I kept waiting for USC to miss a few shots in a row.  It seemingly never happened.  It felt like every Trojan possession ended with a made shot, free throws, or a turnover.  The Trojans shot the ball ridiculously well.  Given his quotes after the Washington State game, I'm sure Sean Miller has been preaching defense all week.  No doubt, that sermon continued during every timeout, all of which the Cats had used well before the game ended.  Our defense was not great.  USC shot the ball at over 61%, but our defense was not that bad.  That's why I have to call bullshit on this one.  That game was a classic case of bad luck.

Consider this. USC has not put up 89 points in a non-overtime game this year.  In their first game of the season against Coppin State, they managed 87.  At McKale, the Trojans only scored 50 points.  How was USC able to nearly crest 90 at the Galen Center against a decent defensive Arizona team?  Lucky shooting.  Sure, they had some gimme's, but I saw a lot of contested fadeaways, floaters, and three pointers.

USC came into the game shooting the ball at 45.5% from inside the arc.  Last night, they went 27-44, or 61.3%.  What is the probability of a team that shoots the ball at a 45% clip going at least 27 for 44?  It's 1.2%. It would be expected to happen only once in about 84 games.

What about shooting the three?  The Trojans were 6 for 10, despite being only around 35% for the year.  The chance of that?  It's around 2.5%.

What about both?  What's the chance of USC doing both in the same night?  It's around 0.03%.  It should happen once every 3,364 games.

I'm glad this game happened when it did and not a few weeks from now.  Don't expect lightning to strike twice.

Wednesday, February 27, 2013

Southern California

It's been a while since I sat down to work on this project.  The demands of real life have forced me to put this aside for about ten days, but the weekday game day is here.  That motivated me to get back in the saddle. The home sweep was nice but not unexpected.  The Washingtons are probably the easiest of the the paired matchups in the Pac this year.  What was nice about the games was that the Cats won both convincingly.   I certainly understand Sean Miller's ire about a poor defensive effort in the second half against WSU.  One thing I think has helped our offense in the last two contests has been bench minutes.  Giving the starters a bit more rest will pay off late in games and as the season goes on.

Speaking of the season, it's hard to believe that it is winding down.  Sitting at 23-4, the Cats have won as many games this year (23-4) as they did last (23-14), and we need one more win in conference to match last year's Pac win total.  Playing the Trojans at Galen, I like our chances.  Here is the match up:

If you look at those stats closely, it should be clear why Arizona is the favorite.  The Cats are better in almost every category.  Our offense is better.  So is our defense.  We turn the ball over less. We are bigger and and deeper.  The Trojans are a slightly older team, but don't expect that to matter in the end.

If you are expecting an easy win, I cannot guarantee one.  The simulation gives us a 40% chance of a double digit victory, but the most likely score is a six point victory of 70-64.   There is a 65.9% probability of winning at any margin.  At home, this game would be nearly a sure thing.  In Los Angeles, it's a bit more of a challenge.  With three four-loss teams at the top of the conference standings, both games this week are critical, and especially the one on Saturday.  But not let's get ahead of ourselves.

Wednesday, February 20, 2013

Washington, Again

The Cats pulled off a narrow win in Seattle.  In that game, both teams played very poorly on the offensive end of the floor.  Three point shooting was especially atrocious.  Expect both teams to shoot the ball better from long range.  Because the Cats pulled off a win on the road, you should expect them to be strong favorites at McKale, and that is the case.  Parenthetically, if you have never read any of Ken Pomeroy's work on home/road rematches, it is worth a look.  Also, most estimates for home court advantage in college hoops are around four points, so the general expectation is a seven to eight point swing for paired home and road games.

The statistical comparison between the two teams is similar to the last time around.  Both teams have declined slightly in offensive efficiency, but the Huskie defense has lapsed more.  The Cats are better across the board on the offensive side, with the sole exception of rebounding.  The Huskies are one of those rare teams that have turned the ball over more than we have.  Washington does have a slight height advantage, something I'm sure Mark Lyons will discover if he spends much time driving the ball toward Aziz N'Diaye in the lane.

The simulation looks favorably upon our chances.  It says we are 11 point favorites with a 79.2% chance of heading into the weekend with our 22nd win.  The most likely score is 73-62 (or maybe 61).  I would be remiss if I did not note that last week's simulation returned a bit of credibility to this exercise, missing the final score of the Utah game by only one point.  To get there required Utah to sink a last second uncontested three, but what the heck, I'll take it.  Finally, it was nice to see Terrence Ross win the NBA slam dunk title, even if that competition is only a shadow of its former self.

Tuesday, February 19, 2013

Why Late Game Three's are Not Helpful

Between the six and seven minute mark against Utah, Mark Lyons took Arizona's first three point attempt.  It was a miss.  About 40 seconds later, Solomon Hill drained one.  Near the ten minute mark, it was Grant Jerrett's turn.  His three put the Cats up 17-12.   Three point shooting is a wonderful thing when the shots are falling.  Nothing frustrates you more, though, than many consecutive misses from behind the arc.  It makes you long for higher percentage shots.  In today's edition of the Wildcat Report, I would like to make the argument that the Cats would be better off largely abandoning the three as games go on, and the reason why is simple.  It's clear that early in games, Arizona shoots the long ball well.  Late in games, they do not.

The graph above shows the evolution of Arizona's three point shooting during the Utah game.  Notice that early on, the Cats were shooting very well.  At the end of the first half, the Cats had made 5 of 12 three's for 41.7%, a very good percentage.  By the end of the game, they were 6-22, or a not so good 27.3%.  In the second half, they went 1 for 10.  They missed their last seven.

It is certainly tempting to argue that you can't generalize from one game to the entire season, but this game serves as a microcosm of the overall trend that I pointed out a few days back.  Here is how Arizona's three-point shooting looks when games are divided into quarters:

That graph includes every three point shot taken this season, except a few from overtimes.  That's more than 520 attempts.  As games go on, the Cats' long range shooting proficiency steadily declines.  For the last ten minutes, the Cats shoot threes at under 30%.  For the first ten minutes, they are over 40%.  This is a big difference.  At the start of games, they are making around 1.3 points per shot.  In the last ten, they are under 0.9.  In an average game this year, the Cats have had 21 three point attempts. For 21 attempts, that's a difference of nine points, a difference that could win or lose many games.

What is driving this decline in shooting ability?  Well, if I had to guess, it's fatigue.  If you have spent any time shooting threes, you know that your legs are critical to the shot.  After running up and down the court for twenty or thirty minutes, it should come as no surprise that guys increasingly miss three point shots, especially by hitting the front of the rim.  If you are looking for a scapegoat , you would be hard pressed to find one.  Here are the same graphs for Arizona's most common three point shooters:

Notice that for three players (Johnson, Hill, and Jerrett), the worst game segment for shooting threes is the final quarter of the game.  For the other two (Lyons and Parrom), the final ten minutes has been their second worse time to shoot the the three.  Johnson and Jerrett have especially struggled at the ends of games.  Johnson is shooting it at 18.2% for the final ten minutes, and Jerrett is at 22.2%.

From a coaching perspective, this is not a trivial matter.  Three point shots are a high risk/high reward game, but what is interesting about this analysis is that the risk involved in shooting three's is not constant.  It becomes increasingly risky as the game goes on.  An ideal strategy would be to take more threes early in games before players get tired and to have the offense slowly shift to an interior approach as the game goes on.  It would be interesting to simulate this process to determine what the optimal mix of two and three point shots would be as a function of game time, but that's another job for another day.  As a general rule of thumb, I would advise players to only take threes toward the end of the game when: 1) it is necessary because it's the only way to make up a deficit given the amount of time remaining, or 2) they are wide open looks.

By the way, here are how our three point shots have been distributed within games:

Sunday, February 17, 2013


With a 3-9 record in conference, the Utes present one of the less challenging road games in the Pac.  However, the Cats have been anything but impressive lately.  It would be nice to see the return of the shooting defense. Cal and Colorado shot a combined 54.4% from the field over the last two, and both teams shot the ball ridiculous well from behind the arc.  The Utes are coming off a nice win against the Sun Devils and gave the Cats a run for the money at McKale. 

On paper, the Utes actually match up fairly well against us.  I should note that the stats above include two incredibly lopsided wins against non-Division I schools, and if those were removed, the match up would appear less balanced.  The executive summary is that, in spite of recent struggles, our offense and defense have been more efficient than Utah's.  The Cats have a distinct size advantage, which should translate to a significant advantage in interior defense and rebounding.  If we can limit the Utes from behind the arc, I think Arizona will bounce back with a win.  Then again, one should always keep this in mind in rematch games.

The simulation, which admittedly hasn't been worth a damn lately, says Arizona is most likely to win by five with a score of 69-64.  It gives us a 63.5% chance of winning.  The Utes slow things down quite a bit, so expect a game that borders on unwatchable.  Last time through Salt Lake City, Solomon Hill was ejected from the game, but the Cats still pulled out a 26 point victory.  Here's to hoping that happens again.

Saturday, February 16, 2013

The Second Half of the First Half, Part 2

Sitting next to me at the game was my old friend, Ken Pomeroy.  Ken and I talked about how players' tendencies change depending upon game situations.  For example, when up big, teams tend to expend less effort on defense. When the game is tight, they work harder.  Something about the second half of the first half has become a time for poor play for the Cats.  It's not entirely clear what that is or what causes it, but it seems be an ingrained habit.  I was hoping to find a simple answer, but instead I found a number of contributory factors.  Here are a few.

 One of the first things that came to mind was that perhaps the Cats shoot more three's during this time of the game, thus lowering their field goal percentage, and indeed that is true.    Of all the shots that are taken, the graph below shows the percentage of which are threes for each quarter of the game.

From 10:00-20:00 into the game, the Cats have been most reliant on the three point shot.  In that game segment, 42% of our shots attempts have been taken from behind the three point line. During the Colorado game in that time frame, I was counting the missed three's.  1 for 7.  1 for 8.  1 for 9. 1 for 10.  1 for 11...   Do the Cats also shoot the three poorly during this time?

In general, the answer is no.  The percentage of three point shots made slowly declines over the course of games.  During the first ten minutes, the Cats are shooting at over 43%.  If they maintained that for the entire games, they would be the best three point shooting team in the country.  For the last ten minutes of the game, however, Arizona is shooting the long ball at just over 30%.  I assume this a product of tired legs.  Given this pattern, I would advise this team  to shoot fewer threes as the game goes on, or at least to take more early on.

Another factor driving poor productivity during the second half of the first half is poor shooting inside the arc, as shown above.  Notice that our two point shooting in the first half is generally poor compared to the second half.  It bottoms out in minutes 10-20 when the Cats shoot around 42%.   So why is this?  Does it have something to do with who is playing, or how those shots are being taken?

If your hunch was that this has to do with substitution and who is likely to be on the floor during this time of the game, that's probably not the case.  Here are the number of two point shot attempts per player from 10:00 to 20:00 into the game:

The top five in two point attempts are the same as our most common starting lineup.  In other words, it's not so much the bench who is slumping during this time, but it's mostly the starters.  Why are the starters shooting the ball poorly, and especially from two point range?  I'm not certain.  If you look at two point field goal percentage during this part of the game relative to each player's overall field goal percentage, here is what you find:

One surprise to me here was Kevin Parrom.  His 2P FG% is down 25% during this time frame compared to his overall shooting.  He is 1 for 11 shooting two's during the second part of the first half.  Bad inside shooting, though is not limited to Parrom. Angelo Chol and Kaleb Traczewski have also suffered, and most importantly, so do the team's volume shooters: Lyons, Hill, and Johnson.  Ashley and Jerrett shoot the ball a bit better in this game segment, and Jordan Mayes has been fine, bearing in mind that he is 4 of 6.

What does all of this mean?  Well, after the ten minute mark and before halftime, I would argue that a few things change: 1) The Cats become increasingly reliant on the three pointer; 2) When they take two's they shoot a very low percentage. 3) In terms of the overall poor shooting of the team and if we take into account the number of shots taken, the biggest contributors the late second half slump are Parrom, Tarczewski, Lyons, Hill, and Johnson in that order. The question of why these guys are struggling to score in this part of the game is difficult to answer.  My hunch is that team play begins to break down as players try to make more individual plays.  I will end with one more troubling graph, which also suggests that quality of play declines late in the first half.  Turnovers also peak at this time:

The Second Half of the First Half, Part 1

The Coors Event Center was loud.  The student section was impressive.  It was the kind of atmosphere that creates home court advantage.  Around the 8:45 mark of the first half, I vividly recall a moment that in my mind was the turning point of the game.  Solomon Hill had the ball at the top of the key, but offset to the right side.  Andre Roberson was guarding him.  Solomon prepared to drive the lane using his usual but effective technique, a couple of cross over dribbles.  He drove to his left, and near the free throw line, spun on his pivot foot as if preparing for a fadeaway.  Askia Booker reached in and poked the ball away.  So begun the fast break.  Nick Johnson and Angelo Chol positioned themselves in the key to stop Booker with the ball.  Neither saw Xavier Johnson streaking down the left side of the floor. Bounce pass.  Dunk.  The loud of the arena became LOUD.  It was a tough place to play.

The Cats hung in for a few more possessions, but about three minutes later, Xavier Johnson hit a three pointer to give Colorado a 23-20 lead, a lead which the Buffs never again relinquished.  At halftime, I spoke with a woman in front of me.  She said she went to every game, at least at McKale.  She and her husband, though, were traveling with the team to Boulder and Salt Lake City.  Despite a 20-3 record (the game wasn't over yet), she was pessimistic about this team.  "They never smile," she said, "They don't play like a team."  It's interesting how different people perceive the game. I have given some thought to that statement, and it seems to be mostly true, at least the smiling part.  I remember Nick Johnson grinning after accidentally banking in a couple of shots a few games back, but other than that, I recall non-smiling faces.  When teams are playing poorly, everyone inevitably looks for cause and effect.  What's broken, and how can we fix it?   Is it the starting lineup?  Is it the inexperience of the freshman?   Is it that Colorado played so well that no team could have beaten them?  Is it unhappiness in the locker room, as my nearby game watcher surmised?

Just compare the number of comments on the stories on the Daily Star after a win to the flood that comes in after a loss.  Everybody has an opinion.  Usually the "fire Miller," "bench Lyons," and "give York more time" guys come out after any loss.  I understand the need to seek explanation for poor play.  I seek it myself.  Just consider Colorado's three point shooting on Thursday night.  They shot the ball better from behind the arc than in front of it.  Was this because they were "hot" or because our defense was not good?  Was it just bad luck?  There is no easy answer to this. From my perspective at the game, it seemed like many contested three's went in, for whatever reason, especially at the end of the shot clock.

I am not going to tell you why the Cats have now dropped two straight because I don't know.  Rather, I am going to focus on one particular time of the game, the second half of the first half.  At the 10:00 mark, the Cats were leading 15-14.  At the end of the half, they were down 30-23.  If you think that poor play in minutes 10-20 is unusual, just check out what I wrote more than two months ago after the Clemson game.  This part of the game has been a problem area for a long time.  Here is how Arizona and their opponent's have shot per 10 minute segment for all of our games this year:

Notice that for every segment but one, we have shot the ball better than our foes.  The exception?  The first half of the second half.  Here's the same chart just for the Colorado game:

The most embarrassing thing about that graph is how Colorado shot the ball after the 10:00 mark, at or above 50% for each game segment.  But the second half of the first half again stands out as an area where there is a huge disparity in shooting.  If you are looking for a problem area in this team, it might be worthwhile to further examine this segment of the game because generally speaking, it looks like after the third or fourth TV timeout, the Cats have not been playing well.  Why?  I'm not sure, so I will crunch some numbers and see what I find.

Wednesday, February 13, 2013

Colorado, Round Two

Tomorrow night, Arizona will play their first rematch of the season. In Boulder, Colorado, the Cats will face a team looking for payback after Sabatino Chen's last second shot was waived off at McKale.  The crowd is going to be raucous and should give the Buffs a stronger than usual home court advantage.  On top of that, the stats point to a much more even match up than the first time around

If you follow that link and compare Arizona's stats for the first time they faced Colorado, you will see some troubling things.  The Cats are not showing many signs of improvement.  Shooting percentages are down across the board, and so is offensive efficiency.  The defense has gotten worse.  Contributions from the bench have declined dramatically, and rebounding is down.  The only good sign is that turnovers have declined marginally.

The net effect of this is that now the Cats and Buffs appear more evenly matched than before.  Perhaps this means that earlier in the season, the sample size was insufficient and gave the Cats more of an edge than they actually had.  Maybe this decline is the product of playing a lot of difficult games in conference.  Whatever it is, it's hardly something to feel good about.  So when I take my seat tomorrow night at the game, I am not expecting an easy win.

The simulation says this one is more or less a coin toss.  I simulated 30,000 games, and the Cats won 15,169 of them, or 52% (13,981 L's and 850 OT's).  The most likely score is 67-66, although it's actually closer than that.  The computer says the Cats are 0.7 point favorites (66.8-66.1).  I was there last year, when Arizona, who led for most of the game, lost in the end.  This year, I hope my luck changes.  Certainly, the Cats are in need of some good luck.  The Bears put up nearly 80 points against us, a relatively unlikely event according to last week's simulation.  It would be nice to see the Cats on the right side of the scoring distribution this week, and ideally way out in the tail.  There is a 26.8% chance that we win by 10 or more. That sounds good to me, much better than dropping two straight.

Monday, February 11, 2013

Bad Defense or Bad Luck?

It took me about 24 hours to shake the bad feeling that comes with the realization that Allen Crabbe alone scored as many points in the game as the entire Arizona team in the second half.  The sad thing was that everyone knew what Crabbe was capable of, but  the Cats were powerless to stop it.  When you add in the 21 put in by Justin Cobbs, it was if we were beat by two guys.  It didn't matter who played defense. they just scored.

When a team does well or poorly, there are two sides to the coin, offense and defense.  Actually, this coin is four-sided because each team plays on both ends of the floor.  Let's just look at one simple aspect of this game- Cal's offense. The Bears shot an embarrassing 58.8%.  They also scored 1.15 points per possession, the most any team has managed against Arizona this year.   Is that because their offense was really good, because our defense was really bad, or was it some combination of the two?   This is not a simple question to answer.

If you think about it, when a team shoots well, it could be because they had many uncontested looks at the basket, i.e., bad defense.  It could also be that they made a lot of difficult shots under duress that they would normally miss.  In other words, the defense wasn't all that bad, but the Cats were just unlucky in that the Bears had a remarkably good (lucky) night of shooting.

To distinguish between the two, you need some independent measure of defensive effort.  I think time of possession can provide us some guidance here.  When the defense is playing really well, possessions tend to get dragged out.  Think of those classic defensive stands when the opponent has to chuck up a prayer at the buzzer.  Contrast that to a fast break uncontested dunk.  The first possession lasts 35 seconds.  The second lasts about three to five.  During good defensive efforts, the Cats spend a lot of time playing defense.

So, how do you measure time of possession?  Well, it's a little tricky, but it can be done using play by play stats like the one from last night.  I've been tracking these stats all season, but it wasn't until today that I decided that they might be of use.  By my estimation, the average Arizona possession lasts 16.3 seconds.  Our opponents' possessions have averaged 18.2 seconds.  To demonstrate that shorter possessions are generally a good thing on offense, the graph below shows the relationship between average possession length and points scored per possession for Arizona and our opponents this season.

This relationship is not strong, but I can assure you that it is real.  That point on the far right side is Utah.  They are outliers because they play a unique brand of slow ball.  The point on the top left?  That's the Cats against NAU when we held onto the ball for an average of less than 14 seconds per offensive bout, and we scored nearly 1.3 per possession.  I removed Utah from this plot, and added a trend line, which shows the expected offensive output for any team given the length of possession.

That yellow dot is the Cal Bears last night.  The average Bears possession lasted 18.42 seconds.  In a typical game, this would equate to an offensive output of 0.93 points per possession.  If the Bears had played to that level instead, they would have scored 72 points and lost the game.  If we measure the effectiveness of Arizona's defense in terms of the average length of Cal's possessions, it would rank 12th, or a middle of the road defensive game.  What this suggests to me is that California's offense was significantly better than what would be expected given Arizona's defense. 

This is kind of how the game felt to me.  Sure, Crabbe had some easy buckets, but many of them were contested.  Regardless, the shots fell.  So to me, the answer to the quandary (I think) is that Arizona's defense was not bad.  In fact, it was average for us or maybe even slightly above average. Cal's offense was outstanding, or the way I prefer to see it is that the Bears had luck on their side.  If the two teams have a rematch, I wouldn't be surprised to see a very different outcome.

Saturday, February 9, 2013

The University of California, Berkeley

Remember the days of the big three?  Those would be Chase Budinger, Jordan Hill, and Nic Wise.  That phrase suggested that the Wildcats were dependent on those three guys, as if the rest of the team was just background noise.  Similarly, the California Golden Bears have the "big two" in Justin Cobbs and Allen Crabbe.   The graph below shows the percentage of points that have been scored by the top two players for every team in the Pac, and Cal is easily leading the way, or in the caboose, depending on you see such things.

I prefer to see this as a disadvantage, as it allows you to key on a couple of guys defensively.  This is no secret, and every team trys to do so when facing the Bears.  The Cats are on the other side of the distribution, ranking ninth.  The Oregon Ducks easily have the most evenly distributed scoring of any team in the league.

Compared to Cal, the Cats have been better in nearly every category.  We are better in shooting, offensive efficiency, defensive efficiency, rebounding, and depth.  The Bears have turned the ball over slightly less and are taller by a smidgeon.   Played at McKale, Arizona would be predicted to be strong favorites, and the simulation says as much.

It gives us an 83.6% chance of victory as 13 point favorites with a 1.7% chance of overtime.  The most likely score is 73 to 60.  If we can shut down any Cal  Bear players with one C and two B's in their last names, I think we could win by more.  If not, I would still expect a win, probably in the double digits.  Parenthetically, I think I'll be in Boulder next Thursday for the second game against the Buffs.  Given what happened in Tucson the last time we played Colorado, it should be interesting.  No doubt the crowd is going to be fired up.

Friday, February 8, 2013

The Rule Breakers

Brandon Ashley officially logged 13 minutes against Stanford before fouling out.  He picked up one foul for every 2:36 he was on the floor.  Part of this was surely bad luck.  I have a lot of sympathy for referees who have to make instinctual calls in a fast-paced game and for players who are on the receiving end of bad calls.  That's inevitably part of this game, and it's one of the many reasons why basketball is an interesting thing to study.

Today I want to look at the Arizona roster and fouling trends.  Ashley's ridiculous fast paced ejection from the game for fouling was unusual, but Brandon has been foul-prone. Of course, in the prior game, Kevin Parrom fouled out after seven minutes with one ill conceived blow to DaVonte Lacey's face, but Brandon has led the team in fouling:

The graph above shows the number of fouls each player has committed per 40 minutes of playing time.  Ashley leads the team in fouls committed with 58, Tarczewski is second with 53, and Lyons is third with 50.  When things are standardized to playing time, Angelo Chol is 2nd in line, averaging 4.9 fouls per 40 minutes, followed by Tarczewski.  It's not surprising that big buys pick up a lot of fouls since they are constantly fighting with other big guys in the paint, both contesting shots and battling for position.  Grant Jerrett is one exception to this rule.  He ranks seventh on the list.  Compare that graph to last year's team:

In the 11-12 season, Angelo was the undisputed king of the foul, averaging over seven per 40 minutes played.  Kyryl was also very foul prone with six.  It would have been difficult for either guy to play 40 minutes in a game without fouling out.  While Angelo is also foul prone this year, he has reduced his foul rate dramatically.  This would suggest that his defensive positioning is improving, although the Stanford game helped his numbers dramatically.  He played 24 minutes and only picked up one personal.

Another thing to note is that every returning player but one is committing fewer fouls.  Solomon has dropped from 3.2 per 40 minutes to 2.5.  Nick Johnson is down to 2.6 from 3.2.  Jordin Mayes was at 3.4 last year and 3.1 this season.  The only player to move in the opposite direction is Kevin Parrom.  Although Kevin has improved his game in many ways, this is not one of them.  How do the two teams compare as a whole?  This year's squad fouls at a slightly lower rate.  The Cats are whistled for an infraction about every 2:27.  Last year, it was every 2:24.  That's a difference of about 0.3 fouls per game.

Thursday, February 7, 2013

Going Streaking

With about five and a half minutes left in the game, the Cats were shooting the ball at 38.2%, were down by five points, and had only 49 points on the scoreboard.  At the time of the final buzzer, they had piled on 24 points and finished the game with a field goal percentage of 46.3%.  Needless to say, the last five minutes of the game were their best.  In those five minutes, they put up nearly 1/3 of their points.  What happened was not likely; they made their last seven shots of the game.

The graph above shows both teams' field goal percentages as a function of game time.  Notice that it took a while for Arizona to get above 0%.  For the first 4:02 of the game, the Cats were scoreless and missed their first five shots.  They followed that by making their next four.  In that graph, every bump up indicates a shot made, and every bump down, a miss. Notice that the two teams track each other fairly well.  During the latter part of the first half, both teams went into a somewhat of a shooting slump.

The most remarkable part of the graph for the Cats is the last five minutes.  Note that Arizona's field goal percentage at the end of the game was the highest it had been for any part of the game.  Making seven shots in a row is not an easy feat to accomplish.  Take a coin out of your pocket, and start tossing it until you get seven heads in a row.  That's not a perfect analogy because when a shot is taken in basketball, on average, it is less likely to be a make than a coin toss is to be heads.  At this point in the season, Arizona has made 558 of 1238 field goal attempts, or 45.07%  At that rate, what's the likelihood of making seven straight? It is .0038, or about in 1 in 265.  In this streak, the Cats made two three's and five two's, so their chances were a bit higher than that at 0.0043, or 1 in 233.  Still, I think you can appreciate that this is not a likely way to finish a game.

The graph above shows how often the Cats have made anywhere from one to seven shots consecutively over the course of this season.  They have never made more than seven, but they have made exactly seven on three occasions. Against Oral Roberts, they did it in a four minute stretch spanning the first and second half.  They also pulled it off in the first five minutes of the game that followed against ETSU.  That it happened last night was not only fortunate but timely in that it's how they ended the game.

On the other side of the coin, missing shots, they have had much longer streaks. This should come as no surprise since the average shot is more likely to be missed than made. Over an eight minute stretch against the Buffaloes, Arizona missed eleven straight.   The odds of that?  1 in 728.  That's really bad luck. 

Tuesday, February 5, 2013


One advantage of looking at team's entire body of work for a season is that it increases sample size.  In other words, it is possible to average out all of the ups and downs that characterize individual games.  The major disadvantage of this approach, however, is that recent trends toward improvement or otherwise are not given greater weight.  The Stanford Cardinal are a good example of this.  When Stanford's entire season is put under a microscope, the Cardinal do not appear to be a strong competitor to the Cats.  If we focus on recent history, however, that's not necessarily the case.  According to Ken Pomeroy, during the conference season, the Cardinal have had the third best offense in the league and the fourth best defense.

Defense has never really been an issue for the team from Palo Alto.  Early in the season, though, their offense was not good, but look at the graph below.  Since late November when they dug themselves into a pretty deep hole, statistically speaking, Stanford's offense has been trending in the right direction.  Compare that to the same graph for the Cats.  While Arizona had a very efficient game against Washington State last week, scoring 1.22 points per possession, in their last game, a defeat of the Beavers, Stanford was better, tallying 1.27.  In seven of nine Pac-12 games, Stanford has scored over 1.0 points per possession, and in three of them, they have been near or above 1.2.  In other words, Stanford is probably a better offensive team now than their season averages suggest. 

This is again one of those games where the Cats should be favorites based on the numbers, and I think they truly are. However, a cautionary note is warranted here.  Their advantage might not be as strong as the simulation and comparison below would indicate.

Across the board, Arizona has been better offensively.  We have higher percentages shooting, and we are better offensive rebounders.  Arizona is also stronger defensively in all aspects.  In fact, we have the advantage in virtually every category, the only exceptions being depth and turnovers.  Stanford's bench is slightly deeper and they turn the ball over at 17.9% rate compared to 19.9% for the Cats.

The simulation gives us a comfortable 78.5% chance of winning as 11 point favorites.  The most likely score is 72-61.   If we gave more weight to recent history, however, I would probably add a few points to Stanford's score.  Against our defense, it's hard to say how the Cardinal will play.  If the team that struggled to make a shot in November shows up, it is going to be an easy victory.  If the team that swept the Oregons last weekend arrives, it could be a nail biter.

Monday, February 4, 2013

Duke on a Neutral Court

It's probably too early to be thinking about things like this, but why not?  March is only one month away.  In the thick of the Pac-12 season, it's easy to become lost in the microcosm of a conference.  There are weekly reminders of how people think the Cats would match up against other teams in the form of the AP and USA Today polls, but other than that, we tend to focus on our proximate competitors.

Today, I thought I would take my game simulator and apply it to a hypothetical neutral court tournament match up against one of the top teams in the nation, the Duke Blue Devils.  If you are like me, you remember the day of euphoria that followed Arizona's beat down of Duke in the tourney a couple years ago.   This year, Duke is also sitting on a 19-2 record, although they are ranked three spots above us.  In a raw comparison of stats, here's how we would match up against the Blue Devils if the game was played today:

There were a few things here that surprised me.  It did not surprise me that Duke's offense has been more efficient than ours, although the difference is slight.  I was surprised that our defense has been better by a hair.  Also, we are a much stronger rebounding team, especially on the offensive glass.   We get more minutes and points out of our bench, although I'm pretty sure their bench is more efficient.  Duke shoots the three much better than we do.  In fact, they are currently ranked #6 in Division I at shooting the long ball.  We are slightly better inside the arc and 5% better from the free throw line.  Given the mixed nature of the statistical advantages in the side by side comparison above, you would expect such a game to be close, and indeed that's was the sim suggests.

The Cats would be underdogs but not by much. The most likely score is a two point loss of 70-68.  The simulation gives Arizona a 45.1% chance of winning, so it's almost a coin toss.   What this says to me is that the Cats are deserving of a high rank, and that they can compete with any team in the country.  They are not a #1 team, and in fact, I have some doubts whether they are really top ten.  Nonetheless, we have a team here that could do good things come March.

Sunday, February 3, 2013

Bouncing Back

The Cougars had the misfortune of playing Arizona after their worst offensive game of the season.  There was little doubt that the Cats would improve things on the scoring side of the floor, but the extent to which they did so was surprising.   By my count, Arizona had 65 possessions with which to work, and within those, they almost crested the 80 point mark, good enough for just over 1.2 points per possession.  I imagine that does not mean much to the casual basketball fan.  Here's how to think about it.

A typical Arizona game this season has 68 offensive possessions.  Scoring 1.0 points per possession results in 68 points.  If you add or subtract 0.1 points per possession, you are adding or subtracting around seven points from the final score.  You might think that the UCLA game was our worst offensive showing given the number of missed layups and dunks, but it was not.  In that game, the Cats had around 0.91 points per possession.  Against the Huskies on Thursday night, the number was 0.84.

At the start of the season, the offense was a well oiled machine.  Over our first five games, we averaged nearly 1.2 points per possession.  The NAU game was off the charts. Beginning with the 27 turnover game against Southern Miss, things started to slow down, and in fact since that time, a 15 game stretch, Arizona has not reached the 1.1 mark, although they came close against Oral Roberts and ASU.  If we look at this cumulatively, it is clear that offensive efficiency has been slowly and steadily declining:

Part of this can be chalked up to the increased level of competition in the latter half of the nonconference season and the first half of conference season.  A lot of it, though, is probably explained by changing offensive tendencies, like this one.  This is why last night's game was important.  The offense played very well, thus the little bump up at the end of that graph.  They almost shot 50% from the field.  The scoring was balanced and distributed with 10 players scoring and four reaching double digits.  All five starters scored at least one point per field goal attempted with Ashley and Tarczewski both getting two points per shot.  Turnovers were in the single digits, a very welcome sign.  Only two of 16 free throws were missed, and yes, it helps when Solo hits a three pointer from the other team's three point line. 

The nice thing about a long season is that there is time to address problems, and I think it's clear Sean Miller is doing that.  I like our chances next week.  The next serious challenge looming on the horizon is on Valentine's Day in Boulder.