The Law Of Averages

Mar 4, 2022

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Math people. Yes, you. You're probably gonna want to sit this one out. I'm going to stray so dangerously close to the Gambler's Fallacy that you'll catch yourself saying WELL ACTUALLY out loud. I'm going to talk Law Of Averages un-ironically. You're going to hate it.

I use that term a lot - Law Of Averages - to talk about how I watch basketball games. If a team that shoots 44% on the season is shooting 62% in the first half, I'm assuming that a whole bunch of misses are coming. If a team is ice cold, watch out because they're about to get hot. Yes, I realize that this is just Regression To The Mean, but I like to speak in terms of Law Of Averages.

It's often dumb to think this when it comes to basketball. You might be shooting 68% one night because you're playing Chicago State and then you might shoot 39% the next game because you're playing Virginia. You can't really expect your numbers to improve in the second half of that Virginia game - you're simply shooting that much worse because you're playing a great defense, not because "well, the shots are not dropping now, but they will in the second half". The percentages aren't going to level off because it's defense, not "we need to get hot."

But I'll often watch Big Ten games like that. Our opponent shoots 28% in the first half? Watch out - the shots are going to start falling. Our opponent is red hot in the first half? They're gonna shoot 32% in the second half. Everyone is gonna shoot around their team average by the time the game is over. (They're not - sometimes they'll be hot, sometimes they won't, sometimes it's great defense, sometimes it's poor defense - but I expect it to at least move in that direction.)

Here's how I see it. Say a team gets 55 shots. They're not the best shooting team, so they're only going to make 23 of those 55 shots in the game. Pretend I'm, like, an elementary school teacher or something, so I make this big display on the wall of the gym and I invite two classes of kids to help me. The 55 kids help me distribute 55 shots. I hand out 32 red dots (for the misses) and 23 green dots (for the makes). My display board has 55 blank circles spread out from the beginning of the game to the end, and I ask each kid, one by one, to come up and pin their circle where they think it will happen in the game.

Wait - I don't think you can give kids pushpins anymore. They might shove it in the hand of the kid in front of them at class. Let's go with... remember those felt display boards from like Vacation Bible School in 1981? You don't because you weren't born until 1992? Well there were these felt display things where you'd just stick the little felt piece to the big felt display and it would stick because it's felt on felt. Let's go with that.

A timeline from the beginning of the game until the end on the wall, spots for 27 shots in the first half and 28 shots in the second half, 55 felt dots given to the kids, 23 green, 32 red. And little Stevie gets to go first. She takes her green circle and puts it on the very first spot. They're going to make their first shot of the game.

Then each kid goes one by one. Some put red dots here, some put green dots there. A lot of the green circle kids put theirs on Stevie's side of the halftime line because Stevie started with green and that's maybe where the green circles should go. And nobody really wants to put their circles at the end of the line. So when there's 12 kids left to go, there's only two green circles remaining and the only spots are at the very end. So the right side of the display becomes 2 green dots and 10 red dots.

That's how I watch a game like last night (somewhere in my story there, my splitting headache became too much and I took some ibuprofen and went to bed, so it's morning now, which is why I'm saying "last night"). Penn State is not good shooting team. At some point they're going to regress towards the mean. So as they kept making these shots, I kept thinking that they were going to use up all their green dots and would eventually start missing shots. Then the law of averages paid me back in a really big way:

They made a jumper with 6:02 left. And then they didn't make another shot until the desperation three pointer with 7 seconds remaining. Nine consecutive missed shots. We win.

Penn State shoots 43.6% as a team on the season. When that three dropped with 6:02 remaining, they were still shooting 50% for the game (and mostly on jumpers as you can see there, so these weren't easy layups). They were simply making shots at an alarming rate.

But by the time the game ended (there was one more miss at the buzzer which isn't shown there), they finished the game 23 for 55, or 41.8% for the game. You might say the kids ran out of green circles. Or you might just say "they were always only going to make 23 shots, and once they reached 22 with 6:02 left, they only had one make remaining."

I fully understand the basketball side of all this. Maybe the refs are calling it tight and you're getting to the line instead of taking these jump shots. Maybe your opponent just can't rebound at all and it doesn't matter if you miss that shot because you're gonna get the offensive rebound and the put-back. There are other factors here that lead to "this team beat that team."

But if you've ever wondered why I like to do that "I'm gonna do the thing" thing, this is it. I like to note that a team is using up their green circles early and put it out there on Twitter that it's about to all fall apart. The best example this year: at Nebraska.

Four minutes gone, 36 minutes remaining, they've already made four threes and I'm predicting they won't make it to eight? Why? Because I was pretty sure they only had 7 green circles and they had already used up four of them. Nebraska is a horrific three point shooting team, and we're pretty good at running people off the three point line (look! another basketball fallacy!), so I was fairly certain they weren't going to make many more threes.

Nebraska's final tally? Six. They made four threes the first four minutes and then two threes the final 36 minutes.

I didn't "do the thing" last night because if I do something like that in a game we're losing by two with 5:30 remaining many of you would attempt to strangle me through the internet. But I did mention it in the first half a couple times. Penn State was shooting out of their minds, and I kept expecting it to stop. Finally, with six minutes to go, it stopped. A "missed nine straight" regression to the mean. Thank you, law of averages.

(Actually, it's probably "thank you, better energy on defense." But I'm on a roll here so nobody stop me.)

Obviously, a lot goes into this. Teams have hot shooting nights and cold shooting nights and those all combine to create the average shooting percentage of 43.6%. You play good defensive teams and shoot 35% and you play bad defensive teams and shoot 55%. You get 60 looks at the rim and shoot 68% and you're forced to shoot 60 long jumpers and shoot 29%. You get to the line 45 times and don't have to worry about your shooting percentage because you made 38 of 45 free throws.

But in a game like last night where Penn State's guards keep posting up down low and making 9' jumpers or kicking out for a three, I will forever think for the entire game "they can't keep making all of these". Eventually they have to start missing.

They eventually started missing. Illini win.

+ I don't know why, but I'm encouraged by winning this game. I'm guessing it's all the times we lost this game in the last 10 years and then I drove back to St. Louis wondering why we couldn't just squeak out a win when we play poorly like we used to do from 1985 to 2006. We used to own "play poorly but still win", but then we went through a dozen-year phase of "if we play poorly, we lose."

I mean, just look at our games with Penn State. Here's the history with Penn State from that horrific game in 2006 (The Night That Illini Basketball Died, a book I should absolutely write) until last night. We had won 10 of 11 over Penn State (the one loss being in overtime at Bryce-Jordan) and then, starting with Rich McBride's three pointer that was 0.2 seconds too late...

L 66-65 in Champaign
W 68-50 in State College
L 68-64 in Champaign
L 52-51 in State College
L 38-33 in Champaign
L 64-63 in State College

W 54-53 in Champaign
W 77-67 in State College
L 57-55 in State College
W 68-51 in Champaign
L 54-52 in State College
W 64-59 in Champaign
W 75-55 in Champaign
W 60-55 in State College
W 60-58 in Champaign
L 86-79 in State College
L 71-67 in State College
L 83-70 in Champaign
L 74-52 in Champaign
L 83-76 in Champaign
L 72-58 in State College

W 62-56 in State College
W 98-81 in State College
W 79-65 in Champaign
W 60-55 in Champaign last night

Talk about the Law Of Averages. I'm pretty sure we're about to beat Penn State 33 times in a row to make up for all those 54-53 losses on that list. Not really, but this is a great collection of "why can't we play poorly yet still squeak it out?" games.

So insane that from 2006 to 2019, we were 8-13 against Penn State in the regular season (I think we had a few BTT wins in there but this list is just regular season). Go tell that to me a few minutes before the 2006 game and I wouldn't believe you.

Actually, let's play that out. You figure out time travel. You find me walking into Assembly Hall on February 4th, 2006 (actually I wasn't there, I was celebrating my wife's birthday and I followed the last four minutes online when we got home, but let's pretend). You're a time traveler, you find me walking into Assembly Hall to see my #6 Illini take on 10-9 Penn State, and you tell me this:

"Hey Robert, Illinois is going to go 8-13 against Illinois the next 14 years, and Penn State will win 6 of those 13 games here at the State Farm Center."

"What's the State Farm Center?"

"Sorry, I'm from the future. This place will be completely renovated and State Farm will buy the naming rights."

"Wow, Guenther actually reseated Assembly Hall? I thought he'd delay the project for decades because he didn't want to re-seat all of his buddies in A-section."

"No, Mike Thomas did it."

"Who is Mike Thomas?"

"He's the AD after Guenther and everyone will eventually hate him even though he serves the purpose of 'did things Guenther refused to do like kick the donors out of the lot next to Memorial Stadium and reseat Assembly Hall' but that's not important. I'm here to tell you that Illinois goes 8-13 against Penn State the next 14 years with the first win coming tonight."

"Wow. That's insane. So Penn State must get crazy good. Penn State basketball is really a rising power?"

"No. In those 14 years they'll only make the NCAA Tournament one time."

"But then that means....."

It's probably just as hard for current me as it would have been for 2006 me to believe that Penn State went 13-8 against us over a 14 year span. So, so many "please just let us pull this out so I can go to bed with 'it was extremely ugly but we won' on my mind." And then we'd always seem to lose every close game.

Now, at home, this year, we've won ugly. Beat Michigan State 56-55. Beat Northwestern 73-66. Beat Penn State 60-55. Three certain losses in the past, three wins this season.

I know that's not the balm you were looking for this morning. I know that "man, it's March and we are ROLLING" feels better. But given all of the drives I made from Champaign to St. Louis late at night from, say, 2014 to 2020, wondering how we just lost to freaking Nebraska at home when the game was right there to be won, it's hard for me to get angry about this one. Yeah, we have a lot to fix, but 14-5 in the Big Ten is 14-5. Perhaps I'm still in the honeymoon phase, but I can't think of anything more beautiful that 14-5 in the Big Ten while winning ugly.

+ "Have Da'Monte's guy just double-team Kofi" is an interesting approach to defense. I'm so glad Da'Monte hit 4 of 10 threes.

That's all there is to this bullet point. Just wanted to point out that the Penn State coaches all sat down and said "what if we, like, DOUBLE TEAM double team Kofi and just not guard another guy." That guy was Da'Monte and he shot 40% from three and we won.

+ Perhaps this is just a first-year thing from Micah Shrewsberry and once he has his roster built he won't play this way, but "grind the game to a halt" basketball is just so, so annoying. 56 possessions for Illinois last night and 57 for Penn State (that was the point of everything Penn State did the entire game).

We played poorly against Northwestern at home, and we only scored 73, but that was on 77 possessions. 60 points on 56 possessions actually isn't awful? It's not great, but when the other team's entire focus is "try to shoot with one second left on the shot clock", it can get so frustrating.

Kinda crazy, these back-to-back games. Michigan? 74 possessions, hot shooting, 93 points. Penn State, 56 possessions, the entire game played with four inches of mud on the court, 60 points.

But both were wins.

+ Now, Iowa. Statistically, the third best team in the country since February 1. Winners of five straight including at Ohio State and at Michigan. Up to 14th in KenPom (we're down to 18 as of this morning). Team with the guy who should be Big Ten Player of the Year (Murray) vs. team with some big issues right now (and possibly no Grandison).

Can't wait to find a way to pull it out.


Altgeld88 on March 4, 2022 @ 09:14 AM

Can't wait to find a way to pull it out.

Yes. And defense did indeed win it for us down the stretch last night. It wasn't simply that PSU went cold; it was that our guys badgered them enough that tired legs couldn't get the shots to fall. Despite the ridiculously bad luck we had on bounces out of bounds in their end. I think they got four shot-clock resets on one possession, and still didn't score.

IlliniJoe81 on March 4, 2022 @ 09:33 AM

Every time I try the “why are Illini fans worried about Game X vs inferior opponent?” comments I always regret it. So I’m swearing those off. Going to stop pretending like I know what we’re getting from this team.

Nashvegas Illini on March 4, 2022 @ 09:33 AM

Thank you Robert for bring me back to a dark place by bring up the 38 -33 Penn State loss. Fun facts. Current assist coach Chester Frazier was starter in that game and had 7 points. Current BTN Basketball analysis Trent Meacham was the other starting guard with 7 points. Those were the two leading scores for the Illini in the game. No player got to double figures for the Illini.

Talor Battle was the only player in double figures for the game with 11 pts. Both team shot under 20% from 3 for the game (setting the game back 40 years).

I think this game should be at the top of Bruce Weber resume for the rest of his life.

ATOillini on March 4, 2022 @ 09:48 AM

I'm surprised you went with "I'm encouraged by winning this game". I must admit I thought your Twitter comment on the "frustrating style" of Penn State led me to believe you were playing tricks on yourself. Felt as if you were looking for some excuse other than "Why are we not easily beating Penn State at home by a comfortable 10-15 points?"

I'll admit that's exactly what I was feeling. As an example, I happened to see another Twitter post indicating 17 years ago to the day (March 3) the '04-'05 Illini beat Purdue at home 84-50. I could be completely wrong, but seems like the Indiana game was the last one where we were really comfortable in the last couple minutes. That was a month ago. We will not have room for error once the tourney starts.

Nabor568 on March 4, 2022 @ 09:51 AM

I'm glad you didn't write 'It's March and we're ROLLING,' because at least for me it definitely doesn't feel like we're rolling.

1978fan on March 4, 2022 @ 10:14 AM

Maybe the O&B can hire those officials more often. That foul difference was absolutely the difference in this game! Illini 15-17 from the charity strip, Penn St. 1-3…ballgame!

Mr.Angry.Eyes on March 4, 2022 @ 10:35 AM

Here is another interesting data point to the season - Every conference team that beat Illinois lost their next game. Purdue even did it 2x. I am putting my orange colored glasses on and assuming this is a sign that the Illini are a tough out and opponents have to give everything they have for the victory and are not able to recover for the next game. (Just found an exception - Maryland, but that was because Illinois beat themselves in that one.)

IBFan on March 4, 2022 @ 10:01 PM

DW hitting 4 threes is great but.....

How much more scoring was prevented all other times DWsX dropped in coverage? Or for every time 1 or 2 extra defenders besieged Kofi?

How many other factors did it impact? Game speed? Offensive set selection/shots? Kofi frustration? Rebounding?

I would let Curbelo, Hawkins, DW sit all day at the three point line and double/triple Kofi. Kofi can shoot 7-10, usually causing multiple fouls and adding a free throw or two.

1978fan on March 5, 2022 @ 09:19 AM

Is Wisconsin claiming to be B1G champions, just a little early?

GO Huskers!! on March 5, 2022 @ 11:57 AM

They are guaranteed at least a share since there is no tie breaker.

1978fan on March 5, 2022 @ 12:29 PM

What I was reading stated the tie breaker went by head-to-head, than entire season record….it must have been old outdated information.

Illini can still tie. Go Huskers. You know, I’m rooting for the basketball team, where the N on the side of their football helmet stands for nowledge!

GilThorpe on March 5, 2022 @ 05:11 PM

tie breakers only apply to seeding for BTT . pure B1G record counts for regular season standings. Thus , Wiscy is assured of a banner.

1978fan on March 6, 2022 @ 03:17 PM


IlliniJedi on March 5, 2022 @ 02:48 PM

We did not have 'Belo our first meeting with the squakeyes which was not as close as the final score appears. I predict an easy win for the beloved.

thegoah on March 5, 2022 @ 08:15 PM

It can’t happen to EVERY drummer now, can it?

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