Reader will brought up an interesting question in a board posting recently: should Michigan have fouled Kentucky with about 20 seconds left, putting them at the line, but (critically) giving Michigan the ball back with a chance to tie or win?
To my surprise (especially given this crowd), there were a lot of "gut" responses based on feelings, emotions, and in some cases, how such options would be hard to explain in the media.
So I did a few small calculations. The simplifying assumptions were these:
- Kentucky has some chance of making each free throw (call this Kft)
- Kentucky has some chance of scoring when we don't foul them (Ks)
- Michigan has some chance of scoring if they have the ball back (Ms)
- There are only two-point baskets (no threes for simplicity)
- If the game went to overtime, odds are 50/50
On a missed free throw by Kentucky, Michigan gets the ball 100% of the time
(clearly a stretch in this game)
- If we let Kentucky play it out, they will get one chance to score and the game will end either with them winning or go to overtime.
- If Michigan gets the ball back with plenty of time, assume they either score (as dictacted by Ms above) or miss; no free throws, etc.
With these assumptions in place, we can start to calculate: what should Michigan have done to improve their chances of winning the game?
There are two options we will compare:
- Traditional (T): This is what we did. Play defense, and hope Kentucky misses.
- Non-traditional (NT): Foul Kentucky (hopefully a bad free-throw shooter) and get the ball back with a chance to tie (if down two), or win (if down one or still tied).
Consider the traditional approach first. Let's assume that Kentucky has a 40% of scoring to win the game in the fashion they did. Thus, 40% of the time, Michigan loses in regulation, and 60% of the time, it goes to overtime. By assumptions above, Michigan's win probability in this case is 30% (half of the overtime outcomes).
Consider the non-traditional approach, which is trickier. Assume here a low rate for Kentucky free throws: 50%. Thus, 50% of the time, Kentucky will miss the first free throw, and Michigan gets the ball back with a chance to score and win; assume again a similar 40% chance Michigan scores when they have the ball. Correspondingly, 60% of the time, the game goes to overtime with 50/50 odds. Thus, on the first miss, Michigan has a 70% win chance.
Unfortunately, 50% of the time, the Kentucky player makes the first free throw. There are two further cases to consider then. If they miss the second (which happens 50% of the time), Michigan has a 40% chance of winning in regulation, but 60% losing. If they make the second, Michigan just has a 40% chance of sending it to OT, where they have a 50/50 shot.
If you add all of those win probabiities up, the Non-Traditional (NT) approach, assuming the numbers above, has a win probability of 50%, which is 20% higher than the traditional approach (T). Thus, assuming the numbers and other things above, fouling was the better option.
However, that is a pretty low free throw percentage, and the chances I gave of Kentucky or Michigan scoring a basket (40%) were chosen arbitrarily. Thus, I varied each of these and produced the following graphs.
This first graph assumes the 50% (Kfs) as above but varies the Michigan scoring chance along the x-axis and the Kentucky scoring chance along the y-axis. Results in BLUE mean that Michigan would have increased its chances of winning with the NT approach; RED means a decrease by fouling early. The value shown is the difference in win probability between the two approaches.
As you can see, the (x=40,y=40) point shows the 20% increase calculated above.
I also made a graph assuming that Kentucky shoots free throws at a 75% rate, not 50%. It looks like this:
As you can see, it looks a bit different, with the non-traditional approach (foul early and get the ball back) not doing as well.
More broadly, what you can see from the graphs are this: if free throw shooting is bad, fouling early makes sense, especially if you have a good offense with a good chance of scoring. Fouling early also makes increasing sense if the other team is likely to make their last-second shot (no surprise).
Given the efficiency of our offense, and the relative non-goodness of Kentucky free throw shooting, I think we did the wrong thing.
Of course, I reserve the right to be wrong in the analysis (it was a little hastily thrown together); critque away, as you always do. :)
OMG IT'S HAPPENING AGAIN!
Ok, so I'm headin to Indy tomorrow evening to attend the game on Sunday, so I wanted to make sure I got this out in time. I hope you enjoy these. I did two slight variations of the same idea. I like how they turned out and, quite honestly, I think these could make SWEET t-shirts. Anyone who knows of a t-shirt maker that could do this quickly, hook me up and I'll send you the files (they're photoshop currently, but I can convert the main graphic to vector for illustrator or indesign printing). I'm honestly not sure the last time I was this excited to attend a sporting event. I didn't get to go to UTL (biggest regret of my sporting life), so I'm hopeful that Michigan has a strong showing against the one-and-done poster boys of UK. Honestly, I was hoping for a revenge game against Louisville, but I'll take it because OMG ELITE EIGHT! As usual, constructive criticisms and/or ideas for new wallpapers are always encouraged/welcome. Enjoy and GO BLUE!
"First Person (Not Just A) Shooter" Desktop (1920x1080):
"CHISELED [Our Workouts Work] SHOOTER" Desktop (1920x1080):
Northwestern finished 11th in the Big Ten last year with a 6-12 record. There is no guarantee that they will get any better as they lose some key players. 10th Year senior Drew Crawford finally graduates, and they also lose seniors Nikola Cerina, and James Montgomery the third. Kale Abrahamson, and Chier Ajou also are transferring. Northwestern loses 26% of their assists, 29% of their rebounds, 32% of their minutes, and 34% of their points. They do bring in 4 freshmen so that could be promising.
Here is their projected roster:
# Name HT WT YR POS
23 Jershon Cobb 6-5 205 RS.SR. G
Cobb will have to be their go to guy, losing Crawford means a huge void in scoring. Cobb showed the ability last year to take over, he may be able to this year as well. Cobb will be the starting Small Forward.
3 Dave Sobolewski 6-1 180 SR. G
The starting Point Guard, got hurt last year, but will continue to start. Takes A LOT of shots, but does not make many of them.
14 Tre Demps 6-2 193 RS.JR G
Demps was another player that could score in bursts, he will be the starting Shooting Guard and the second go-to scorer.
22 Alex Olah 7-0 265 JR. C
Olah is a foul magnet, but is a large body that hopefully can continue his defensive prowess. The latest installment in the old looking young guy series. Starting Center.
34 Sanjay Lumpkin 6-6 210 RS. SO F
Lumpkin will be the starting Power Forward, and will look to add to his 3.8 points per game. He will most likely add to his points due to the large amounts of minutes he will get.
31 Aaron Liberman 6-10 215 RS.SO C
Liberman did not play much this year, and probably won't play that much this year either.
32 Nathan Taphorn 6-7 190 SO. F
The 6th man, Taphorn averaged 2.5 points last season and he is going to be an important piece going forward.
Victor Law 6-6 185 FR. F
Northwesterns highest touted recruit, a Four star, that could be playing meaningful minutes right away.
Bryant McIntosh 6-3 175 FR. G
A three star, will most likely be the first guard off the bench.
Scott Lindsey 6-5 180 FR. F
Another three star, probably a 8 minute a game kind of guy.
Johnnie Vassar 5-11 175 FR. PG
Most likely a redshirt
Projected Starting Lineup:
Point Guard: Dave Sobolewski
Shooting Guard: Tre Demps
Small Forward: Jershon Cobb
Power Forward: Sanjay Lumpkin
Center: Alex Olah
Northwestern will not be good. I think they will finish 12th in the conference with a 5-13 record. They are very thin, and not uber experienced.
Michigan plays them at Home and Away, which again is very favorable.
Next up... Indiana.
I vowed to have a wallpaper done for ya'll for tomorrow's game and HERE IT IS! I actually made two, and while I definitely like the first one best, the second actually took me longer to put together. I just was TOO frustrated with my keyboard/mouse combo that I have yet to replace to go any further in refining it. Hope you like them. As always, constructive criticism and/or ideas for future wallpapers are welcome. BEAT THE VOLS! CHARLES WOODSON! 2014!
"Simply Sixteen" Desktop (1920x1080):
"I'll Take That One" Desktop (1920x1080):
It has been discussed a few times on the board that Michigan is typically very good at dictating the game to its opponents, and there is definitely evidence of that in the team’s offensive efficiency numbers. During the season to date, Michigan has maintained an average offensive efficiency of 1.20 with a standard deviation of 0.163 (0.118 during conference play only), which seems to me to be a relatively narrow band considering that the standard deviation for Michigan’s possessions per game was only 4 against an average of 62 (and 61 possessions with a standard deviation of 3 in conference play). Long story short, the play was relatively consistent in its production and pace. When we talk about how it is vital to impose your will early in a game, there aren’t too many teams that can do it quite in the way that Michigan has.
Below is the normalized graph for offensive efficiency:
You’ll note right away the relative handful of games on the extreme ends of performance. There are only four games with a Z-score greater than 1.00, meaning that offensive efficiency was greater than one standard deviation above the mean. On the other end, there were five games where efficiency was more than one standard deviation below the mean, all of them losses.
The story is a little different when we flip to defense, of course:
Here you can see a little more in the way of erratic behavior, but for those of us who kept saying that the defense “is what it is”, well, this is it. Interestingly, the distribution has a similar look to the offensive one with a standard deviation here of 0.168 against an average of 1.04. Seven games actually are greater than one standard deviation above the mean compared to six games more than one standard deviation below the mean. There is a marked jump in the number of “extreme” performances in this aspect of the game.
From this data, we can build a nice little set of histograms and get an idea of what the probability distributions looked like for efficiency on both offense and defense, but I would also like to throw scoring margin in here because it is interesting in the case of Michigan. Actually, let’s discuss that first.
For each of these next graphs, I broke the cumulative function into fifths (hence, for example, “0.00-0.20”, which represents the first fifth of the total area under the curve) and made the histograms based on relative position. For scoring margin, it is important to note that for the season to date (postseason included for giggles) our average margin is +9.45 points with a standard deviation of 16.08 points.
Here’s what the histogram for scoring margin looks like:
So, what you see here is a lot of close games basically. Indeed, we played in 20 games where the scoring margin was +10 or less (12 of which were wins), compared to only 13 games won by more than 10 points (also, two where the margin was exactly 10 points).
Here is offensive efficiency getting a similar treatment:
Again, the relative steadiness of the offense is seen here. If you look at the three bars in the middle, that more or less represents the two-thirds of Michigan’s games which sit in their “zone” around the 1.20 line, if you will.
Yeah, this one is decidedly wobbly and definitely skewed towards “meh” performances. Many of the games on the left (“better” defensive efficiency, in this case) represent our out-of-conference schedule actually.
Like everything else, this is for the board’s perusal. The only thing I hoped to do was perhaps give some numerical credence to some of the themes on the board of late.
Oh, and here's a gem...Super Mario 3, a cappella...
Continuing after the Purdue preview, I decided to start at the bottom and work my way up what I think will be the standings next year. Rutgers was not very good this year, finishing 5-13 in the not-so-good American conference. A lot of people would say, "you can only get better from here". This may be true for this Rutgers team. Rutgers loses seniors Wally Judge and J.J Moore. Jerome Seagears and D'Von Campell, and Craig Brown are also transferring. Losing these five players means a loss of 48% of their points and 41% of their rebounds per game, along with 50% of their minutes. They do bring in 4 freshmen who, unless they contribute right away will leave Rutgers pretty awful.
So here is their projected roster:
# Name HT WT YR POS
11 Kadeem Jack 6-9 230 SR. PF
Starting Power Forward, averaged 14.3 points per game with 6.8 rebounds. A close second to Mack.
4 Myles Mack 5-9 175 SR. PG
Starting Point Guard, averaged 15 points per game with 4.3 Assists. Rutgers' best player.
13 Malick Kone 6-5 200 SR. SF
The starting Shooting Guard, averaged 3.5 points per game last year.
44 Kerwin Okoro 6-5 220 JR. SF
Does not play meaningful minutes.
21 Stephen Zurich 6-5 205 JR. SF
Same as Okoro.
23 Jalen Hyde 5-8 160 JR. PG
Same as Okoro.
35 Greg Lewis 6-9 260 JR. PF
The starting Center that has a decent rebound rate. With him starting Rutgers actually has a pretty big lineup.
10 Junior Etou 6-7 225 SO. SF
The starting Small Forward, averaged 5.3 points per game.
30 Khalil Batie 5-10 175 SO. PG
5 Mike Williams 6-2 180 FR. SG
3 Star, offers from Dayton, Iowa, ST. Johns, Temple...
3 Bishop Daniels 6-3 185 FR. SG
3 star, no other offers
14 Ibrahima Diallo 6-9 215 FR. C
Rawer than sushi. 3 Star
22 Dwayne Foreman 6-7 215 FR. PF
Offers from Iowa State, Minnesota, Pittsburgh...
My projected starting lineup:
Point Guard: Myles Mack
Shooting Guard: Malick Kone
Small Forward: Junior Etou
Power Foward: Kadeem Jack
Center: Greg Lewis
Michigan plays Rutgers at home and on the road next year, which is favorable for us.
In all, Rutgers is a pretty small team that is losing a lot of players of. They do not have depth, or much skill. The junior class looks to have nothing so the team will rely on mostly seniors. I project Rutgers will go 4-14 and tie with Purdue for last.
Next up... Northwestern.