Usually when a player takes a redshirt, it is because they are a freshman and need time to build strength, develop a skill, or are just buried on the depth chart and are biding their time until they will have more opportunities. The Badgers have used the redshirt rule liberally over the years, as they have often had a core of upperclassmen waiting to eat up most of the minutes. Brian Butch redshirted despite being the most heralded Badger recruit in years.
Most of the time when a redshirt occurs after the freshman season it is due to a medical redshirt when a player gets hurt early in the season. However the Badgers have used the redshirt for non-freshman for the same reasons as above. Most notably this occurred with Duje Dukan, which allowed him to develop enough to be a contributor on the best Badger team of all time. It also occurred with current Badger Jordan Hill, who played as a freshman, redshirted as a sophomore, then played last year as redshirt sophomore.
The Badgers had several freshman last season that at least contemplated a redshirt, but none did (although Pritzl was later granted a medical redshirt after reinjuring his foot in the non-conference season). The Badgers had to deal with the loss of Van Vilet due to academic reasons, Pritzl due to medical, and Dearing due to transfer shortly after the season started. This left them with just 9 scholarship players last year, including no seniors and 4 freshman. With so few bodies those freshman had chances to play, and while some could have used the year to develop, none turned down the opportunity to play.
This year could be different. The Badger had a lot of questions last year beyond Hayes, Happ, and Koenig. Both Brown and Showalter were question marks going in, and if they had not improved so much could have been surpassed by a younger player. Both are now firmly entrenched as starters and should get major minutes. The bench will need to be sorted out, but I don't see how there are enough minutes to go around for all the big men, barring injuries.
In the backcourt things are more simple. Koenig and Showy will start, and since Pritzl and Hill have both used their redshirt already, they have to play. Throw in that Gard likes to play some 3 guard lineups and there should be enough minutes to go around. If Trice is good enough he could take minutes from either backup, or could redshirt. Since this post isn't about freshman redshirts I'll move on the the frontcourt.
Hayes, Happ, and Brown will all start and should all play a lot of minutes. Hayes played 36 minutes per game last year and it's hard to see that going down much. Of the 3, Vitto played the fewest minutes per game at 25, so it's hard to see how there will be enough minutes for the rest. That includes Iverson, Thomas, Illikainen, and Van Vilet. You could also throw true freshman Aleem Ford into the mix here, but I'm assuming he will not be ready to be a major contributor this year. Let's look at each of the 4.
Van Vilet- Seems very unlikely to redshirt. Having not seen him play or practice it is hard to say how good he is, but rumors indicate he can play and will be ready to this year. How much is hard to say, but I can't see him redshirting after sitting out all of last year due to academics, and spending 2 full seasons not playing.
Iverson- Seems very unlikely to redshirt. Having seen him play all last year he looks like a star waiting to explode. He led the freshman other than Happ in games played, and minutes played. He will be buried this year behind Hayes, but he should get opportunities because of his defense. He can guard 3 or 4 positions, and if he has developed any kind of jump shot he could play a lot.
Thomas- Possible, but not likely. Thomas was not your typical freshman at UW last year. He came in with the grown man body that most kids need 2-3 years to develop. He also has a decent jump shot for a man that big, and does not lack the confidence to let it go. He played a lot early when Bo was still coaching, but got fewer minutes once Gard took over and played more smaller lineups. He does need to work on post moves of which he showed none last year, but he could have worked on that this summer. Since physical development is not needed, a redshirt seems unnecessary. This only happens if the other 3 kids have moved so far in front of him on the depth chart that no minutes are likely.
Illikainen- Possible. Illikainen was the closest to redshirting last year, but with so little depth last year he ended up playing in 33 games and getting almost 10 minutes per game. He looked good earlier in the year when he was shooting the ball with confidence, but struggled with that shot as the season went along. He showed pluck in defending the post against bigger players, but you could see he was outmuscled sometimes. He has had all summer to bulk up, so maybe he won't need the time to get stronger. I think it's possible that he ends up as the best player in the 2015 class 4 years from now, but right now I think he's the most likely to redshirt.