Any educated fan can tell you that penalties are huge in roller derby. If you read my stats study earlier this year on Queen of the Rink, then you have a pretty good idea of just how big they can be. —And it seems like the effect that penalties have on the game is getting larger. As teams begin to get closer in skill level and strategies continue to advance, losing skaters to the penalty box becomes more and more hindering.
Because of this, there is also an increased need for good penalty management tools. I had experimented with some penalty frequency statistics like "minors per jam" [(majors × 4 + minors) / jams], but I was never satisfied with the usefulness of something like that. I've seen other statistics like fractional penalty minutes that attempt to factor in the impact of minors to scale with majors, but again, those kinds of statistics are not very useful because of the difficulty in comprehending them. In my opinion, a stat is only as useful as it is understandable.
One of the big problems is measuring penalty frequency by jams skated. Jams skated is a good divisor in basic roller derby stats like points per jam or lead jam percentage. It can give you useful averages for a lot of things, but not for penalty frequency. The reason for this is because with penalty frequency statistics, serving a penalty turn can actually help a player's rating.
To illustrate what I'm talking about, let's look at 2 skaters who commit the same penalty. Fannie Flash goes into the penalty box at the beginning of a jam and exits later in the same jam. She skates in 1 jam and gets 1 major penalty. That's a 1:1 ratio of penalties:jams skated. In the next jam Rascal Rae goes to the penalty box for committing the same penalty, but the jam is called off shortly after she sits down. Another jam passes, and then Rascal Rae exits the penalty box in a third jam. In this case, the ratio of penalties:jams skated would be 1:3. The problem is that Fannie and Rascal commit penalties at the same frequency. Fannie had no control over the jam continuing and Rascal had no control over being in 2 more jams. Using jams skated for penalty frequency statistics is unreliable.
The real question at hand is: "How often do skaters go to the penalty box when you send them into the game?" The number of jams a skater is actually in is irrelevant. If you subtract the number of times a skater begins the jam in the penalty box, from the number of jams she was in, you'll get the actual number times she was sent onto the track. —Something I like to call Jams Fielded. Hopefully, your lineup trackers are recording when skters enter and exit the penalty box. If they do, this should be an easy stat to calculate.
Using Jams Fielded can really highlight how often skaters are actually sent onto the track and how often skaters just end up in the penalty box, stuck in the game for another jam. Once you divide the jams fielded by the number of penalty turns a skater has incurred, you'll get the average number of times a skater is fielded before she goes to the penalty box. This is the Jams Fielded Per Penalty Turn. I love this stat because it's very simple to read. A score of 6.25 means that every 6.25 times a skater has been sent into a jam, that skater has gone to the penalty box. It's simple; the higher the score, the better.
So, how is this useful? Well, obviously it's very useful to know how penalty prone every skater has been. Keep in mind, though that you also have to take into account how active the skater is in the pack. A skater who is an actively hitting blocker (doing the heavy lifting in the pack) is simply going to garner more penalties than a skater who usually just positionally blocks. Still, it can be really helpful to know when you only have 2 blockers on the track because in that situation, you're need to get your team out of the penalty box carousel of doom. Maybe in stead of putting in you 2 strongest blockers, you might want to put out a couple of clean blockers for a jam to try and get back to a 3-pack or a 4-pack for the following jam. Sure they might not be as strong as other blockers, but sometimes losing a jam or two can be worth it if you are stronger in the pack for several jams afterwards.
Also, I highly recommend splitting this stat between jammer and blocker statistics (keep in mind that any poodling jammer is going to have a bad blocker score). Obviously, it's far more important to have a clean jammer than a clean blocker. One or two power jams is often the difference in winning or losing a bout. If you can put together a clean jamming rotation, it can be a huge advantage.
In the end, this is all about managing penalties. Your average 60-minute bout is going to be approximately 40-42 jams. You can use Jams Fielded Per Penalty Turn to get an idea of how many penalties to expect from blockers team based on your lines. You can use it to help predict the number of power jams you are likely to surrender based on your jamming rotation. Sometimes just knowing what to expect ahead of time can help a team keep their heads and avoid compoinding penalties. There are a lot of ways you can apply Jams Fielded Per Penalty Turn to help manage the game and give your team the best chance at winning.