Mark Lebedew ran a poll on his Twitter account which produced some interesting results. He asked at what point you would dedicate a defender to tip coverage. Basically, the question was “How often must the other team tip/shot for you to decide to dedicate someone to take that?”
Rather surprisingly – and potentially irrationally – more than 60% of the respondents said when tips happen from 10% to 30% of the time. That’s on top of 6.5% who basically say they always have some defending tips.
Now, admittedly, this wasn’t a big poll. Nor was it as well structured as it could have been. For example, Mark cut things off at 30%. That means people who, for example would have said 50% were forced to pick the “never” category.
Also, it’s possible there was confusion over what Mark meant by “dedicated”. Knowing Mark as I do I know he meant moving someone into a short defensive position (e.g. 3m line) specifically to take tips. Some, though, might have interpreted it to mean assign someone in a normal attack defending position to also have responsibility for getting tips (we tend to see this a lot with line defenders). But for the sake of this discussion let’s assuming at least most people interpreted the question properly.
You may have noticed that I used the term “irrationally” above to describe the 70% who would assign someone to tip defense in the case where 30% or fewer attacked balls were tips. Why? Because that means they’re not defending the 70%+ balls that aren’t tipped!
Here comes the math!
There’s actually a pretty easy bit of math we can do to see if this makes any sense at all.
PtPct = [PT x PtPctTD] + [(1-PT) x PtPctHD]
PtPct = Point Percentage, which is the probability we get a point in transition from our defense (keeping in mind the whole purpose of defense).
PT = Probability of a Tip
PtPctTD = Probability of scoring a transition point when the other team tips.
PtPctHD = Probability of scoring a transition point when the other team hits.
We use decimals to express all the probabilities. So, for example, if the other team tips 30% of the time, then PT = 0.3. Obviously, we’re talking here about balls that get past the block or are playable block touches.
Let’s look at the example of a line defender who either plays deep to dig a spiked ball or behind the block to get the tip. We’ll assume 30% tips, and that in both cases the defender digs every ball and we get a transition point.
PtPct for tip = [0.3 x 1] + [(0.7) x 0] = 0.3
PtPct for spike = [0.3 x 0] + [(0.7) x 1] = 0.7
So this tells us that for every ball the other team attacks past our block we earn 0.3 transition points when we dedicate someone to tips, but 0.7 points when we have them stay back to defend spiked balls. To put it another way, out of every 10 attacks we would expected to score 3 transition points if we commit to the tip, but 7 points if we commit to the spike. As such, we are MUCH better off keeping that player back.
You’re probably thinking, “Yeah, but spiked balls are harder to defend.” Let’s say we only turn 50% of those into transition points.
PtPct for spike = [0.3 x 0] + [(0.7) x 0.5] = 0.35
Committing to the hard hit ball still has about a 17% better expected outcome.
What if the player didn’t fully commit to either tip or spike. Assuming we’re only half as likely to be successful to each compared to full commitment, that would look like this.
PtPct when uncommitted = [0.3 x 0.5] + [(0.7) x 0.25] = 0.325
Better than committing to tips, but not as good as staying back for spikes.
Need to know your own values
Of course, to make a good decision in your particular situation you need to use values appropriate to your team. For example, while you might dig 100% of the tipped balls if you have a dedicated tip defender, even the best offensive teams don’t turn anywhere near all those balls into points. If all those tips are going to your setter and your team isn’t very good attacking out-of-system then PtPctTD could be very low – like <0.1.
In fact, just coming up with the numbers for your team could be a really useful exercise. Not only would it help you make decisions about defensive schemes, it can point out particular areas of strength and weakness in your team’s play.
The best way to get value for PtPctTD and PtPctHD is to base them on live play across a variety of opponents, if you can. Look at all the situations where you had someone up for tips and figure out the transition point percentage ( Trans Points / Opp Attacks Past the Block). Then do the same for when you keep everyone back. Alternatively, you can use good attacks (however you define that for your level) in place of transition points). If you’re stuck with basic stats you can use digs as a rough proxy.
Remember you can change
Don’t forget in all this that you can – and should – change as circumstances dictate. If a team is tipping a lot, for example, then you need to redo the math. Same if they aren’t tipping at all.
These are where in-match adjustments come in. Just try to make sure you have something like usable values to base you judgements on.