Predicting a set, by starting setter's position

[FrancescoOleni]

MatchUp.pdf

I'm working on this Match Up tool and I need some feedbacks...
First of all, sorry because the slides are in Italian.
Some keys are clear, like SO%, BP%, S=%.
What I really need to understand, is how to predict the result of a set depending by the starting phases, the starting setters positions, the SO% and BP% of both teams.
Basically, first I need to estimate who is going to win a rally.
At the moment, I'm doing in this way:

• I take the SO% of the SO team in the current rotation
• I take BP% of the BP team in the current rotation
• I take the S=% of the BP team in the current rotation
  I assume that S=% of the times, the SO wins the point.
  Then I have to decide how to split the (1- S=%) of the chances.
  I think that each team has more possibilities to win the rally if they have highest SO% or BP%, but the total between the two chances must be (1 - S=%).
  So for the SO team I calculate the chance: ((mod SO)/(mod SO + opp. mod BP))(1 - S=%)
  For each rally I roll a "0 to 1" dice and I assign the point comparing the number from the dice to the chances of the teams.
  I update the score, the phases and the setters position.
  I run a new rally, till the end of the set.
  I repeat for a new set.
  I repeat... 10.000 times, using different setter's starting position.
  I estimate wich of the 6 could be better.
  Any idea to make it work better?

[raymondben]

My attempt at an answer, but first some context. The general method you're using (Monte Carlo simulation) is basically the same as our volleysim R package uses. That's a good thing, we've converged on the same method! Ours uses a more elaborate breakdown, where the serve can be an error, or ace, or continue to reception-phase play. That can result in an attack kill, ball handling error, blocked attack, ball back over the net without an attack, etc. And so on, with each outcome having a probability that can be estimated from data. This type of simulation approach is very accurate at reconstructing the outcome of a match IF you know the actual parameters (SO, BP, etc) that each team exhibited during the match. The challenge with using it in a predictive sense is that you have to be able to predict the performance parameters that each team will exhibit in that specific, future match. Data from prior matches is helpful, of course, but it's not straightforward.

I think the "correct" answer here is to do some fairly elaborate statistical modelling that attempts to predict those parameters for each team, based on observed data and factoring in the opponent and rotation and so on. We've used generalized linear and mixed models for this in the past, with some success, but still needs work.

In a more practical sense, for something that can be much more easily implemented (I assume yours is in Excel or similar?) your method looks pretty good to me. S= is presumably each team's average serve error rate (against all opponents)? And even though we know that teams tend to make more serve errors against stronger opponents, it seems reasonable to use this as their predicted serve error rate for the matchup. Then once play progresses past the serve error stage, I think your method using modSO and modBP is probably reasonable. I'm not convinced about the actual equation though.

The probability that the receiving team wins is (probability of serve error) + (probability of sideout given no serve error) * (probability that there wasn't a serve error)

which is S= + modSO * (1 - S=)

If we used modBP (of the serving team) instead of modSO (of the receiving team), it would be S= + (1 - modBP) * (1 - S=)

And since we don't know whether to use modBP or modSO, we take the average of the two, which would be

S= + (modSO + 1 - modBP) / 2 * (1 - S=)

??