Posted by Maybe you are getting bored with reading my never ending rantings on errors, but then again if you’ve stuck around for the timeout stuff maybe not. If not, by all means read on.
Fifteen odd years ago I was reading an article (probably in Sports Illustrated back when human beings used to write for them) about an NBA player in the middle of a breakout season. The player’s name was Steve Nash and one of the points of wonder for observers and fans was not that he was good at passing, that was obvious, but the types of passes he made. The types of passes he made were the types of passes that had hitherto been considered too risky, such as one hand passes or wraparound passes. Risk averse coaches (ie all of them from the beginning of time) had taught generations of players to always pass with two hands so as to reduce the chances of turnovers. All of a sudden here was the prospective MVP not only doing the opposite of the conventional wisdom but thriving because of it. It was postulated that the reason he was prepared to go down that path was that he had been brought up playing soccer (technically not football as he is Canadian). In soccer, the cost of a turnover is very low, especially in the attacking third. He tried those passes because he had a different concept of risk.
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I have thought more about that concept in recent times, partly to try to explain why in (men’s) volleyball errors don’t have much relationship to winning and losing. I noticed that while total errors (for the record, opponent aces are NOT reception errors) were unrelated to winning, total errors that were not service errors seem to explain something (see charts below from 2021 Olympics). How can that be? An error is an error. One point is one point. Surely. But if we have ever watched any match of any sport we know that not all points are equal and not all errors are equal. So I came up with the idea of the opportunity cost of errors. In men’s volleyball, the chance of winning a point on serve is relatively small. So an error loses us only ‘relatively small’ chance of winning a point. An attack error on the other hand costs us a lot more as the chance of winning a point if an attack is in the court is relatively high. The time of the set also changes the cost of error. We have already studied that winning / losing points at different parts of the set have different impacts on win probability. So it seems the approach might be logical. We might even be able to put number values to different kinds of errors using expected values from our league datasets.
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I think I disagree that the baseline probability of winning is the principal factor in guiding risk-taking, or indeed that it matters at all. The risk:reward ratio is much more important. Say I’m in a situation where I have very little chance of winning the point. I might be tempted to try some risky things on the grounds that I was unlikely to win from that situation anyway. But if hypothetically there was nothing whatsoever that I could do that would actually increase my chance of winning – all I can achieve is increasing my chance of error – then the increased risk is not worth taking because it does not offer any chance of increased reward. Equally, I might be in a situation where I am very likely to win (about to hit a quick attack off a perfect reception). The “cost” of an error here is high so I might be tempted to play conservatively to reduce my risk of error. But what if that led to a small decrease in error rate but much higher increase in the opponent successfully defending the ball? My expected reward has plummeted relative to my decrease in risk. Maybe I should take *more* risk here, if I think I can increase my chances of winning more than I can increase my chances of making an error.
For me, this explains e.g. why men’s volleyball has evolved to the point of high risk taking on serve. It’s got little if anything to do with the low baseline breakpoint percentage (~35%) – it’s because there is opportunity for reward. If I take risks, I increase my chance of serve errors but I can outweigh that with the reward (aces, but also putting the opposition out of system on their first attack and overall winning more points). At the same time I can’t afford to not take *enough* risk on serves, because if give away easy serves with no errors, I’m also giving away too many points on opposition first attack.
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1) I think most fans / commentators are in the 1 = 1 understanding of errors. We know from data and experience that is not true. Players/coaches intuitively understand to some degree as evidenced by serving strategy, but I think a lot are still in or around the 1 = 1 group.
2) I wrote the first draft of this and went away. While I continued thinking I got to the point that there are more variables involved in reality. But I already had the draft more or less done and I figured that it was enough as a thought experiment to start a conversation.
My next line of thinking was: an ace is 1 point and a minus reception is 0.25 expected points. So my potential reward is 0.75 points v potential loss of 1 point. I think that is the same line of thinking as you, although I think I have confused myself.
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I would agree that not all errors are equal, and also thought that the example of Steve Nash’s unconventional passing also tells us that the opportunity cost of errors is not a constant and may change depending on the novelty of the technique or tactical choice employed that resulted in error. As the sport catches on (scouting, player preparedness) with more novel techniques and tactics, the opportunity cost of the same exact error probably increases.
Maybe a crude example of this would be errors of a left-handed middle blocker (Japan’s Suntory Sunbirds had one?) on a quick attack not being equivalent to errors made by a right-handed middle blocker if the left-handed middle blocker forces a lot more attentiveness from the opposing middle blocker, making more opportunities for outside attackers to score against poorly organized block.
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