Totals

[OnKPDuty]

Hi, is anyone here familiar with predicting the total points scored in a game? I am having trouble with this sample problem I was given:

"All things being equal, how would a total be affected by whether, say, Isiah Thomas plays or sits out?"

I don't want to lead anyone as I don't want to influence any answers (perhaps wrong ones anyway), but how would you go about solving this hypothetical? Thank you.

[Mike G]

I have the answer!
Isiah has been retired 22 years, so it makes no diff where he sits.
http://www.basketball-reference.com/pla ... ais02.html

[Crow]

He most likely meant Isaiah.

I assume most of the gamblers that play totals have answers, various approaches and layers; but they may not want to share.

Obviously you have the substitution affect (someone replaces Thomas), the substitute for the substitute, the impact of each on teammates and opponents, possible change in pace, change in what plays get attempted / executed, change in who leads, especially in clutchtime (likelihood of garbage time), etc. Home / road and quality of opponent obviously matter on their own and also affect how much this change in PG matters. I don't have a step by step model but I'd think about all these things and maybe there is more.

[OnKPDuty]

Hi, thank you, I did mean the current one playing, but either way it's just an example, so any player will do. I was hoping someone would be willing to get into the nitty-gritty of the math. Or at least start me in the right direction. Ty.

[Nate]

... the nitty-gritty of the math ...

A little bit less nitty-gritty and more conceptual.

There's a lot of techniques you can use to get a number. A simple example is to take the average total for Celtics games with Thomas, and the average total for Celtics games without Thomas and take the difference. An even simpler (but stupid) option is to just say the number is 0. Instinctively we want to say that the difference of averages is better, but why is that better, and is that the best option?

(If you just want a way to calculate a number, you can use the difference of averages and stop here. Heck, you could just use 0, but we all know that's silly.)

So, really, the question is really either, what's a way to predict the impact of Thomas sitting that's "good enough," or what's the "best" way to predict the impact of Thomas sitting. Without more insight, "good enough" and "best" are pretty vague notions here.

So let's take a step back. When you ask a question like "what's the numerical impact of X", you probably already have some kind of formula in mind that you want to use to predict point totals going forward. That formula is going to include things that you can measure directly or see in advance (for example, whether Thomas sits) and things that you can only get at indirectly (like how much it matters whether Thomas sits).

So what we can do - at least in principle - is we go back to every game in the past and write out the formula for it, filling in the things we know directly, and leaving the things we can only get at indirectly as variables. This gives us a "prediction" (in terms of those variables) for the point total in each game.

Then we start working out values for the variables so that the predictions in total for those past outcomes are as good as possible. (That means that we need to make up a 'goodness formula' too.)

It turns out that this is particularly easy, or works particularly well for certain kinds of 'prediction formulas' and 'goodness formulas'. For one of the simplest examples you can find youtube videos about 'least squares regression'. One part of the math knowledge is knowing the kind of prediction formulas that work well.

A convenient thing is that you can use the 'goodness formula' to estimate how well your prediction formula works. However, that's dangerous because we made up the prediction formula and the goodness formula so we can't really be sure that they'll work well for new data points, and it's also dangerous because there might be something important that's different between the data points we have, and the situation we're trying to predict.

So, in addition to working out how to deal with particular kinds of prediction formulas, people also work on identifying overly naive predictions. This part of the math is more subtle, but can help you avoid overconfidence.

[DSMok1]

Hi, is anyone here familiar with predicting the total points scored in a game? I am having trouble with this sample problem I was given:

"All things being equal, how would a total be affected by whether, say, Isiah Thomas plays or sits out?"

I don't want to lead anyone as I don't want to influence any answers (perhaps wrong ones anyway), but how would you go about solving this hypothetical? Thank you.

RPM or BPM is well suited to this, since they're single-number metrics denominated in points per 100 possessions better or worse than average. So for your example, I'd say--how good is Thomas? How many possessions would he normally play? Who will replace him for those possessions? How good are they? Take Thomas's points above average and subtract out the replacements, and you've got an answer for your question. Obviously there are second-order effects, synergies, etc that aren't accounted for, but at least it's a rough number.

[sndesai1]

overall rpm and bpm are probably more useful for a spread than a point total
replacing al horford's possessions with andrew bogut is likely to result in less total points being scored even if their overall ratings are pretty similar


now, maybe you could use o and d splits in the calculation

Code: Select all

                 ORPM     DRPM     RPM
Andrew Bogut    -2.24     5.45     3.21
Al Horford       0.89     2.08     2.97

ORPM: -2.24 - 0.89 = -3.13
DRPM: 5.45 - 2.08 = 3.37
so the team scores 3.13 fewer pts / 100 poss when bogut is on offense and allows 3.37 fewer pts / 100 poss when bogut is on defense.
the difference in their overall ratings implies little to no effect. however, unless i totally messed up my interpretation, using the o and d splits implies a -6.5 pts / 200 poss impact on the point total

of course you're not going to actually beat sportsbook point totals doing something this simple, but it might be somewhere to start