APBRmetrics

I just thought of this question. While it's pretty simple, I would like to put numbers on it. As I am traveling (and without a computer for the next 10 weeks), I won't be able to look into it until I get back home.

My thought is that it doesn't matter if you're increasing your win probability by the same rate. IE there is no difference in increasing your chances of winning from 40 to 50% compared to 80 to 90%. Improving your chances of winning by 10% is the same benefit, no matter who a team is playing. That being said, the change in probability of a team winning increases based on how similar each team's rating is (adjusted for HCA).

This supports the standard practice of sitting players against garbage teams. However, I feel as if the flip side of this isn't widely understood. Teams should be more willing to scratch their stars against really good teams. If Houston is competing for the playoffs and needs to rest Harden, and they have games against the Bucks and Thunder coming up, they should pick the Thunder to rest him. If the Raptors need to rest Kyle Lowry, they should pick Golden State rather than a team like Washington. Lastly, this also means (contra Popovich) that teams should usually not rest multiple players on the same night (theoretically, the numbers might rarely work out, but less often).

Has anyone run the numbers before?

Thoughts?

-- the slightly more challenging, and possibly more interesting question is how valuable the day off really is, so I also welcome any thoughts on that as well.

It's a reasonable approximation to say that the scoring is normally distributed, so the best games for scratching starters are going to be the biggest mismatches.

So if your team is a huge underdog, it might make sense to rest multiple players. If your team is a huge favorite, then resting players will make things closer, so resting multiple players is not such a good idea.

Edit: The 'entertainment' side of the business also informs the decisions about who to rest.

I think it depends on your team's quality/situation. If you're a top playoff team that needs wins to get or hold a certain position, I think you would rest against crummy opponents because you're still likely to get the win. But if you're a top team that's running away with things, I think you would rest against good teams because you still have a shot and a loss doesn't hurt too much; those are also more exhausting games, so the rest might count more in some sense; plus, you should be able to rest players via short minutes in blowouts.

If you're a middling team you probably can't afford to rest again anyone, but again you have to bank more likely wins. Unless you're trying to lose to get into the lottery (which also potentially applies to bad teams), in which case I think you actually rest against bad opponents as well. Those are your most likely wins, and you don't want to win, so you rest a starter to drop your chances.

So as I type it all out, I think you always rest against bad teams unless you're a really good team that doesn't mind a potential loss. Then you rest against good opponents.

Another approach might be to try to maximize your chances in swing games. If you think your team has >75% or <25% (to make up numbers; maybe you prefer 80/20) chance of winning, you consider that game a lock and feel free to rest someone, barring a big swing in probability by sitting that person. Anywhere in the middle is a game with a highly uncertain outcome, which makes it attractive as an opportunity to steal a win for yourself and give an opponent a loss. So you would never rest a starter against a team you were even with, assuming you want to maximize those iffy wins, but you would consider resting against anyone else. I don't know if this strategy would be better than the first one.

But if the outcome of a basketball game is probabilistic, there is no such thing as conceding a win/loss.

If you go from a 95% chance of winning a game vs a bad team, to a 80% chance of winning after sitting your star, this is the exact same as going from a 57% chance of beating another team, to 42% after sitting the star.
The only thing that changes is that impact of a player sitting is more pronounced the closer in team rating (adjusted for HCA) the two teams are.

Actually - after thinking about this further, it seems as if the variation in winning percentage based on a similarity in team rating opposed to a large discrepancy in team rating is marginal.

This means that the counter intuitive truth about scratching starters is that it shouldn't matter who your opponent is.
There is no real difference between scratching James Harden against the Lakers then there is against the Mavs.

I have no evidence to suggest that resting players is good or bad, but if a team wants to do it, then there strategic concern should be solely on when the rest is most optimal, and not when they are playing a bad team.

I got fed up and wrote this up quickly on a borrowed laptop.


http://danfrank.ca/when-should-a-team-r ... eir-stars/

It's obviously written for the non-analytics audience, but before I post it elsewhere, I'm curious if anyone on here disagrees with it. The impact for NBA teams is negligible, but considering how often backup goalies play in the NHL, I actually think the conclusion is pretty meaningful.

Thoughts? I ofcourse welcome any and all criticism.

I would expect that there are non-linearities in the relationship between win probability and point differential, and that these non-linearities may be masked because your graph and equation seem to be using aggregate data (seasonal total for each team) rather than data on individual games.

A really good NBA team will win about 75% of its games. That's its overall winning percentage, therefore when say the Spurs play the 76ers, the Spurs must have a probability of winning that is higher than 75%, probably substantially higher.

But this is where ceiling effects come in. The Spurs' win probability can't keep increasing in constant increments to say 85%, 95%, and 105% because 105% is physically and mathematically impossible. So the linear relationship has to depart from linearity at some point.

This is why logit and probit models were invented, to fit a sigmoid curve to the data.

The vast majority of games may be on a part of the curve which is effectively linear. Teams that are around 0.500 may find themselves in that situation even when they're facing their strongest or weakest opponents.

But the very strongest teams will I think be at a point of diminishing returns when they face a very weak opponent, i.e. subtracting or adding talent for that game will affect their win probability less. And the weakest teams will find themselves in a mirror image situation: when facing the strongest opponents they can sit or play their best players without much affecting their win probability, because they're going to lose anyway.

mtamada wrote:I would expect that there are non-linearities in the relationship between win probability and point differential, and that these non-linearities may be masked because your graph and equation seem to be using aggregate data (seasonal total for each team) rather than data on individual games.
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A really good NBA team will win about 75% of its games. That's its overall winning percentage, therefore when say the Spurs play the 76ers, the Spurs must have a probability of winning that is higher than 75%, probably substantially higher.
...

It's certainly non-linear. The question is how significant that non-linearity is.

If we assume that scoring is normally distributed with a standard deviation of around 12 points, and that the productivity of the best players is around 5 points better than their replacements, then we can plug in some numbers.

If the Lakers play at the Warriors this year, the SRS advantage is around 18.5 points, and there's another 3 points or so for home field. That works out to 21.5 points. I think this is a reasonable approximation of the biggest mismatch you can expect to see in an NBA game. If the Warriors rest Curry in that game, they roughly loose an estimated 5% win probability.

If, instead, the Warriors play at OKC, the SRS plus home field difference is less than a point, and resting Curry costs them around 19% win probability.

Of course, if you plug in different numbers, you'll get different answers.