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Tuesday, April 15, 2014

A (Limited) Defense of Saving Players for "Crunch Time"

If you love sports and you’re interested in empirical methodology, the last ten-plus years (call it the Moneyball Era) have been very good indeed. The increase in attention to statistical studies of sports has grown a ton (though of course it has much longer roots that date at least back to Bill James and early sabermetrics in the late 70s). 

One of the most interesting parts of this movement has been to do what good research so often does: Take a longstanding belief and show that it’s nothing more than smoke and mirrors. For instance, does icing the kicker work? According to this study, the answer is simple: Nope (not that it’s stopped NFL coaches from doing it, of course).

Consider as well the practice in basketball games of sitting players early on so that they will be available (and not in foul trouble) when it’s late in the game and “crunch time” arrives. As many people, including Richard Thaler, have argued, this strategy is probably counterproductive because you get just as many points for baskets scored early in a game as you do during late-game moments, so that sitting players to save them for late-game heroics probably just means you’re shortening their total on-court minutes to the team’s detriment.

The point of this post is not to propound a full defense of the crunch time strategy. This is because I think it’s basically right that basketball coaches are too cautious with saving players for late-game situations, and would probably do better to just max out their points earlier on even if that meant more players would foul out.

The point of this post, rather, is to point out one reason why the story of the crunch time strategy may be more complicated, and somewhat more compelling, than its critics have let on. I elaborate this point below the fold.

To start with an orthogonal observation, the strategy of sitting basketball (and, for what it's worth, hockey) players periodically throughout a game is not only to save them for crucial late-game moments. It also is a necessity (or at least is very advisable) given the highly intense pace of basketball. If you didn’t give cagers regular breaks, by the end of the fourth quarter (or earlier) even the fittest players would be totally gassed, regardless of whether they were close to disqualification via foul accumulation. 

That point aside, though, consider a reason that the crunch time strategy might not be a total loss. First, the critique of the strategy assumes that players are equally likely to score baskets throughout a game. If they are, then it makes the most sense to just maximize their on-court time, regardless of whether that court time occurs early or late in a game. 

But if players’ likelihood of scoring is not constant, and in particular if players are more likely to score later in games, then saving them for the times when they tend to be more productive may be a good strategy. This sort of discontinuity in scoring aptitude is plausible—indeed, one of the hallmarks of what makes a player great may be their tendency to perform well in late-game high-pressure situations.

A related point is that great players have the dynamic effect of making others around them better, either through abstract qualities like inspiring leadership or more concrete ones like making good passes, setting effective screens, etc. These dynamic effects of a star player on their team could also vary throughout a game, and if they were greater at the end of a game, then reserving a star player’s minutes to allocate them later in a game could make more sense than crunch-time critique acknowledges. 

This is, of course, only a limited defense of the crunch time strategy. This post has sought to add one underappreciated possible reason that sitting players early in a contest in order to save them for later-game moments might make more sense than the prevailing critique of the crunch time strategy lets on. And since, as I observed above, sitting players to some extent at intervals throughout a game is inevitable, it’s not possible to just play your best players until they successively foul out, even if this were the optimal strategy.

So given that it is necessary in basketball to sit players periodically throughout a game, one factor that might help craft the optimal strategy for when to sit players would be their likelihood of performing well later in a game (which is, of course, different than the prevailing wisdom that stars should always be saved for “crunch time”). And it bears noting that even if a given star performed marginally better later in games, that slight advantage might well not be great enough to justify reducing his overall on-court minutes by sitting him out earlier in the game. 

This is, though, as the man says, an empirical question with an empirical answer. Do stars actually perform better later in games? Perhaps it’s true that some stars do while others tend to wilt under the perceived pressure. And why limit the inquiry to star players? It could be that all players' performance varies differently throughout a game, which could help a coach figure out when it's optimal to put anyone on the court. The broader point is that while we look at players' statistics as constant given that most basketball stats are based on games (points per game, assists per game, etc.), that may mask discontinuities in when during a game players are at their best, and that uncovering patterns in these discontinuities may be a strategically helpful insight.

Posted by Dave_Fagundes on April 15, 2014 at 11:45 AM in Science, Sports | Permalink


You may be right about that, Bobbo. The study linked in my original post shows that kickers have a lower conversion rate when they are *not* iced. This suggests that since icing is the dominant strategy, not-icing may be better.

The other reason I think not-icing may be a better strategy is that icing gives kickers a free realistic practice opportunity. They can assess the quality of the field, the actual (not just predicted) effect of the wind, etc. It seems like a kicker should *want* to be iced to take advantage of the chance to get a meaningful practice rep.

Posted by: DF | Apr 18, 2014 1:43:59 PM

Re: icing the kicker, I would think that if there is any difference between icing vs. not icing, the optimal strategy would be to do the opposite of what the rest of the league is doing. I.e., if 90% of teams always call a timeout before a big kick, not calling a timeout might throw the kicker off more than a timeout?

Just a thought.

Posted by: Bobbo McBobertsonton | Apr 18, 2014 1:39:56 PM

But I think we already do know: The players needed late in the game are those who can "create their own shot," probably complemented by one guy who can hit the corner 3 (who sometimes is a journeyman). That is almost always your best player.

Posted by: Howard Wasserman | Apr 16, 2014 4:56:20 PM

Hi all,

Thanks for the comments.

Tom, I think that's right. The greater point is that the critique of crunch time assumes that the only reason to sit players is to save them for late game situations. But there are many reasons to sit players--avoiding fatigue as I mentioned in the post, your point about psychological costs of rapid foul accumulation, and I'm sure there are others. It's a more sophisticated calculus than just deploying the best players as early and often as possible.

Howard, yes it seems like the game must change over time, and this is more reason to look to time-specific deployment as a means of maximizing player value. But that doesn't necessarily mean stars have to be featured later in games. Perhaps the slower pace of the end of basketball games is more conducive to the style of journeyman players. The global strategy that would be best would be to figure out when players--stars and others--play best and feature them at their optimal times.

Sparkle, sure, the analysis may well not apply to hockey, hence my almost exclusive focus on basketball and the only one parenthetical reference to hockey. The second point is worth thinking about in terms of why crunch time strategies are bad, though--you not only lose out on your best offensive players but (assuming they are good two-way players) you also lose out on their defensive contributions.

Posted by: DF | Apr 16, 2014 1:10:50 PM



I thought hockey players sat "periodically . . . throughout the game" because that's how a sport with 90-second shifts and perpetual line changes is actually played. Silly me.

Two related, little-known facts:

1. When Wayne Gretzky scored 215 points during the 85-86 season, he never came off the ice. Not once. Not even during period breaks.

2. Everyone remembers that Boston beat Vancouver in the Stanley Cup Finals a few years ago. What most folks don't remember, though, is that the pivotal goals in the series were all scored when Roberto Luongo, the Canucks' star goalie, was off the ice BEING RESTED FOR CRUNCH TIME!!!

Posted by: SparkleMotion | Apr 15, 2014 2:24:23 PM

One unique thing about basketball is that the game changes in the final minutes--it slows down, teams take longer to shoot (especially when nursing a lead), they may shoot more 3s (when trying to catch-up), and defensive intensity picks up. That may suggest the need to have the best players--the ones who perform best in this different game--on the floor late. Which means they need to rest early.

People trying to bring advanced metrics to hockey describe "score effect" to account for the way the style of the game (and thus individual stats) changes depending on the score.

Posted by: Howard Wasserman | Apr 15, 2014 2:18:09 PM

Meh. Sometimes you sit a player who has fouled often and early so that they might regain composure and thereby decrease the likelihood that they would foul later on.

There have been a number of articles on when to use closers in baseball - might be worth a look.

Posted by: Tom | Apr 15, 2014 1:49:40 PM

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