<commit_before>---
layout: post
title: Quantifying Clutch Performance
comments: true
---

Just as some people are unusually good at finding the perfect gift to put under the Christmas tree, some tennis players are unusually good at pulling out a win when it matters most. This is the quintessential characteristic of the "clutch player". 

<div style="float:right;padding:2%;width:400px;height:250px;">
<a href="https://twitter.com/Tennis/status/680863246937620480/photo/1?ref_src=twsrc%5Etfw"><img src="/assets/shot_heard_round_world.png" width="90%" height="85%"/></a><p style="font-size:10px;"><NAME>'s shocking service return winner facing a match point at the US Open Final in 2011</p></div>

The idea of the clutch player is easy to describe, and some notion of clutch performance exists in every sport. Actually measuring clutch ability is much more challenging. And, in tennis, when one starts to consider how this could be done, one quickly discoveries that, despite how frequently the concept of clutch is discussed and applied with authority, it is rather vague. 

In reviewing some proposed metrics for [clutch performance](http://www.tennisabstract.com/blog/category/clutch/), I have found that they have generally focused on one point type at a time (e.g. break points) and one side of the game at a time, either serve or return. This approach has the upside of acknowledging that some points are more critical than others. But it has the drawback of discounting that criticality is a continuum and points that are critical, even if not <i>the most</i> critical, can still tell us something about how a player performs under pressure. Imagine if surgeons were judged only on the skill of their incisions. We would probably be missing a lot of the picture, no?

A more complete assessment of clutch ability should include all points played in a match but count the points played under greater pressure more heavily than less critical ones. Effectively, we want to isolate the part of a point that was really important and separate that from what was just average. If this could be done, we could then compare how much more a player is likely to win than lose when it matters most.

Thinking over these features, I realized that the hypothetical metric being described is something like <i>importance plus-minus</i> (IPM). An IPM could be calculated with the following formula, 

$$
IPM = \frac{ \sum Imp\;\times Won - Imp\;\times (1 - Won) }{ (Total\; Points) }
$$

Here, $Imp$ is the importance of the point played and $Won$ is an indicator of whether the point was won ($Won = 1$) or lost ($Won = 0$). The difference between points won and lost is averaged over all points played. In the version shown here, points on serve and return are counted equally. One could also imagine variants of this that were specific to the service or return game or weighed one side of the game more heavily than the other.

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layout: post
title: Quantifying Clutch Performance
comments: true
---

Just as some people are unusually good at finding the perfect gift to put under the Christmas tree, some tennis players are unusually good at pulling out a win when it matters most. This is the quintessential characteristic of the "clutch player". 

<div style="float:right;padding:2%;width:400px;height:250px;">
<a href="https://twitter.com/Tennis/status/680863246937620480/photo/1?ref_src=twsrc%5Etfw"><img src="/assets/shot_heard_round_world.png" width="90%" height="60%"/></a><p style="font-size:11px;"><NAME>'s shocking service return winner facing a match point at the US Open Final in 2011</p></div>

The idea of the clutch player is easy to describe, and some notion of clutch performance exists in every sport. Actually measuring clutch ability is much more challenging. And, in tennis, when one starts to consider how this could be done, one quickly discoveries that, despite how frequently the concept of clutch is discussed and applied with authority, it is rather vague. 

In reviewing some proposed metrics for [clutch performance](http://www.tennisabstract.com/blog/category/clutch/), I have found that they have generally focused on one point type at a time (e.g. break points) and one side of the game at a time, either serve or return. This approach has the upside of acknowledging that some points are more critical than others. But it has the drawback of discounting that criticality is a continuum and points that are critical, even if not <i>the most</i> critical, can still tell us something about how a player performs under pressure. Imagine if surgeons were judged only on the skill of their incisions. We would probably be missing a lot of the picture, no?

A more complete assessment of clutch ability should include all points played in a match but count the points played under greater pressure more heavily than less critical ones. Effectively, we want to isolate the part of a point that was really important and separate that from what was just average. If this could be done, we could then compare how much more a player is likely to win than lose when it matters most.

Thinking over these features, I realized that the hypothetical metric being described is something like <i>importance plus-minus</i> (IPM). An IPM could be calculated with the following formula, 

$$
IPM = \frac{ \sum Imp\;\times Won - Imp\;\times (1 - Won) }{ (Total\; Points) }
$$

Here, $Imp$ is the importance of the point played and $Won$ is an indicator of whether the point was won ($Won = 1$) or lost ($Won = 0$). The difference between points won and lost is averaged over all points played. In the version shown here, points on serve and return are counted equally. One could also imagine variants of this that were specific to the service or return game or weighed one side of the game more heavily than the other.

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