# A Closer Look at the Winner-Unforced Error Ratio

Few tennis statistics are more frequently cited than winners and unforced errors. Nearly every broadcast displays them, and the ratio between the two numbers is discussed during matches as much as any other metric in the game.

If we set aside the problems with unforced errors, the winner-unforced error (W/UFE) ratio does appear to have some value. Winners are unquestionably good, so more winners must be better than fewer winners. Errors are definitely bad, so fewer is better.

It’s one small step from those anodyne assumptions to the conventional wisdom that a player should aim to tally more winners than unforced errors, resulting in a ratio of 1.0 or more.

Like any metric, this one isn’t perfect. With the help of detailed stats from over 1,000 matches in Match Charting Project data, we can take a closer look.

Is the W/UFE ratio all it’s cracked up to be?

If you compare two players’ W/UFE ratio, you’ll find that the player with the better ratio almost always wins. No surprise there, since winners and unforced errors directly represent points won and lost.

It isn’t perfect, though. In both men’s and women’s matches, the player with the lower W/UFE ratio wins the match 11% of the time. Winners and unforced errors only represent about 70% of total points, so if the remaining 30% of points tilt heavily in one direction–especially in a close match–we’ll see an unexpected result.

Things get a little messier when we test the magic W/UFE ratio of 1.0. That’s the number commentators cite all the time, as if it is the line between winning and losing. W/UFE ratios differ quite a bit by gender, so we’ll need to look at men and women separately.

In the 512 men’s matches logged by the Match Charting Project, players recorded a ratio of 1.0 or better only 41.3% of the time. In over a quarter of those “successes,” though, they lost the match. That means we have plenty of false positives and false negatives:  losers who beat the target ratio as well as plenty of winners who failed to meet it.

Players who met or exceeded a 1.0 ratio won 74% of men’s matches. But the range just above the target–from 1.0 to 1.1–only resulted in wins about 60% of the time.

There’s no clear line separating a good ratio from a bad one: Even at 1.2 W/UFE, men only win about 70% of matches. As low as 0.8, they win nearly half.

Much of the problem here is that players influence each others’ numbers. Against a defensive baseliner, an average player will see his winners decrease and his unforced error count rise. In that hypothetical match, both players will have ratios below 1.0. Against an aggressive, big server, that same player will hit more winners, and because rallies end sooner, will tally fewer unforced errors. That scenario will often give you two ratios above 1.0.

A different story for women

In the sample of 552 women’s matches, players only recorded W/UFE ratios of 1.0 or better 26% of the time. Because the average ratio is so low–about 0.7–there aren’t very many false positives. Players who met the 1.0 standard won 89% of matches.

For women, a more reasonable target is in the 0.85 range. It’s roughly equivalent to 1.2 for men, in that a ratio at that level translates into about a 70% chance of winning.

There’s certainly no magic number. Even if we settle on revised targets like 0.85, winner and unforced error counts leave out too much data. In yesterday’s up-and-down match between Sara Errani and Jelena Ostapenko, Errani tallied 11 winners against 24 unforced. Ostapenko struck 54 winners against 49 unforced. A 0.46 ratio, like Errani’s, results in a win only 29% of the time, while a 1.1 ratio, like Ostapenko’s, is good for a victory 87% of the time. Yet, Errani is the one still standing.

Targeting the components

The Errani-Ostapenko match suggests another way of looking at the subject. Errani’s ratio was dreadful, but by keeping her unforced error rate low, she achieved at least half of the goal, leading to more Ostapenko errors. And while Ostapenko hit tons of winners, her own unforced error count was high enough to keep Errani in the match.

Looking at winners and unforced errors independently still doesn’t give us any magic numbers, but it does tell us more than the W/UFE ratio reveals by itself. Errani committed unforced errors on only 14% of points, which–taken by itself–results in a win about 70% of the time. Ostapenko’s error rate of 28% translates into success only 20% of the time.

By isolating the two components of the ratio, we can come up with clear targets for each. In women’s tennis, an error rate between about 14% and 16%–taken by itself–results in a 70% chance of winning. Consider winners independently, and we see that a winner rate of 19% to 20% also implies a 70% chance of victory.

These findings also cast a bit of light on another frequent question: Which is more important, increasing winners or decreasing errors? Based on this evidence, the answer is decreasing errors, but only by a whisker–and only in women’s matches. The player with more winners claims 68% of contests, while the player with fewer errors wins 73% of matches. A more sophisticated look, in which I separated all matches into buckets based on winner rate and error rate, suggests an even narrower margin. The relationship between error rate and winning percentage was very slightly stronger (r^2 = 0.92) than the relationship between winner rate and winning percentage (r^2 = 0.90).

Men’s components

For men, the 70% thresholds are different. Taken alone, a winner rate of about 22% will get you a 70% chance of winning. An unforced error percentage of 15% will achieve the same goal.

The relative importance of winners and unforced errors is different on the ATP tour, perhaps because aces–which are counted as winners–are such a large part of the game. Again, the difference is minor, but here, the relationship between winner rate and winning percentage is a bit stronger (r^2 = 0.94) than the relationship between error rate and winning percentage (r^2 = 0.92).

I’m almost done

Most men play plenty of matches in which they meet the W/UFE target of 1.0 and still lose. Most women fail to reach the 1.0 standard much of the time, and some players, like Errani, put together excellent careers despite almost never reaching it. We could do a lot better.

For a generic rule-of-thumb, the W/UFE target ratio of 1.0 isn’t horrible. But as we’ve seen, a slightly more nuanced view–one that takes into account the differences between men and women, as well as the independent value of winner rate and error rate–would be considerably more valuable.

## 11 thoughts on “A Closer Look at the Winner-Unforced Error Ratio”

1. Dami1 says:

Nice article!
Biggest bias for W/UE is when a match involves a player who often comes to the net. It gives lot of easy winners(volleys/pass) for every player but when you got the W/UE ratio you usually also got the net points won stat so if you take it into account in a certain way it can surely improve again the reading of W/UE.

2. Randy Burgess says:

Reading the article, my impression is that although this metric can be massaged to produce somewhat more meaning, I’m hard pressed to think how it might translate into actionable advice from a coach or actionable goals for a player. What would be an example of such advice or such goals? I can’t come up with anything, myself.

Which makes me think that the ratio has very limited utility. And even when separated, the two metrics still don’t have that much utility. What is a coach supposed to say – “Hit more winners?” Or, “Make fewer errors?” Even trying to back it off to cliches such as “Go for your shots” or “Play such-and-such a point a bit safer” don’t mean much.

Players have to play situationally & these are not situational metrics. Thus the limited utility – or so it seems to me.

1. Jeff says:

Yep, I don’t think something this broad can be turned into something actionable. *Maybe* knowing these numbers, along with an opponent’s tendencies (e.g. Errani is not going to hit many winners or make many errors) would suggest an adjusted game plan, but even that is probably a stretch.

1. Randy Burgess says:

Right. And I think the reason I even thought of the question “Is this actionable?” is that tennis commentators (ESPN being notorious for this) have a habit of introducing these & other stats early on in a match broadcast as targets for the player; or else bring them up as the match progresses as signs the player is doing well/poorly. This particular ratio is pretty much always brought up that way & your analysis suggests it’s not being done so with much meaning. Of course if the real purpose of these metrics is not meaningful analysis but simply to provide talking points for the commentators, the simpler the better. I wonder what someone like Darren Cahill, who clearly has a brain, would think of all the stats hurled at his broadcasting team by the likes of IBM.

1. Jeff says:

In fairness, there’s a big gap between ‘unactionable’ and ‘worthless.’ With a little bit of nuance, winner rate and UFE rate would do a decent job of analyzing what *has* happened, and when pundits stick to that, it can be valuable and accurate. Even if it’s just to say, “Errani usually wins by keeping her error rate very low, but the numbers show she’s committing x% errors than usual.”

But as you say, all stats tend to be used for off-the-cuff forecasting, which basic tennis statistics aren’t nearly good enough to do.

3. skip1515 says:

The missing component in this conversation is that one doesn’t *have* to hit winners to win points, but an unforced error *always* results in a point lost. See: Errani. The Winner/Unforced Error ratio falsely implies that they are the obverse of each other, when that’s not the case.

The definitions of Winner (untouched? off the outstretched frame?) versus Unforced Error (who’s deciding what was forced or unforced, i.e., an error completely of the hitter’s failure) only complicate this further.

4. pseudospin says:

A better statistic than W/UE that will “translate into actionable advice” is something like (W+FE)/(aggressive UE). Aggressive UE as opposed to the passive ones.

I mean, really, from a tactical point of view what’s the difference between winning a point with a winner and a winning it through a forced error? Both involve taking the initiative with aggresive play.

You should really be interested in how many points you win when you take it on versus how many you lose. Similarly when analysing your passive play you should look at how many points you win through your opponents UE versus how many you lose through their chosen level of aggressive play.

The interplay of those two things – which is specific to how your game matches up to your opponent – should give you a clear idea of whether you should be being more aggressive or more passive, and by how much.

This is clearly analysis that produces actionable advice.

5. Andrew Burton says:

For a fan (and player) the most interesting stat, I think, is the attacking ratio: (W + opponent’s FE) / Total points won. This can also be written as (W + opponent’s FE) / (W + opponent’s FE + opponent’s UFE).

Suppose Mary & Maria are playing: Mary is a grinder, Maria an attacking player. Maria wins in straight sets (commiserations to Mary fans). Suppose Mary wins 55 points to Maria’s 65. Mary hit 12 winners and made 10 UFES: Maria hit 36 winners and made 38 UFEs.

Arithmetic gets us to Mary won 5 points through FEs, and Maria 17 points through FEs. 55 of Maria’s 65 points were won through attacking play

6. Andrew Burton says:

(Sorry, accidentally posted before finishing the comment.) Maria won 85% of her thoughts through attacking play. Mary won 31% through attacking play 17/55).

Mary’s W/UFE ratio is 1.2: Maria’s is 0.95. I’m not sure that this really helps us to understand the match. But 85% vs 31% tells us a lot.

7. Andrew Burton says:

Or, alternatively, consider two ATP players – let’s call them Fabio and Rafael. Fabio hits 70 winners, 57 UFEs. Rafael hits 30 winners and 18 UFEs. Fabio wins 154 points, Rafael 152. We have Fabio (70 + 66)/(70 + 66 + 18) = 88%, while Rafael = (30 + 65)/(30 + 65 + 57) = 63%. Neither Fabio nor Rafael are overly defensive, but we know who was making the running.

8. Beta says:

Nice article and interesting comments!

Btw: Thiem lost vs. Anderson in R3 at this USO with a W/UFE of 2.1 (44/21).