How to see how many comp FFA games I played

According to Jeff Kaplan,

We match based on skill, ping and group size.

So, level shouldn't matter. To further break down what each of those categories are, this post here describes what the matchmaking system looks for when trying to balance teams.

"Skill" in this context refers to two things: your win rate and your MMR. Your win rate is calculated by taking the number of games you've won and dividing that by the total number of games you've played. Your MMR is an invisible number that goes up when you win and down when you lose and is supposed to represent how good you are at the game. Your MMR has to start somewhere, and while your account is new it will fluctuate wildly with each game played as the system is trying to figure out what number best represents your skill based on your average. As you continue to play games, the system becomes more confident in your MMR and the fluctuating decreases. A good matchmaking system will pair up players with similar confident MMR scores, in theory creating even games every time.

"Ping" is a number, measured in milliseconds (0.001 of a second), that represents how long it takes your console to send information to the host or server and receive a response back from the server. High ping is a direct cause of things such as shots not registering, people teleporting around, getting kills by shooting thin air, and other issues that people generally associate with lag. Thus, a low-ping environment is preferable.

"Group size", in theory, should refer to pairing up premade teams of similar size against each other, mitigating the inherent advantage of premades (communication, consistent roles, confidence in the skill of your teammates, etc.) by giving that advantage to both teams. Bigger premade should = bigger advantage, thus the need for groups of similar size on each team.

Though, it should be noted, the longer you are searching for matches, the looser the constraints will become in attempt to get you into a game.

At the end of a match, character win/loss statistics are attributed as a fraction corresponding to the percentage of the match's duration played as that character. On the character statistics display, however, character wins/losses are rounded to the nearest integer, which is responsible for much of the confusion surrounding the statistic.

As stated by Scott Mercer on the Battle.net forums:

When you get a win, each hero is credited for a portion of the win corresponding to the % of the match's playtime as that hero.

So if you play Mercy 60% of a match you won, and Lucio 40% of that same match, the hero specific win totals on the career overview are credited by 0.6 and 0.4, respectively. We then round the displayed value of games won by hero to the nearest integer.

In Scott's example, assuming 0 wins for both Mercy and Lucio prior to the match, the character statistics would display 1 win for Mercy and 0 for Lucio. The next time a match was won with at least 10% of the game spent playing Lucio, he too would display a win.