## Help

### How Tennis Neutral (TN) works

The TN team derived an algorithm for calculating the neutral ratio of games between two players in a simple way that cannot be wrong.

They did it by assuming that UTR is right — that UTR accurately predicts the statistically most likely ratio of games won in a match between two players of differing abilities. This is not a big assumption — it is one that UTR makes about itself as well.

Because tennis matches in any format have a limited number of final results (ie. tennis scores are clunky), the statistically most likely ratio of games will in most situations not be achievable. For example, in a one-set match, a winning ratio of 0.6 corresponds to a score of 6-4 and a winning ratio of 0.67 corresponds to score of 6-3. However, a predicted winning ratio of 0.65 (or any other ratio between 0.6 and 0.67) cannot be achieved in a one-set match, even if this ratio is statistically most likely, since there are no match results between 6-4 and 6-3.

However, as the results of multiple matches between players with the same UTR difference accumulate, the average ratio of games in those match results will tend towards the statistically most likely ratio (0.65 in the example above). TN uses a large number of results and linear regression to produce an algorithm that best accords with available match result statistics. (The team also tested other regressions but linear regression produced the most reliable outcome.) The match results used have some biases (geographical, etc) but given UTR's claim to be universal, the source(s) of results should have little impact on the algorithm produced.

#### Limitations

TN is useful only for determining where lies the UTR neutral point in a match between players of differing UTRs. TN does not estimate how much impact a result will have on the calculation of a player's UTR, only whether that impact is positive or negative. Obviously, the extent to which a player over- or under-performs the predicted outcome will affect the extent to which that result impacts on the calculation of that player's UTR. However, other factors (such as format, competitiveness, reliability and time degradation) also affect the impact of a result on UTR calculation. More detailed information about how these factors affect match weight can be found on the Universal Tennis website.

A UTR positive outcome from a match does not correspond directly to a higher UTR. All else being equal it would. However, a player's UTR also has momentum. The 3 month Trend that appears on a player's UTR STATS page reveals whether that momentum is rising or falling. In most cases, a UTR positive outcome will show as a positive effect on the player's momentum. A UTR positive outcome will accelerate positive momentum or decelerate negative momentum, depending on whether the player's 3 month Trend is higher than their current UTR (ie. the player has positive momentum) or lower (ie. has negative momentum). Other factors, such as the performance of other players in other matches, may also have some impact.

Nothing prevents Universal Tennis from changing the way that UTR works. They can change it without informing users. The TN team will continue to monitor results for changes.

Updates to the app may be available from time to time.